## 3 Results
### Stability Analysis of Canal Slope under Different Working Conditions
#### 3.3.3 Stability Analysis of Replacement-Reinforced Collapsible Slope  
The above analysis confirms that the c, \(\varphi\), and E of the loess at the base of the canal exhibit different degrees of reduction after several WD-FT cycles. During the shutdown period, the canal slope will be in an unstable state after three cycles, and sliding damage has occurred or will occur. In the reinforcement of the hazardous canal section, excavation to remove the surface layer of deteriorated loess and gravel replacement are used to improve the overall stability of the canal slope. Among them, the strength parameters of the initial gravel replacement layer [38; 44] are presented in Table 4.  
To investigate the effect of replacing the surface layer of deteriorated soil with sand and gravel on the safety and stability of the canal slope, the stability of the canal slope before and after the reinforcement was calculated and analyzed. Considering the existence of the water level behind the impermeable membrane under the most unfavorable conditions during the shutdown period, the calculation conditions of 0 m for the water level in the operation period and 4.5 m for the water level behind the impermeable membrane were set in the stability analysis. Meanwhile, the depth of gravel replacement was set as 0.3 m, 0.6 m, 0.9 m, 1.2 m, and 1.5 m, respectively, and the numerical model was run for nine cycles.  
According to the stability calculation results of the canal slope before and after the reinforcement, the variations in \(F_{s}\) of the canal slope with the WD-FT cycles with different replacement depths are plotted in Figure 12. Meanwhile, to visually obtain the limiting effect of gravel replacement on the canal landslide displacement, the displacement programs of the replacement-reinforced canal slope after nine WD-FT cycles are presented in Figure 13.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Natural Dry** & \multirow{2}{*}{**Friction**} & \multirow{2}{*}{**Elastic Modulus**} & **Relative** \\  & **Density** & & & **Density** \\ \hline Gravel & 2.01 g/cm\({}^{3}\) & 38.5\({}^{\circ}\) & 45 MPa & \(\geq\)0.75 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of sand and gravel used in the numerical simulation.  
Figure 12: The \(F_{s}\) of the canal slope with different replacement depths.  
Figures 12 and 13 confirm that the \(F_{s}\) of the canal slope during the shutdown period undergoes a significant reduction compared to that during the operating period after nine WD-FT cycles. The sliding damage of the slope with a replacement depth of 0.3m is reduced to some extent compared to the non-replaced slope. A slope with a replacement depth of 0.9 m or more is still able to be maintained above the limit equilibrium state after nine WD-FT cycles. With the increase in the replacement depth, the sliding displacement of the canal slope is effectively controlled. However, after the depth of replacement reaches 1.2 m, continuing to increase the depth of replacement has little effect on the improvement in the \(F_{s}\) of the canal slope.