浅埋隧道开挖扰动下含空洞地层位移响应解析  

Analytical solution of ground displacement responses induced by shallowly tunneling in stratum with a cavity

作　　者：孙凡文 张顶立 方黄城 SUN Fanwen;ZHANG Dingli;FANG Huangcheng(Key Laboratory for Urban Underground Engineering of Ministry of Education,School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京交通大学土木建筑工程学院,城市地下工程教育部重点实验室,北京100044

出　　处：《中南大学学报（自然科学版）》2023年第3期1109-1120,共12页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(51738002)。

摘　　要：针对非圆形地层空洞问题,提出一种全新的基于几何边界拆分的子域分解方法。该方法将含空洞的浅埋隧道多连通区域以几何边界为单位分解成1个半无限域与若干个含孔洞的无限域,并结合Schwarz交替法建立适用于含非圆形空洞地层位移响应分析的一般性解析方法。通过与数值模拟的计算结果相对比,验证本文方法的精确性。最后,利用本文方法对含非圆形空洞地层的地表变形响应进行系统性参数分析。研究结果表明:(1)非圆形空洞对地表沉降的影响较圆形空洞更为显著,其主要因素来源于空洞的高跨比而非空洞形状本身,随着空洞高跨比的减小,空洞对地层沉降影响愈加明显。(2)在不同空洞姿态的工况中,椭圆形空洞长轴处于水平状态时对地表沉降的影响最为显著;(3)空洞与隧道之间的距离大于4倍洞径时,对地层沉降造成的影响可以忽略不计。Deformation response analysis of the stratum with a cavity with tunnel construction disturbance was crucial for construction safety.Currently,most analytical studies were confined to shallow circular holes.A domain decomposition approach using a geometric boundary was proposed to solve the problem of non-circular formation cavity.The multi-connected domain was decomposed into a semi-infinite domain and numerous infinite domains with holes according to the geometric boundary.Combined with the Schwarz alternating approach,an analytical solution of ground displacement responses caused by shallow tunnelling in the stratum with a cavity was established.Accuracy of the method was verified by comparison with the numerical simulation results.On this basis,a systematic investigation of the response of surface deformation under the effect of non-circular voids was conducted.The results are shown as follows.(1)Non-circular voids in the stratum on ground subsidence have a significantly greater influence than circular voids,and the void's flatness is more important than the void's shape.The voids'influence on subsidence becomes more significant as the voids'flatness increases.(2)Among various rotation attitudes of the cavity,the cavity's influence on the ground subsidence is the most significant when the long axis of the elliptical cavity is horizontal.(3)The influence on the subsidence can be ignored when the distance between the cavity and the tunnel is more than four times the tunnel's diameter.

关 键 词：浅埋隧道 非圆形孔洞 子域分解法 复变函数理论 SCHWARZ交替法 

分 类 号：TU452[建筑科学—岩土工程]