Abstract: In consideration of the mechanical process of support delay, the analytic solutions of stress and displacement for a non-circular tunnel subjected to in-situ stress and internal water pressure are derived by using the complex variables function under the assumption that the interface between lining and surrounding rock is fully slip. The basic equations for solving the analytic functions of surrounding rock and lining are obtained according to the stress boundary condition along the inner boundary of the lining and the condition of stress and normal displacement continuity along the rock-lining interface. The basic equations can be solved by the power series method, and the stresses and displacements in the surrounding rock and lining can be calculated. The analytic solutions are verified by finite element method. An inverted U-shaped tunnel is taken as an example to analyze the distributions of tangential stresses along the excavation boundary, the inner and outer boundary of the lining as well as the normal stresses along the rock-lining interface in the presence of different displacement release coefficient, lateral pressure coefficient and internal water pressure.

Key words: non-circular tunnel, full-slip contact, conformal transformation, power series method, internal water pressure, analytical solution of stress, analytical solution of displacement