工程力学 ›› 2019, Vol. 36 ›› Issue (11): 102-111.doi: 10.6052/j.issn.1000-4750.2018.11.0610

• 土木工程学科 • 上一篇    下一篇

含空洞缺陷的圆形硐室围岩应力弹性解析解

许德明1, 王媛1,2, 黄景琦1, 李庆文1, 王培涛1, 董致宏1   

  1. 1. 北京科技大学土木与资源工程学院, 北京 100083;
    2. 河海大学土木与交通学院隧道与地下工程研究所, 南京 210098
  • 收稿日期:2018-11-13 修回日期:2019-03-20 出版日期:2019-11-13 发布日期:2019-10-25
  • 通讯作者: 王媛(1969-),女,江苏阜宁人,教授,博士,博导,主要从事岩土工程渗流理论与测试、裂隙岩体应力和渗流耦合等方面的教学与研究工作(E-mail:wangyuan@hhu.cn). E-mail:wangyuan@hhu.cn
  • 作者简介:许德明(1995-),男,河北保定人,硕士生,主要从事隧道稳定性分析研究(E-mail:Demint_X@163.com);黄景琦(1988-),男,安徽亳州人,讲师,博士,主要从事岩体隧道等地下结构抗震性能研究(E-mail:huangjingqi11@163.com);李庆文(1986-),男,辽宁朝阳人,副教授,博士,主要从事爆破振动研究(E-mail:qingwenli1118@gmail.com);王培涛(1987-),男,河北沧州人,讲师,博士后,主要从事工程岩体稳定性与控制方面研究(E-mail:wangpeitao@ustb.edu.cn);董致宏(1994-),男,甘肃武威人,硕士生,主要从事块体理论、DDA方面研究(E-mail:1024060@qq.com).
  • 基金资助:
    国家自然科学基金项目(51608015);中央高校基本科研业务费专项资金项目(FRF-TP-17-074A1);973项目计划项目(2015CB057902)

ELASTIC ANALYTIC SOLUTION OF CIRCULAR CHAMBER SURROUNDING ROCK WITH VOID DEFECTS

XU De-ming1, WANG Yuan1,2, HUANG Jing-qi1, LI Qing-wen1, WANG Pei-tao1, DONG Zhi-hong1   

  1. 1. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China;
    2. Tunnel and Underground Engineering Institute, Hohai University, Nanjing 210098, China
  • Received:2018-11-13 Revised:2019-03-20 Online:2019-11-13 Published:2019-10-25

摘要: 基于复变函数理论,建立真实平面上含空洞缺陷硐室外域和复平面上单位圆外域之间的映射关系,得到了在远场应力作用下含空洞缺陷圆形硐室围岩弹性应力解析解,分析了围岩应力分布规律以及缺陷位置、缺陷凸出程度和场地应力比对孔口应力分布的影响。结果表明:硐室缺陷部位应力分布与无缺陷情况具有明显区别,在缺陷中部应力集中效应明显,但在硐室孔壁与缺陷相交部位应力明显较小,甚至会出现环向应力为拉应力的情况;较轻微的缺陷便可引起较大的应力集中现象,且随缺陷凸出程度的增加,缺陷中部应力集中现象明显加剧;随着缺陷凸出方向与最小主应力方向夹角的减小,缺陷中部的应力集中现象加剧;当缺陷凸出方向与最小主应力方向平行时,随围压应力比的减小缺陷处的应力集中程度增大,而两者处于垂直状态时,随围岩应力比的减小缺陷处的应力集中现象逐渐降低。因此,在实际工程应用中应充分考虑空洞缺陷所引起的应力集中现象的影响。

关键词: 地下工程, 解析解, 复变函数理论, 空洞缺陷, 围岩应力

Abstract: Based on the complex variable function theory, the mapping relationship between the outer space of a chamber with defects and the outer space of a unit circle is established. The elastic analytic solution of the stress of the surrounding rock with defects under the action of far-field stresses is obtained. The stress distribution and the influence of the defect location, defect protrusion degree and stress ratio are analyzed. It is shown that the stress distribution in the defective part of the chamber is different from that in a non-defective chamber. The stress concentration is obvious in the middle of the defect, but the stress at the junction of the chamber and the defect is small and the circumferential stress may even become tensile stress. A slight defect can cause a significant stress concentration. The extent of stress concentration in the middle of the defect increases with the increase of the protrusion degree of the defect. It also increases with the decrease of the angle between protruding direction of defect and the minimum principal stress direction. If the protruding direction of the defect is parallel to the minimum principal stress direction, the stress concentration increases with the decrease of the stress ratio, while the relationship reverses if protruding direction is vertical to the minimum principal stress direction. Therefore, the effect of stress concentration caused by cavity defects should be fully considered in engineering applications.

Key words: underground engineering, analytic solution, complex variable function theory, void defect, surrounding rock stress

中图分类号: 

  • U451
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