| 基于复变函数方法的水下隧道围岩弹性分析 |
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| 引用本文： | 蔚立元,陈晓鹏,韩立军,王迎超.基于复变函数方法的水下隧道围岩弹性分析[J].岩土力学,2012,33(Z2):345-351. |
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| 作者姓名： | 蔚立元 陈晓鹏 韩立军 王迎超 |
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| 作者单位： | 1. 中国矿业大学 深部岩土力学与地下工程国家重点实验室，江苏 徐州 221008；2. 中国矿业大学 力学与建筑工程学院，江苏 徐州 221116； 3. 中国水电顾问集团 成都勘测设计研究院，成都 61007 |
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| 基金项目： | 国家自然科学基金委青年科学基金资助(No.51109209);中国博士后科学基金面上项目资助(No.20110490043);中央高校基本科研业务费专项资金资助(No.2011QNA15) |
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| 摘 要： | 水下隧道属于浅埋隧道，故其围岩的应力位移分析从力学角度可简化为含圆孔半平面弹性体在水平边界上受任意分布荷载的问题。与深埋隧道不同，浅埋隧道围岩分析在数学处理上历来存在较大的困难。借助Verruijt提供的共形映射函数，把含圆孔半无限平面映射为圆环域，然后将像平面上的解析函数展成Laurent级数，利用Muskhelishvili 的复变函数解法，求得问题的应力场和位移场，最后用Fortran语言编写了计算程序。利用该程序给出一个水下隧道算例的围岩应力、位移结果，并分析了其受力变形特点。
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| 关 键 词： | 水下隧道 复变函数 共形映射 围岩 应力场和位移场 |
| 收稿时间： | 2012-02-05 |
Elastic analysis of surrounding rock for underwater tunnels based on functions of complex variables method |
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| YU Li-yuan,CHEN Xiao-peng,HAN Li-jun,WANG Ying-chao.Elastic analysis of surrounding rock for underwater tunnels based on functions of complex variables method[J].Rock and Soil Mechanics,2012,33(Z2):345-351. |
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| Authors: | YU Li-yuan CHEN Xiao-peng HAN Li-jun WANG Ying-chao |
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| Institution: | 1. State Key Laboratory for Geomechanics&Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China; 2. School of Mechanics & Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China; 3. Chengdu Hydro China Chengdu Engineering Corporation, Chengdu 610072, China |
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| Abstract: | The underwater tunnels can be regarded as shallow tunnels. So the classical problem of an elastic half plane with a circular cavity, loaded arbitrarily on the horizontal boundary can be used to analyse the stress and displacement fields of the surrounding rock for underwater tunnels. As is known to all, it is much more difficult to deal with shallow tunnels than deep tunnels via the analytical way. Using Verruijt’s conformal mapping function, the region of exclusion of a hole in a half plane is tansfered into a cirque. Then the analytic functions can be expanded as Laurent series in this region. The stress and displacement can be solved by the function of complex varibles method founded by Muskhelishvili. The corresponding calculation program is coded by Fortran. As an example, a specific underwater tunnel is analysed by the Fortran calculation program eventually. |
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| Keywords: | underwater tunnel function of complex variables conformal mapping surrounding rock stress and displacement |
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