Analytical solution for the soil-lining interaction in cold region deep tunnel considering the delayed installation of the lining

In this paper, an analytical solution is deduced for estimating the soil-lining interaction in a deep tunnel subjected to freezing action. The complete solution is found by the superposition of a frost heaving model and an excavation model considering the lining delayed installation. By treating the tunnel lining as a thick-walled shell, the internal force is discussed considering the convergence–confinement method. Then, specific consideration is given to the influence of the freezing process (increasing freezing depth). Generally, the results show that normal soil pressure around the lining increases significantly with increasing freezing depth. The frost heaving pressure and the lining's delayed installation contribute to reducing the nonuniformity of the axial force. Furthermore, to identify the key influencing factors, an orthogonal experiment is designed and conducted by the analytical solution mentioned. An increasing lining thickness could improve the axial force at the sidewall and weaken the axial force at the crown. The freezing depth is not statistically significant to the bending moment around the lining of the cold region tunnel. Overall, this study offers novel insights into the soil-lining interaction in deep tunnels built in cold regions and helps avoid frost damage at tunnel linings.