Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay

• The Analytic solutions for a non-circular tunnel with closed support are obtained.
• The stresses and displacements in the rock and lining are calculated.
• Analytic functions are represented in series expression.
• The series number affects significantly the results.

The stress and displacement field for a non-circular supported tunnel subjected to in situ stress is derived based on the conformal transformation method. The basic equations for solving the stress and displacement solutions were obtained according to the boundary conditions on the inner boundary of lining and the liner-surrounding rock–mass interface. If the analytic function was represented in terms of series expression, the coefficients in the series expressions were undetermined. Combining with the basic equations, linear equations for solving the coefficients can be derived. The stresses and displacements in the surrounding rock–mass and lining were calculated with support delay taken into consideration. If it is assumed to be a plane strain problem and the displacement completed in the surrounding rock–mass before support installation is given, the stress and displacement solutions for a tunnel at great depth can be obtained. The distributions of tangential stresses on the excavation boundary, the inner and outer boundaries of lining, of contact stresses on the lining-surrounding rock–mass can be obtained. If the number of terms in the series exceeds 100, the boundary conditions can be well satisfied and the stresses, displacements results will be accurate.