## 5 Discussion  
1. The simulation results indicate that rainfall infiltration significantly affects slope stability. During the 10 h rainfall simulation, the following trends were observed:  
Figure 7: The variation of slope safety factor with time for different slope ratios 5–30 m higher than the downhill slope.  
In the early stages of rainfall, the safety factor decreases sharply as water begins to infiltrate the slope. This is due to the rapid increase in pore water pressure, which results in a corresponding reduction in effective stress. After 4-5 h of rainfall, the soil reaches saturation, and the rate of decrease in the safety factor slows down. At this point, the permeability and drainage rate of the soil tend to reach equilibrium. After 10 h of rainfall, the safety factors of some slopes approach critical values, especially for steeper slopes, indicating that the slope is on the verge of instability due to increased pore water pressure caused by water accumulation in the soil. 2. The impact of slope ratio on stability is significant. Under rainfall conditions, steeper slopes exhibit poorer stability. The rate of decrease in the safety factor for steep slopes (e.g., 1:1.5) is much faster than for gentler slopes (e.g., 1:2.25). This is attributed to the fact that steeper slopes concentrate the forces acting on the soil, thereby increasing shear stress and reducing shear strength, making the slope more prone to failure. For slopes with ratios of 1:1.5 and 1:1.75, failure occurs after 7-8 h of rainfall, especially for slopes exceeding 10 m in height, where the safety factor decreases significantly, reaching a minimum of 0.9. In contrast, slopes with gentler ratios (1:2.0 and 1:2.25) exhibit better stability. For example, a slope with a ratio of 1:2.25 maintains a safety factor above 1.1 even after 10 h of rainfall. 3. The results of this study have important implications for slope design and maintenance in areas prone to rainfall and erosion. In regions with frequent rainfall, slope designs should adopt gentler slope ratios (e.g., 1:2.0 or 1:2.25) to minimize the risk of instability. Steep slopes, especially those with greater heights, should be avoided, as they are more susceptible to collapse during prolonged rainfall. For existing slopes, measures such as improving drainage, reducing water infiltration, or using stabilization techniques (e.g., slope reduction and counterpressure at the slope foot) can help maintain stability during heavy rainfall events. 4. Although the results provide a solid basis for decision-making, this study also has some limitations. The study relied entirely on numerical simulation for stability analysis, and the model was not calibrated and verified by physical experimental models or field monitoring data. Although the simulation results are consistent with theoretical expectations, they are not directly compared with the actual slope behavior, which may affect the applicability of the model in real complex geological conditions. In the future, the numerical model should be verified by physical experiments and field monitoring data to improve the empirical reliability of the results; the simulation assumes homogeneous soil conditions, while in reality, the cohesion, permeability and compaction of the soil may vary. Future research should also consider the impact of soil heterogeneity on slope stability. In addition, this study focuses on short-term heavy rainfall events, while long-term low-intensity rainfall may have different effects on slope stability. Future research should explore the impact of such events on long-term slope stability. Although the numerical simulation results provide valuable theoretical insights, further field studies and verification using real data are needed to confirm the research results and improve modeling techniques.