Solution to surrounding rock stress of shallow tunnel under ground load and dead weight

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. © 2015, Chinese Academy of Railway Sciences. All right reserved.