Abstract: In this study, analytical viscoelastic solutions were derived for the lined circular tunnels by the correspondence principle and complex variable method under full contact and smooth contact conditions between liner and ground in non-hydrostatic stress field. In the solutions, all kinds of viscoelastic tunnels with an elastic liner was considered and the delayed installation of the liner was also taken into account. Therefore, the obtained analytical solutions can be applied to all linear viscoelastic models. The analytical solutions were verified by the solutions of references and numerical results. According to the solution, the surrounding rock was assumed to conform to the generalized Kelvin (H-K) viscoelastic body. The results showed that the radial, tangential stress, the circumferential displacement of the lining and the bending moment of the lining increased with time until converged to the fixed value. Under two kinds of contact conditions, there were quite differences on the displacement of the surrounding rock, the stress distribution of the lining, the distribution of the displacement and the internal force. Furthermore, the above differences between these two conditions increased with the time. Compared with the existing solutions, the solutions derived in this paper are more suitable and reasonable for practical deep buried tunnels especially for the full contact condition. The comparison between the two solutions can provide a useful reference for selecting liner and construction reasonably.

Key words: non-hydrostatic stress field, lined tunnel, full contact, smooth contact, viscoelasticity, analytical solution