深埋隧洞围岩应力的精确解与近似解的对比分析
摘要
Deep buried tunnels with different cross-section shapes were analyzed through comparison between the analytical solutions and the approximate solutions obtained by the equivalent radii for the surrounding rock stresses. Firstly, according to the basic theory of complex variable functions, the stress components were obtained and the analytical expressions for the surrounding rock stresses of deep tunnels with various section shapes including the circle, the ellipse, the rectangle and the straight-wall arch, were given. Secondly, with the converted forms of the equivalent radii, the section boundary was transformed into a standard circle and the surrounding rock stress components were calculated by means of the Lamé solution. Finally, in view of the variable parameters of the tunnel cross-section shapes, comparisons between the exact solutions and the approximate solutions were conducted based on numerical examples, and the accuracy of the converted equivalent radii was discussed. The accuracy of the analytic solutions of the complex variable functions was proved, and the accuracy of the equivalent radii was verified for different cross-section shapes. The results show that the similarity between the solutions of the converted forms and the exact solutions of the equivalent radii is closely related to the cross-section shapes of the tunnels and the geometrical parameters.