Failure Mode of Rectangular Shallow Tunnel in Unsaturated Fine-Grained Soil Under Temperature Influence

Failure analysis has always been among the key research focuses in underground tunneling, particularly in forecasting the collapse risk of tunnel crowns, which bears great engineering and practical significance for tunnel safety assessment. In practical engineering, the soil surrounding shallow tunnels and other underground chambers is typically unsaturated. With the advancement of tunneling technology, shallow tunnels affected by ground temperatures are increasingly common, making it essential to incorporate temperature effects into the stability analysis of unsaturated shallow tunnels. This paper proposes a novel framework for analyzing the stability of shallow rectangular tunnel crowns under temperature influence. By adopting a temperature-dependent effective stress model for unsaturated soils combined with the soil–water characteristic curve, temperature influence is integrated into the calculation of apparent cohesion in unsaturated soils. The upper bound theorem and a multi-rigid-block failure mechanism are adopted to assess crown stability, with the geometry of the failure mechanism determined through a compatible velocity field. New analytical expressions are derived. Through calculating the internal energy dissipation rate, considering temperature effects and external work rate, the critical support pressure at the tunnel crown is obtained using the Sequential Quadratic Programming (SQP). Discussions of temperature and other unsaturated soil parameters are carried out to explore their effects on the stability of shallow tunnels. Results demonstrate that temperature significantly influences the tunnel’s critical support pressure, with the extent of this impact primarily dependent on the unsaturated soil type and seepage conditions. Furthermore, the theoretical framework developed in this study provides a more accurate description for unsaturated fine-grained soils. This study introduces a novel integration of thermal influences into the upper bound theorem, applying this enhanced methodology to the stability assessment of shallow rectangular tunnel crowns. The resulting failure model and analytical framework establish a rigorous upper bound solution for crown stability, thereby furnishing a more accurate theoretical foundation for subsequent tunnel face support strategies.