## 6 Conclusions  
This study develops a new framework to calculate the critical required support force of face pressure to estimate the stability of tunnels in unsaturated inclined-layer soils. What distinguishes it from the previous literature is that this study employs a distribution formula for multi-layer soil suction heads to consider the spatial variability of matrix suction distribution in inclined layered soil. Of course, to fully address tunnel face stability considering both spatial variability, a three-dimensional discrete rotational mechanism was constructed for tunnel face failure. The different results generated by various failure mechanisms were compared. A further analysis was conducted to compare the stability of tunnel faces under various conditions, including different types of inclined layered soils, subjected to variations in the geometric parameters of soil layering and changes in the unsaturated parameters of soil at different locations. Additionally, we employed the grey relational analysis method to calculate the degree of correlation between various parameters and their impact on tunnel face stability under different scenarios. This approach has helped us identify the sensitive regions where changes in unsaturated parameters significantly influence tunnel face stability. Further conclusions can be summarized as follows:  
(1) The analysis of the critical support pressure for inclined layered soils under varying strike and dip angles reveals the profound impact of both the stratification geometry and the hydraulic conditions on tunnel stability. When the soil layer interface intersects the tunnel face, the required support pressure exhibits greater variability, with infiltration conditions leading to the highest support pressures due to the destabilizing effects of seepage forces. Conversely, when the soil layer interface is located above the tunnel face, the stabilizing influence of the upper soil layer reduces the destabilizing effects, resulting in more consistent and lower support pressures. These findings highlight the critical importance of accurately accounting for the position of the soil layer interface in tunnel design, as its interaction with the tunnel face directly influences stability. The use of grey relational analysis further strengthens these insights by quantifying the correlation between critical support pressure and various hydrological conditions. The analysis reveals that under the no-flow condition, the grey correlation is highest, indicating a stronger relationship between strike angles and support pressures. In contrast, infiltration conditions consistently result in lower grey correlations, pointing to a higher potential for instability. These results emphasize the significant role of water movement within unsaturated soils in altering the stability of tunnel faces, particularly under varying seepage conditions. The slope geometry, specifically dip angles, plays a critical role in determining the system's stability, with steeper dip angles exacerbating the destabilizing effects of seepage forces. (2) This section investigates the influence of unsaturated soil parameters on tunnel stability in inclined layered soils under different seepage conditions (infiltration and evaporation). The results highlight the significant role that variations in unsaturated parameters play in determining the safety factor (FS) and overall tunnel stability. In particular, the absolute value of the suction coefficient (1q/kc1) has a marked effect on the safety factor,