摘要
半无限空间中孔洞受均布位移作用下的问题已由Verruijt采用复变函数解答,而本文中给定椭圆化位移边界条件下的解答尚无文献报导。本文应用Verruijt的基本解法,采用共形映射方法,把含括一个圆形孔洞的半无限空间区域映射为圆环域。然后把这个区域内的解析函数展成Laurent级数的形式。利用Muskhelishvili的复变函数解法,求得隧道洞周给定位移条件下的应力场和位移场。分析了不同埋深、不同泊松比对位移场的影响、不同埋深对应力场的影响。最后分析了5个盾构隧道实测数据与4种不同位移边界条件解的对比情况。分析结果表明:笔者给出的第三、四边界条件的精确解对盾构隧道的设计有重要的实践意义。
Using the conformal mapping ,the region of exclusion of a hole in a half plane was tansfered into a cirque. Then the analytic functions could be expanded as Laurent seriers in this region. The stresses and displacements under given displacement could be solved by the complex method founded by Muskhelishvili. The influence of the displacements due to different depth and different Poisson＇s ratio was discussed ,and the influence of the stresses due to different depth was discussed too. It was shown that the exact solutions of the third boundary condition suggested by the author was important in the designing of shield tunnling after the comparision of the solutions under four different conditions with the data observed in five different tunnels.
出处
《岩土工程学报》
EI
CAS
CSCD
北大核心
2007年第3期319-327,共9页
Chinese Journal of Geotechnical Engineering
关键词
共形映射
半无限空间
洞周给定位移条件
应力场与位移场
conformal mapping
a half plane with a hole
oval deformation around the hole
stress and displacement
