## 3 Results and Analysis
### Migration Law of Wetting Front
#### 3.2.2 Influence Law of Substrate Thickness on Wetting Front  
The relationship between the advancing distance and time of wetting fronts of different substrate thicknesses in the direction of two positions of the slope is shown in Figure 11. It can be seen from the figure that the rate of advancing distance of wetting fronts of each slope becomes slower as the infiltration time increases, and the advancing rate of wetting fronts on the slope and in the slope is different due to the formation of slope runoff and under the action of gravity, i.e., middle of slope \(>\) top of slope. At any moment throughout the observation time, the wetting advance distance of the slope decreases with increasing cement content. The relationship between the migration rate of wetting fronts and time for different substrate thicknesses is shown in Figure 12, from which it can be seen that the migration rate of wetting fronts decreases rapidly from 0 to 130 min for each slope, the trend of decreasing migration rate of wetting fronts slows down from 130 min to 240 min and the migration rate of wetting fronts tends to stabilize after 240 min. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(Y=m\cdot x+n\)} \\ \cline{2-7}
**Parameters** & \multicolumn{3}{c}{**Top of the Slope**} & \multicolumn{3}{c}{**Middle of the Slope**} \\ \cline{2-7}  & \(m\) & \(n\) & \(R^{2}\) & \(m\) & \(n\) & \(R^{2}\) \\ \hline \(a\) & \(-0.5183\) & \(3.2695\) & \(0.9402\) & \(-0.2515\) & \(2.9887\) & \(0.9980\) \\ \(b\) & \(0.0390\) & \(-0.4064\) & \(0.9285\) & \(0.0110\) & \(-0.3642\) & \(0.9900\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fitting table of different cement contents with power function parameters. Figure 11: Different substrate thickness wetting front advance distances versus time. The power function \(V=a\cdot t^{b}\) pair was fitted (\(a\) and \(b\) are constants), where \(V\) is the wetting front transport rate and \(t\) is time. The results of fitting the wetting front transport rate versus time without the cement content slope are shown in Table 8.  
As shown in Table 6, the \(V\)-\(t\) relationship is fitted with a coefficient of determination \(R^{2}\) greater than 0.9605, which indicates that the wetting front transport rate has a good power function relationship with time at 2 positions on the slope and in the slope for different substrate thicknesses; moreover, there is a law that parameter a decreases and parameter b increases with increasing substrate thickness. The power function \(y=m\cdot x^{n}\) is used to fit the parameters \(a\) and \(b\) (\(m\) and \(n\) are constants), \(y\) is the power function parameters \(a\) and \(b\) and \(x\) is the thickness of the substrate. The results of fitting the relationship between different substrate thicknesses and power function parameters are shown in Table 9.  
As shown in Table 9, the fitted results for the relationship between the different substrate thicknesses and the power function parameters show that the fitted coefficient of determination \(R^{2}\) is greater than 0.8263, indicating a non-linear relationship between the cement content and the power function parameters \(a\) and \(b\). That is, as the thickness of the substrate increases, parameter a non-linearly decreases and parameter b non-linearly increases. In conjunction with the previous functional relationship, the thicker the substrate thickness, the slower the rate of wetting front migration. Therefore, in the design of ecological slope substrate, an appropriate increase in substrate thickness will help to suppress the migration of wetting fronts if it is beneficial to plant growth; at the same time, using this  
Figure 12: The transport rate of wetting fronts with different substrate thicknesses versus time.