Abstract: The surrounding rock mass and the lining are regarded as orthotropic and isotropic medium, respectively, with continuous, homogeneous and linear-elastic properties. The effects of support delay and water pressure during tunnel operation are also taken into consideration. Based on the above assumptions and the power series method of complex variable theory, the analytical method and solution for the arbitrary-shaped hydraulic tunnel that is buried in the orthotropic rock mass is established. Taking an inverted U-shaped tunnel for example, the analytical solution is perfectly satisfied with the stress boundary condition on the inner boundary of lining and stress boundary condition on the contact interface between lining and surrounding rock mass. Besides, the displacement continuity condition along the contact boundary can also be accurately satisfied. The numerical solution simulated by finite element software ANSYS is introduced to be compared with the analytical solution. The comparison indicates that the analytical results are in good agreement with the numerical analysis. With the presented analytical method for the problem, the influences of anisotropic degree of surrounding rock mass, the angle of elastic symmetric plane and the water pressure are discussed based on investigating the stress and displacement distributions of lining and surrounding rock mass.

Key words: analytical method, orthotropic rock mass, lined hydraulic tunnel, arbitrary-shaped tunnel, water pressure