## 5 Result
### Analysis of the Unsaturated Parameters of Different Soil Layers  
In this section, an inclined soil model is established to investigate how unsaturated parameters influence the stability of the tunnel face at various locations under infiltration and evaporation conditions since the variation of \(k_{\rm s}\) will not affect the unsaturated forces under no-flow conditions. As depicted in Figure 10, the angles of the inclined soil interface are shown along with the geometric parameters and the soil's inclined stratification parameters are: \(\alpha_{h}=\alpha_{v}=45^{\circ}\). The groundwater level aligns with the bottom of the tunnel face, while the top of the tunnel face sits precisely at the boundary of the inclined stratification. Figure 9: Average grey correlation degree coefficient calculations regarding the critical support pressure and strike \(\alpha_{\rm h}\) under three kinds of unsaturated seepage conditions via varying dip \(\alpha_{\rm v}\). (**a**) clay-loess. (**b**) silt-loess. It is important to emphasize that the unsaturated parameters estimated vary between the upper and lower layers, while all other soil properties remain consistent. According to the value of the hydrological parameters displayed in Table 1, the settings of the changing interval of the hydrological parameters are: the absolute value of \(q/k_{s}\) from 0.1 to 0.2, the value of \(n\) from 3 to 6, and the value of \(1/\alpha\) from 100 to 200. When a hydrological parameter of a certain soil layer changes, the other parameters of that soil layer and the three parameters of another soil layer all remain within the minimum range of variation. As depicted in Figure 11, the safety factor FS will monotonically decrease as the absolute value of \(q/k_{s}\) increases in the upper soil layer whereas the safety factor FS will monotonically increase when the absolute value of \(q/k_{s}\) increases in the lower soil layer under evaporation condition. The opposite phenomenon occurs in the case of infiltration. As shown in Figure 12, the addition of the results in a decrease in the safety factor FS for all scenarios. When differentiation is needed, changing the value \(1/\alpha\) of the lower soil layer results in a relatively gentle slope of the ascent curve, whereas changing the value \(1/\alpha\) of the upper soil layer leads to a noticeably steeper ascent curve. As presented in Figure 13, under infiltration conditions, as the \(n\) value increases, the safety factor FS increases. In the case of evaporation conditions, the situation is more complex. When changing the \(n\) of the upper soil layer, the relationship between \(n\) and the safety factor FS is negatively correlated, while when changing the lower soil layer, this relationship is positively correlated. The grey relational analysis method is adopted to further analyze the degree of correlation between various unsaturated parameters under different conditions and among different unsaturated parameters on the stability of tunnel face. The reference sequence consists of the 11 incrementing numerical values of the three unsaturated parameters \(q/k_{s}\), \(1/\alpha\), and \(n\) on the main and sub-scales in the figure, and the corresponding calculated nominal support force results serve as the primary sequence. Figure 10: The inclined soil model for analyzing the influence of unsaturated parameters. Grey relational analysis is used to investigate the varying degrees of influence exerted by three distinct unsaturated soil parameters, taken as sub-sequences, on the nominal support force, which serves as the reference sequence. The primary objective is to analyze how changes in these unsaturated parameters, under different seepage conditions and at varying soil layer positions, affect the outcome. Figure 11: The safety factor FS versus the absolute value of \(q/k_{\mathrm{s}}\) varying in different layers of soil. Figure 12: The safety factor FS versus \(1/\alpha\) varying in different layers of soil.