## 2 The Types of Slide Surface and the Influence of Immersion  
### Slide Surface in Shallow Buried Loess Tunnel  
The characteristics of the surrounding rock slide surface of a shallow buried tunnel can be described with three factors of surrounding rock, namely, failure point, fracture angle \(\beta\), and slide surface shape, as shown in Figure 1(a). Table 1 illustrates the characteristics of three typical slide surfaces. As shown in Figure 1(a), the first is the slide surface proposed by [PERSON] and [PERSON], whose failure point of the surrounding rock is located at the arch foot. The fracture angle \(\beta\) is \(45^{\circ}+\varphi/2\), and the slide surface is an oblique line [7]. This slide surface is widely applied in the calculation of surrounding rock pressure [6]. The second is the slide surface proposed by [PERSON], whose failure point of the surrounding rock is also located at the arch foot, and the shape of this slide surface is the same as the first slide surface. However, the failure angle needs calculating from the friction angle \(\varphi\)c of surrounding rock and the friction angle \(\theta\) of slide surface [20]. Considering the universal vertical joints in the loess, [PERSON] et al. have put forward a different shape of slide surface [21], as shown in Figure 1(b). The slide surface above the horizontal depth of the tunnel vault is vertical, the failure point of surrounding rock is still arch foot, and the slide surface is the broken line AEB and CFD. The fracture angle \(\beta\) can be calculated from the thickness H of the overlying loess, the tunnel excavation width B, and the friction angle \(\varphi\) of the loess. Figure 2: Schematic diagram of the surrounding rock slide surface: (**a**) Slide surfaces proposed by [PERSON] and [PERSON] [6; 7]; (**b**) Slide surfaces proposed. The generation of the slide surface is closely related to the displacement of the overlying strata layer of the tunnel, and the magnitude and law of the overlying strata layer displacement are considerably different due to different tunnel construction methods [8]. Therefore, the influence of construction methods should be considered in the generation of the slide surface. To control the surrounding rock settlement effectively and avoid collapse, the loess tunnel generally adopts the partial excavation methods, such as the two-steps method, three-steps method, the center diagram method (CD), and the center cross diagram method (CRD), as shown in Figure 3; the number in the figure is the excavation sequence. The collapse boundary inside the tunnel can represent the location of the failure points of the slide surface. Table 2 shows the statistics relationship of construction methods and failure points of sixteen shallow buried loess tunnels, the relevant data are obtained from the literatures [22]. It can be seen that the collapse of surrounding rock is most common during the excavation of upper and lower steps. When the collapse occurs during the excavation of the upper or middle steps, the failure point is generally located near the arch waist, and the failure point caused by the lower step excavation is at the arch foot of the tunnel, as shown in Figure 3. Therefore, there are two possible locations for slide surface failure points in the shallow buried loess tunnel, which are the arch waist and the arch foot. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Proposer** & \
\begin{tabular}{c} **Surrounding Rock** \\ **Failure Point** \\ \end{tabular} & **Failure Angle \(\beta\)** &
\begin{tabular}{c} **Shape of the** \\ **Slide Surface** \\ \end{tabular} \\ \hline [PERSON] and [PERSON] & arch foot & 45\({}^{\circ}\) + \(\varphi\)/2 & oblique line \\ [PERSON] & arch foot & B = f(\(\varphi_{c}\), \(\theta\)) & oblique line \\ [PERSON] & arch foot & B = f(H, b, \(\varphi\)) & broken line \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the typical surrounding rock slide surface.