Boundary equation of plastic zone of circular roadway in non-axisymmetric stress and its application

At present,it is difficult to obtain the exact analytical solution of elastic-plastic problem of circular roadway under bidirectional non-axisymmetric stress. Based on Mohr-Coulomb strength criterion, the approximate boundary equation of plastic zone is studied by substituting Kirsch equation into plastic condition. Also,the influencing factors and mechanics mechanism of formation of plastic zone are analyzed. The results show that the lateral pressure coeffi- cient affects the shape of plastic zone,the direction of in-situ stresses affects the position of butterfly leaf of butterfly- shaped plastic zone,and the radius and lithology of roadway affect the radius of plastic zone. When the value of lateral pressure coefficient is not equal to 1. 0,the direction of maximum principal stress is not parallel to the tangent direction of roadway,and the direction of the minimum principal doesn’t go through the radial direction of roadway,which cau- ses the change of shear failure direction of surrounding rock. The expansion of plastic zone is controlled by the distri- bution of maximum shear stress,and the shape of plastic zone deviates from the circle. The peak point curve of shear stress and the boundary of plastic zone change with the change of lateral pressure coefficient,but the boundary of plas- tic zone always locates at the peak value in the contour of shear stress. The smaller the lateral pressure coefficient,the greater the change of principal stress direction,and the more obvious the irregular shape of plastic zone is. The approx- imate method for solving the boundary of plastic zone does not consider the effect of plastic zone on the stress in elastic zone,but the shape and development of plastic zone are consistent with the results of numerical simulation. The study has a guiding role in solving engineering problems,which proves that the approximate solution of plastic zone boundary equation is valid. Through the approximate method,the development law of plastic zone in surrounding rock can be ob- tained. The support technology of butt long bolt can effectively solve the problem of roof fall triggered by the break of cable bolt and the overall subsidence of bolt with overall subsidence of roof,and better eliminate the hidden danger of roof fall. The field test results show that the equation of plastic zone has a theoretical significance and engineering ap- plication value.