浅埋含空洞地层圆形隧道开挖引起的位移
复变函数弹性解

doi:10.16285/j.rsm.2018.0616

岩土力学 ›› 2018, Vol. 39 ›› Issue (S2): 25-36.doi: 10.16285/j.rsm.2018.0616

浅埋含空洞地层圆形隧道开挖引起的位移复变函数弹性解

杨公标^{1, 2}，张成平^{1, 2}，闵博^{1, 2}，蔡义^{1, 2}

1. 北京交通大学城市地下工程教育部重点实验室，北京 100044；2. 北京交通大学土木建筑工程学院，北京 100044

收稿日期:2018-04-12 出版日期:2018-12-21 发布日期:2019-01-02
通讯作者: 张成平，男，1975年生，博士，教授，博士生导师，主要从事隧道与地下工程方面的研究。E-mail:chpzhang@bjtu.edu.cn E-mail: gbyang526@163.com
作者简介:杨公标，男，1989年生，博士研究生，主要从事隧道与地下工程方面的研究
基金资助:
北京市自然科学基金项目（No.8172037）；国家自然科学基金面上项目（No.51378002）

Elastic solution of soil displacement induced by shallow circular tunnel with a cavern in a stratum using function of complex variable method

YANG Gong-biao1, 2, ZHANG Cheng-ping1, 2, MIN Bo1, 2, CAI Yi1, 2

1. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China; 2. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Received:2018-04-12 Online:2018-12-21 Published:2019-01-02
Supported by:
This work was supported by the Beijing Municipal Natural Science Foundation (8172037) and the National Natural Science Foundation of China (51378002).

摘要/Abstract

摘要： 针对浅埋隧道临近地层空洞施工问题，建立了解析模型。该模型中隧道满足变形边界条件，空洞满足0面力边界条件，采用Schwarz交替法原理和复变函数法对模型进行了理论求解，并通过编程实现了迭代计算，结合数值计算特点对求解精度进行了讨论。通过算例分析了在不同隧道变形边界条件下空洞位置、大小及净距对地表沉降的影响。结果表明，与无空洞工况相比，空洞对地表沉降产生较明显影响，空洞较大或净距较小时影响尤为显著，隧道变形边界不同或空洞位置不同时地表沉降变化规律的差异性较大，当空洞位于隧道两侧位置时均匀收缩和椭圆化变形边界下差异沉降关于空洞轴线呈对称分布，隧道和空洞正上方地表沉降均增大；竖向位移变形边界下差异沉降关于空洞轴线呈反对称分布，隧道一侧地表沉降增大，另一侧地表沉降减小。当空洞位于隧道斜上方位置时均匀收缩变形边界下差异沉降关于空洞轴线呈反对称分布，空洞轴线处地表沉降曲线斜率明显增大。当空洞位于隧道正上方位置时3种基本变形边界下隧道正上方地表沉降均减小。

关键词: 浅埋圆形隧道, 地层空洞, 地表沉降, 复变函数, 弹性解

Abstract: A corresponding analytical model is established to solve the construction problem of shallow circular tunnel with a cavern in a stratum. In this model, the tunnel conforms to the specified deformation boundary condition, and the cavern satisfies the zero surface force boundary condition. Schwarz alternating method and function of complex variable method are used to solve the problem; meanwhile the iterative computation is realized by a program. In addition, combining with the characteristics of numerical calculation, the calculation accuracy is discussed. The influences of tunnel boundary conditions, location and size of the cavern, and clear distance between the tunnel and the cavern on surface settlements are analyzed. The results show that, compared with no cavern conditions, the cavern has an obvious influence on surface settlements. The rule of surface settlements is different significantly, when the tunnel boundary condition and the cavern’s location are changed. When the cavern is located at the lateral sides of the tunnel, the differential settlements are distributed symmetrically about the cavern axis for uniform radial displacement and oval deformation boundary conditions, but the regulation is opposite for vertical subsidence boundary condition. When the cavern is located at the inclined top of the tunnel, the differential settlements are anti-symmetric for uniform radial displacement and oval deformation boundary conditions. All of the surface settlements above the tunnel are reduced for the three basic deformation boundary conditions when the cavern is located at the top of the tunnel.

Key words: shallow circular tunnel, cavern, surface settlement, function of complex variable, elastic solution

中图分类号:

U452

杨公标, 张成平, 闵博, 蔡义, . 浅埋含空洞地层圆形隧道开挖引起的位移复变函数弹性解[J]. 岩土力学, 2018, 39(S2): 25-36.

YANG Gong-biao, ZHANG Cheng-ping, MIN Bo, CAI Yi, . Elastic solution of soil displacement induced by shallow circular tunnel with a cavern in a stratum using function of complex variable method[J]. Rock and Soil Mechanics, 2018, 39(S2): 25-36.

参考文献

相关文章 15

[1]	张治国, 李胜楠, 张成平, 王志伟, . 考虑地下水位升降影响的盾构施工诱发地层变形和衬砌响应分析[J]. 岩土力学, 2019, 40(S1): 281-296.
[2]	胡之锋，陈健，邱岳峰，李健斌，周兴涛, . 挡墙水平变位诱发地表沉降的显式解析解[J]. , 2018, 39(11): 4165-4175.
[3]	魏纲，林雄，金睿，丁智，. 双线盾构施工时邻近地下管线安全性判别[J]. , 2018, 39(1): 181-190.
[4]	曾癸森，吕爱钟. 考虑构造应力作用下浅埋圆形隧洞的解析解[J]. , 2017, 38(S1): 79-86.
[5]	李银平，孔庆聪，施锡林，李硕，杨博进，杨春和，. 盐穴地下储库地表沉降的黏弹模型及应用[J]. , 2017, 38(7): 2049-2058.
[6]	魏纲，周杨侃. 随机介质理论预测近距离平行盾构引起的地表沉降[J]. , 2016, 37(S2): 113-119.
[7]	朱才辉，李宁. 隧道施工诱发地表沉降估算方法及其规律分析[J]. , 2016, 37(S2): 533-542.
[8]	沈路遥，钱建固，张戎泽,. 挡墙水平变位诱发地表沉降的简化解析解[J]. , 2016, 37(8): 2293-2298.
[9]	饶军应，傅鹤林，谢涛，王小敏，尹泉，李文博，. 内压对管状双椭圆洞室围岩应力影响的解析解[J]. , 2016, 37(1): 76-86.
[10]	顾剑波，钱建固 , . 任意柔性挡墙变位诱发地表沉降的解析理论预测[J]. , 2015, 36(S1): 465-470.
[11]	蔡海兵，彭立敏，郑腾龙,. 隧道水平冻结壁强制解冻期地表沉降的预测方法[J]. , 2015, 36(12): 3516-3522.
[12]	张强勇，王保群，向文,. 盐岩地下储气库风险评价层次分析模型及应用[J]. , 2014, 35(8): 2299-2306.
[13]	徐长节，成守泽，蔡袁强，罗志元,. 非对称开挖条件下基坑变形性状分析[J]. , 2014, 35(7): 1929-1934.
[14]	杨泽飞，魏纲，林磊磊，张世民. 盾构法隧道施工工后横向地表总沉降研究[J]. , 2013, 34(S2): 338-343.
[15]	侯永茂，郑宜枫，杨国祥，葛修润，邱裕华 . 超大直径土压平衡盾构施工对环境影响的现场监测研究[J]. , 2013, 34(1): 235-242.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

浅埋含空洞地层圆形隧道开挖引起的位移复变函数弹性解

Elastic solution of soil displacement induced by shallow circular tunnel with a cavern in a stratum using function of complex variable method

PDF (Chinese)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

浅埋含空洞地层圆形隧道开挖引起的位移 复变函数弹性解

Elastic solution of soil displacement induced by shallow circular tunnel with a cavern in a stratum using function of complex variable method

PDF (Chinese)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

浅埋含空洞地层圆形隧道开挖引起的位移复变函数弹性解