## 4 Discussion  
In this portion, a comparative work with [PERSON] et al. (2019) [30] is used to verify the influence of unsaturated flow and the layered soils towards this framework. The pure  
Figure 5: Flowchart of obtaining the optimized face support.  
unsaturated conditions are performed in [PERSON] et al. (2019) [30], and the strength reduction technique is employed to find the evaluative metric safety factor \(FS\):  
\[FS=\frac{{c_{1}}^{\prime}}{{c_{1d}}^{\prime}}=\frac{{c_{2}}^{\prime}}{{c_{2d}}^{ \prime}}=\frac{\tan{\varphi_{1}}^{\prime}}{\tan{\varphi_{1d}}^{\prime}}=\frac{ \tan{\varphi_{2}}^{\prime}}{\tan{\varphi_{2d}}^{\prime}} \tag{34}\]  
where \(FS\) represents the safety factor. During each reduction process, the effective cohesion and effective internal friction angle of soils are decreased by an identical coefficient (in layered soils for soils from all soils). The \({c_{d}}^{\prime}\) and \({\varphi_{d}}^{\prime}\) represent the reduced effective cohesion and internal friction angle at the critical state. This adjustment appears to be a cyclic fine-tuning of the soil strength to achieve a safety factor that meets the criterion where external work equals internal energy dissipation work.  
As shown in Figure 6, a comparison with [PERSON] et al. (2019) [30], the \(FS\) of clay and silt versus a different \(C/D\) is displayed, and we established a comparative group of inclined soil layers with clay in the upper layer and silt in the lower layer. The parameters of the soil are equivalent to [PERSON] et al. (2019) [30] with \(c^{\prime}/\gamma D=0.1,\ \varphi^{\prime}=20^{\circ},\ \gamma=20\ \mathrm{kN/m^{3}}\), and the infiltration rate is \(q=0\). The geometry parameters are also the same: \(D=10\ \mathrm{m},\ d_{w}=0\), and the unsaturated parameters can refer to Table 1, which is also the same as in [PERSON] et al. (2019) [30].  
It can be known that the results from this work roughly align with the trajectory of [PERSON] et al. (2019) [30], with each safety factor's results correspondingly reduced by nearly the same portion. The construction of the failure mechanism by [PERSON] et al. (2019) [30] is supported  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Soil Type** & \(\mathbf{\alpha}\ (\mathbf{kPa^{-1}})\) & \(\mathbf{n}\) & \(\mathbf{k_{s}}\ (\mathbf{m/s})\) & \(\mathbf{c^{\prime}/\gamma d}\) & \(\mathbf{\gamma}\ (\mathbf{kN/m^{3}})\) & \(\mathbf{\varphi^{\prime}}\) \\ \hline clay & 0.005 & 2 & \(5\times 10^{-8}\) & 0.05 & 18 & 20\({}^{\circ}\) \\ silt & 0.01 & 3 & \(5\times 10^{-7}\) & 0.03 & 17 & 25\({}^{\circ}\) \\ loess & 0.025 & 4 & \(1\times 10^{-6}\) & 0.001 & 16 & 28\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hydrological parameters of typical soils.  
Figure 6: Comparison with previous studies of safety factor on unsaturated seepage effect with varying \(C/D\)[30].  
by the horn-like mechanism suggested by [PERSON] and [PERSON] (2002) [31], which cannot validly reflect the failure block covering the entire tunnel face. Using spatial discretization in this work makes the results more conservative than those of [PERSON] et al. (2019) [30] for this reason. The condition of the comparative group is set as: \(\alpha_{v}=30^{\circ},\alpha_{h}=30^{\circ},dt=D/4\). The outcome initially exceeds the pure clay layer and the pure silt layer, and then rises more gradually than clay and, finally, its value is between the one of pure clay and pure silt, relatively close to clay. This verifies the impact of soil stratification on stability under overall unsaturated seepage conditions. The proximity to the clay may be due to the spatial positioning of the interface. In tunnels under unsaturated seepage, the higher the vertical distance of the groundwater level from within the soil, the greater its contribution to the overall structural suction stress. Therefore, its characteristics will be more similar to those of the upper soil layer.