基于高效保角变换的单个复杂洞室围岩应力场解析解研究

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摘要基于高效的、边界点搜索的地下洞室外域映射函数解法，以及柯西积分公式和弹性力学中的复变函数解法，简化并总结求解单个复杂洞形围岩应力场解析解的一般性步骤，推导出势函数的解析表达式，然后根据应力组合的复势表达式求解出各应力分量的解析表达式。在映射函数已知的情况下，利用该表达式能够快速精确地求出任意复杂形状洞室的围岩应力场解析解。通过与数值计算结果相比较，得出该解析解法能够计算出更为精确的应力场，并且求解效率很高。同时，求解直臂马蹄形洞形平面问题的应力场解析解，分析在3种不同远场应力情况下的应力集中情况。最后，结合锦屏一级水电站主厂房的实际情况，求解出开挖后的围岩应力场解析解。

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关键词 ：岩石力学, 围岩应力场, 保角变换, 解析解, 单洞室, 柯西积分公式

Abstract：The general steps of calculating analytical solution of stress field of the surrounding rock of single hole with arbitrary shape and analytical expression of the two potentials were obtained，based on highly-efficient conformal mapping of external area of underground cavern with arbitrary shape based on searching mapped points on the boundary，Cauchy integral formula，combined with complex function method. Then，the stresses at any point z inside the surrounding rock can be computed by using the Kolosov-Muskhelishvili formulae fast. Compared with numerical result，the result acquired by this analytical algorithm could be much more precise than that of the numerical simulation，and the former is much more efficient，too. Then，the analytical result of stress field of the surrounding rock of hole with straight wall and horseshoe shape under three cases of remote loading were obtained using this method，and zones of stress concentration were denoted emphatically. Finally，using this method，the analytical solution of stress field of the surrounding rock of the main power house of Jinping I hydropower station was calculated.

Key words： rock mechanics stress field of surrounding rock conformal mapping analytical solution single hole Cauchy integral formula

收稿日期: 2010-07-05

引用本文:

皇甫鹏鹏，张路青，伍法权. 基于高效保角变换的单个复杂洞室围岩应力场解析解研究[J]. 岩石力学与工程学报, 2011, 30(S2): 3905-3913.
HUANGFU Pengpeng，ZHANG Luqing，WU Faquan. RESEARCH ON ANALYTICAL SOLUTION OF STRESS FIELD OF SURROUNDING ROCK OF SINGLE HOLE WITH ARBITRARY SHAPE BASED ON HIGHLY-EFFICIENT CONFORMAL MAPPING. , 2011, 30(S2): 3905-3913.

链接本文:

http://www.rockmech.org/CN/Y2011/V30/IS2/3905

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