# Temperature Effect on Stability of Tunnel Face Under Unsaturated Seepage Condition
## 1 Introduction
These studies, which utilized different models, experimental approaches, temperature ranges, and stress conditions, all demonstrated that temperature has a significant influence on the strength of unsaturated soil. Incorporating temperature as a critical factor in the geotechnical stability analysis of tunnel faces during excavation is essential. Classic plasticity theory includes the lower bound limit analysis ([PERSON] et al. [14]; [PERSON] et al. [15]; [PERSON] et al. [16]) and the upper bound limit analysis ([PERSON] and [PERSON] [17]; [PERSON] and [PERSON] [18]; [PERSON] and [PERSON] [19]; [PERSON] et al. [20]). Through the research of these scholars, it can be discovered that the upper bound method calculates the ultimate load of a structure by assuming a failure mechanism (such as a sliding surface, crack, etc.). This method is supposed to be intuitive and easy to understand, it and can handle complex failure patterns. The lower bound method, on the other hand, determines the ultimate load of a structure by considering all possible stress states, and can provide more accurate results theoretically. However, it is generally considered to require solving complex mathematical problems, and its application may be limited for problems involving non-homogeneous materials or complex boundary conditions. In the context of upper bound methods, achieving an exact solution requires identifying a kinematically admissible velocity field that minimizes the rate of energy dissipation. This velocity field must satisfy the velocity boundary conditions, geometric equations, and the condition of volume constancy. If the identified velocity field also happens to meet the conditions of static equilibrium, then the upper bound solution is the exact solution. Conversely, for lower bound methods to achieve an exact solution, it is necessary to find a statically admissible stress field that maximizes the rate of energy dissipation. This stress field must satisfy the conditions of force equilibrium, stress boundary conditions, and yield criteria. If the identified stress field also happens to satisfy the conditions of kinematic admissibility, then the lower bound solution is the exact solution. The upper bound method is more suitable for the analysis of dynamic problems and complex failure patterns, while the lower bound method is more suitable for static problems and homogeneous materials. Therefore, the upper bound method is adopted by this work. In the context of tunnel face stability analysis utilizing the upper bound method, delineating the structural failure mechanism is deemed essential. A variety of failure mechanisms for tunnel faces have been suggested by researchers. [PERSON] et al. [21] integrated a three-dimensional discrete model into their analysis using spatial discretization methods, which provided outcomes that are more aligned with practical engineering scenarios, though the methodology is notably complex. [PERSON] and [PERSON] [22] introduced a mechanism based on a 3D logarithmic spiral, employing kinematic methods of limit analysis to predict tunnel face failure. This approach was further developed in this paper to include a 3D logarithmic spiral failure mechanism of tunnel faces, drawing on the concept of curved conical failure model. This study seeks to research how temperature affects the stability of tunnel faces in unsaturated soils by analyzing the relationship between soil matric suction, shear strength, and temperature, all within the context of unsaturated soil mechanics. We developed a work rate equilibrium equation that matches external work rates with internal energy loss. The tunnel face's stability was assessed through a 3D logarithmic spiral failure model. The safety factor (FS) for the tunnel faces under the influence of temperature and unsaturated seepage was determined by adopting the strength reduction method ([PERSON] and [PERSON] [23]), calculating the ratio between the soil's initial strength and its strength at the point of critical failure.