Elastic solution for a deep twin tunnel's stress based on complex variable theory and the superposition principle

Zihong Guo, Xinrong Liu, Zhanyuan Zhu


Complex variable theory and the superposition principle are useful ways to study a tunnel’s stress and deformation. Accordingly, an elastic solution is presented for a twin tunnel’s stress distribution in homogeneous and isotropic rock subjected to non-uniform stress. Taking into account the influences of the supporting pressure, spacing distance and stress coefficient, the elastic solution and infinite element method are applied to analyze the twin tunnel’s stress distribution and concentration. The results demonstrate that the twin tunnel’s maximum stress appears at the middle rock wall, and the spacing distance has most evident influence on the stress concentration. The largest difference in the stress distribution between the analytical solution and the finite element method is at the twin tunnel’s left and right hances, but the analytical data are highly consistent with the numerical data. Nevertheless, the difference may become significant if the twin tunnel’s spacing distance is less than 0.25 times the tunnel diameter and the stress coefficient is less than 0.7.


Complex variable theory; deep twin tunnel; elastic solution; superposition principle; stress distribution

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