Analytical Stress Model for Cold-Region Weakly Cemented Soft Rock Tunnels: Considering Non-uniform Stress and Temperature Fields
摘要
Tunnel construction in cold regions faces critical challenges from frost heave. This paper proposes an analytical framework for analyzing cold-region weakly cemented soft rock tunnels under non-uniform stress fields with a temperature field, based on the superposition principle of elastic mechanics. Then, a Mathematica-based symbolic-numerical solver is developed to implement the framework, enabling rapid stress computation. Additionally, validation against existing studies, model test and field measurements confirms its reliability. The influences of temperature and the elastic modulus (El) of the lining on the stress field were thoroughly explored. The results show that decreasing temperatures amplify circumferential stress in the lining as well as the surrounding rock near its inner boundary, while decreasing in the deep surrounding rock, and the radial stress in both the lining and the surrounding rock increases. Temperature variation affects the surrounding rock more significantly than the lining. Furthermore, frost heave reduces stability near the tunnel boundary but enhances it in deeper zones. Increasing El elevates circumferential stress in the lining and radial stresses in both the lining and the surrounding rock, with a more pronounced effect on the lining. Although higher lining elasticity improves surrounding rock stability, excessive values may cause lining failure and are therefore not recommended. This study provides a theoretical foundation for the design of tunnels in cold regions with weakly cemented soft rock.