中文摘要：

基于复变函数解法,借助Verruijt提供的保角映射公式,将含孔洞的半无限平面映射为圆环域,然后利用解析函数将圆环域内的复势函数展开成Laurent级数,并利用地表及洞周边界条件的级数展开式在圆环域上的收敛性对其进行求解,从而得到地面荷载及围岩自重作用下浅埋隧道的围岩应力场。利用该解析解研究各因素对隧道围岩稳定性影响的结果表明：当隧道埋深较小时围岩以拉—剪综合破坏为主,埋深较大时围岩主要发生边墙剪切破坏,且埋深越大剪切区的范围及半径越大;地面荷载越大,围岩产生的塑性区范围及其半径越大,且随着地面荷载的增大,塑性区沿着一定角度向地表方向扩展,容易产生地层坍塌;侧压力系数较大时,围岩以剪切破坏造成的整体失稳为主,侧压力系数较小时,围岩以拉—剪综合破坏为主,且侧压力系数越小越易发生地层坍塌。

英文摘要：

Based on the complex function method, the semi-infinite plane with a hole was mapped into a ring domain by means of Verruijt＇s conformal mapping formula. Then, the complex potential functions in the ring domain were expanded as Laurent series using analytic functions. The surrounding rock stress of shallow tunnel under ground load and dead weight was solved by converging the series expansion of the ring domain under the boundary conditions of ground surface and hole surrounding. The influence of different factors on the stability of surrounding rock was studied using the analytic solution. Results show that, there is mainly the comprehensive tensile-shear failure in surrounding rock when the buried depth is smaller. The major failure mode of surrounding rock is shear failure at the side wall when the buried depth is larger, and the range and the radius of shear region become larger as the buried depth increases. With the increase of ground load, the range and the radius of the plastic region of surrounding rock become larger. The plastic region extends to ground surface along a certain angle, which may result in formation collapse. Global instability caused by the shear failure of surrounding rock is dominant when the lateral pressure coefficient is larger. Comprehensive tensile-shear failure is dominant for surrounding rock when the lateral pressure coefficient is smaller, and smaller lateral pressure coefficient is more liable to result in formation collapse.