# Evolution Process of Toppling Deformations in Interbedded Anti-Inclined Rock Slopes
## 4 Discussion  
### Uniqueness of the Interbedded Toppling  
The lithology significantly influences the toppling behavior of the anti-inclined rock slope. Soft rocks often undergo ductile, flexural toppling, and the mechanism tends toward self-stabilization due to the face-to-face contacts among rock columns. Hard rocks tend to form brittle, catastrophic block toppling due to the loosened structure created by numerous edge-to-face contacts within the slope [1; 7; 18; 46]. However, actual slopes often contain various kinds of lithology and exhibit a more complex interbedded structure. For example, the lithologies exposed in western China primarily comprise phyllite, schist,  
Figure 9: Average velocity of the slope model versus the operation time of the base friction apparatus. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Monitoring Point**} & \multicolumn{3}{c}{**Displacement (mm)**} & \multicolumn{3}{c}{**Velocity (m/s)**} \\ \cline{2-7}  & **Monitoring Value** & **True Value** & **Relative Error (\%)** & **Monitoring Value** & **True Value** & **Relative Error (\%)** \\ \hline a-1 & 221.3 & 225.6 & \(-1.9\) & \(5.8\times 10^{-5}\) & \(5.5\times 10^{-5}\) & 6.1 \\ b-1 & 375.2 & 391.7 & \(-4.2\) & \(6.9\times 10^{-4}\) & \(7.5\times 10^{-4}\) & \(-7.7\) \\ c-1 & 275.8 & 286.5 & \(-3.7\) & \(10.3\times 10^{-4}\) & \(10.8\times 10^{-4}\) & \(-4.6\) \\ d-1 & 158.6 & 164.8 & \(-3.8\) & \(8.5\times 10^{-4}\) & \(9.0\times 10^{-4}\) & \(-5.0\) \\ e & 10.7 & 11.1 & \(-4.0\) & \(1.5\times 10^{-4}\) & \(1.4\times 10^{-4}\) & 8.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error analysis of monitoring results. slate, metasandstone, and limestone [37]. Intense tectonic activities in geological history commonly led to the development of a set of cross joints within hard rocks. During the slope deformation process, soft rocks can withstand significant bending deformation without fracturing due to their ductility. Although hard rock blocks cannot accommodate substantial bending deformations, they can adapt to the bending deformations of surrounding soft rocks by accumulating sliding and overturning along numerous cross joints (Figure 10a). Therefore, the toppling deformation on interbedded anti-inclined rock slopes is a combined result of the flexure of soft rock layers and the accumulated motions of hard rock blocks along cross joints. Compared to block toppling, interbedded rock masses have fewer edge-to-face contacts and a higher degree of constraint from surrounding material. Therefore, the interbedded anti-inclined rock slopes often possess large deformation depths, and the deformation process often tends toward stabilization through its evolution (Figure 10b). The kinematic analysis can help us intuitively understand the variations in boundary conditions of rock columns during the rotation process. The tensile fracture between two adjacent rock columns can be described by the length parallel to the THS in a rotational column (\(d\)). As shown in Figure 11a, the initial value of this length (\(d_{i}\)) can be calculated by:  
\[d_{i}=\frac{b}{sin\omega_{\text{d}}}, \tag{4}\]  
where \(b\) is the thickness of a rock column. \(\omega_{\text{d}}\) is the angle between the undeflected rock layer and the THS. After the slope deforms, the value of \(d\) in the deflected rock columns can be calculated by:  
\[d=\frac{b}{sin\omega_{\text{t}}}, \tag{5}\]  
where \(\omega_{\text{t}}\) is the angle between the deflected rock layer and the THS. Since rock layers of the prototype slopes are nearly vertical [37], the value of \(\omega_{\text{d}}\) is less than \(90^{\circ}\). The rotation of the rock columns will cause an increase in \(sin\omega_{\text{r}}\), thereby resulting in a decrease in the value of \(d\). Therefore, the formation of the tensile fracture between two adjacent rock columns can be explained by the contractional effect of rotated rock columns parallel to the THS (Figure 11b).