Abstract: Based on the complex variable method, and the stress boundary conditions on the surface and the excavation boundary, the analytical solutions of the stresses and displacements of a shallow circular tunnel under the gravity and tectonic stress are deduced. Introducing the , which reflects the level of the horizontal stress on the ground surface, the solution become general, suitable for the case whether the horizontal stress on the ground surface is zero or not; and the correction can be verified by the ANSYS software. The distributions of the stresses and displacements field are analyzed. The results show that tangential tensile stress may appear on both sidewalls when the surface horizontal stress is non-zero; and the value of the tensile stress increases with the horizontal stress. Meanwhile, the vertical displacements on the surface, the vault’s upward deformation, the sidewalls’ extrusion deformation are influenced greatly by the surface stress as well.

Key words: shallow tunnel, elastic half-plane, function of complex variable method, conformal mapping, tectonic stress