圆形巷道围岩弹性应力场的复变函数解析

Analysis of the complex functions of the surrounding rock stress field in the elastic circular tunnels

为得出圆形巷道围岩弹性应力分布特征,采用复变函数对圆形巷道围岩弹性应力进行解析,得到了与应力函数解法相同的应力场解析表达式,证明了复变函数解法求解巷道围岩应力场的可行性。对圆形巷道边界应力分布规律及沿水平线的应力分布规律进行了分析,结果表明:1)圆形巷道边界的径向应力和剪应力等于0,环向应力集中系数随侧压系数和位置角度变化而变化,与巷道半径无关;2)沿水平线的圆形巷道围岩剪应力等于0,径向应力和环向应力集中系数随侧压力系数和巷道半径变化而变化;3)沿水平线方向,侧压系数对巷道围岩径向应力的影响大于环向应力影响。还分析了侧压系数对巷道围岩应力的影响规律,讨论了侧压系数等于0、大于0小于1、等于1和大于1等4种情况下的巷道边界环向应力分布情况,得出了巷道边界环向应力的拉压区域及环向应力集中系数最大位置。

The paper intends to introduce an analysis of the complex functions of the surrounding rock stress field in the elastic circular tunnels. The said analysis has been done in hoping to find the distribution features of the elastic stress of the surrounding rock in the horizontal line with the complex function method for the analysis,which can help to get the analytical expression of stress field almost in the same way as the stress function method.Thus,it can prove that it would be feasible to use the complex function method to solve the surrounding rock stress field. What is more,by analyzing the boundary stress distribution regulation of the circular roadway of the surrounding rock stress distribution features horizontally,we can arrive at the following conclusions：（ 1） The hoop stress concentration factor changes with the side pressure coefficient,whereas the position and the angle has nothing to do with the radius on the condition that the radial stress and the shear stress of the circular roadway boundary are equal to 0.And,（ 2） The radial and hoop stress concentrations change with the side pressure coefficient and roadway radii,when the shear stress of the circular roadway surrounding rock in the horizontal direction is equal to 0. And,（ 3） in the horizontal direction,if the impact of the surrounding rock radial stress on the side pressure coefficient is greater than the hoop stress,it would be of great need to analyze the impact of different side pressure coefficients on the surrounding rock stress. Besides what is said above,we have also made a discussion on the circumferential boundary stress distribution in the above said four cases and found that the lateral pressure coefficient should also be equal to zero,greater than zero,less than 1,equal to 1 and greater than 1,which helps to determine the tension and the compression of the hoop stress and the effect of the maximum hoop stress concentration factors on the tunnel boundary. Thus,it can be concluded that the paper has provided a theoretical basis for predicting the deformation and breakage of the roadway surrounding rock stress.