## 3 Results Analysis
### Effect of Vegetation Root Reinforcement on Slope Stability  
In order to visually evaluate the influence of poinsettia root systems on the stability of expansive soil slopes, an analysis was conducted on the displacement variations at the slope crest and toe under four rainfall conditions. The horizontal displacement changes are shown in Figure 10. The presence of roots can delay the development of horizontal displacement on the slope surface, and the trend of the results is consistent with the results of existing studies [33]. The model is established in ABAQUS, with the slope direction along the negative \(x\)-axis. From Figure 10a, it can be observed that with and without reinforcement, the final horizontal displacements at the slope crest for Condition 1 are in the opposite direction to the sliding surface, while for Condition 2, the displacements are also in the opposite direction but larger than those for Condition 1. The sliding pattern appears to be arc-shaped, as shown in Figure 11. The reason for this phenomenon is that after the expansive soil absorbs moisture and expands, its strength decreases, resulting in the formation of a high-stress zone in the surface layer (weathered layer). Under the self-weight accumulation of the slope, sliding occurs first at the slope toe. The vegetation root system increases the stiffness of the surface layer, and the sliding at the slope toe causes rigid body rotation of the surface layer, resulting in displacement of the slope crest along the positive \(x\)-axis. From the variations in horizontal displacement at the slope crest and toe, it can be observed that considering root reinforcement can limit the horizontal sliding displacement of the slope. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Rainfall Conditions**} & **Time Step Length** & **Time Step Length** & \\  & **for Failure without** & **for Failure with** & **Percentage Increase** \\  & **Reinforcement** & **Reinforcement** & \\ \hline Condition 1 & 0.6386 & 0.7965 & 24.72\% \\ Condition 2 & 0.6080 & 0.7628 & 25.46\% \\ Condition 3 & 0.5730 & 0.7212 & 25.86\% \\ Condition 4 & 0.4897 & 0.6318 & 29.02\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time steps required for plastic zone propagation with and without reinforcement. Figure 10: Horizontal displacement change: (**a**) horizontal displacement of slope top; (**b**) horizontal displacement of slope toe. The slope safety factors were obtained using the strength reduction method, as presented in Table 7. The calculation results indicate that for the expansive soil slope, regardless of whether vegetation reinforcement is considered, the safety factor decreases as the rainfall intensity increases. The larger the increase in rainfall intensity, the greater the decrease in the safety factor and the faster the deterioration in the slope stability. By comparing the safety factors with and without vegetation reinforcement at the same rainfall intensity, the following observations can be made: at a rainfall intensity of 10 mm/d, the safety factor increases by 63.2%; at a rainfall intensity of 30 mm/d, the safety factor increases by 67.7%; at a rainfall intensity of 60 mm/d, the safety factor increases by 73.9%; at a rainfall intensity of 120 mm/d, the safety factor increases by 67.6%. Based on the changes in the safety factor, it can be concluded that vegetation root reinforcement can improve the stability of the surface layer (weathered layer) of the expansive soil slope, and the improvement becomes more significant as the rainfall intensity increases. However, when the rainfall intensity exceeds the infiltration capacity of the slope, the ability of the safety factor to increase starts to decline. Plant root systems have strong tensile and shear strength, and they play a significant role when the slope gradually becomes unstable under high rainfall intensity.