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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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

Received: 05 July 2010

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

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