Abstract: The method of complex variable function is used to study the deeply buried non-circular lined tunnel in the orthotropic surrounding rock under far-field biaxial compression. The stress functions in series form of surrounding rock and lining are obtained, thus the analytical solutions of stress and displacement can be derived. Considering a two-lane tunnel common in engineering as an example, the analytical solutions of stress and displacement along the inner and outer boundaries of the lining are given. The complete contact interface condition, boundary condition, and the symmetry condition are all satisfied. At the same time, the numerical solutions of stress and displacement are given by using the finite element software ANSYS, which are in good agreement with the analytical solutions. The results also show that the tangent stress variations of the inner and outer boundaries of the lining are not consistent, and the maximum value of the inner boundary is about 2 times than that of the outer boundary, which occurs at the arch springing. While the displacement variations of the inner and outer boundaries of the lining are consistent, and the values are close. The maximum settlement, uplift and horizontal displacement occur at the roof, floor, and waist of the tunnel, respectively. In the design of the tunnel, the stress and displacement at those positions on the inner boundary of the lining should be paid more attention to meet the requirements.

Key words: lined tunnel, orthotropic surrounding rock, complex variable function, stress, displacement