| Based on the plane elastic complex function method of the conformal mapping, the analytical solution of the non-circular tunnel under the in-situ stress can be obtained. This paper were considered two different excavation conditions between the lining and surrounding rock based on the actual project, namely:(1) the surrounding rock and the lining completely contact; (2) the surrounding rock and the lining smooth contact. When the first contact condition was considered, the basic equations of the analytic functions can be obtained by Cauchy integral method according to the stress and displacement continuity conditions. When the second contact condition was considered, the basic equations of analytic functions can be obtained by the power series method rather than the Cauchy integral method. Taken the analytic functions expressions as series forms, the basic equations are derived by solving linear equations of the coefficients in the series expressions. The stress and the displacement can be calculated. Taken the straight wall tunnel and the horseshoe tunnel as example, the stress distributions of the boundaries can be obtained.In the paper, the stress distributions of the boundaries by ANSYS software were used to compare to the analytic solutions. The results of the two methods were in good agreement. It can prove that the derivation process of the analytic functions do not have errors. The stress distributions of the boundaries under the smooth contact condition are better than the full contact condition. Stress distribution can be obtained when the conduct of the tunnel support, optionally incorporated in the concrete can reduce the friction coefficient of the additive help to improve the stability of the lining and the surrounding rock. It can be obtained that, additives added in the concrete to reduce friction coefficient are of great help to improve the stability of the lining and the surrounding rock, when setting the support of the tunnel. |
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