## 4 Stability Analysis of Single-Step Slope with Different Slope Ratios Under Rainfall Conditions  
### Changes in Slope Stability Under Continuous Rainfall  
Figure 4 illustrates the final state of a single-step slope composed of tailings clay with a slope ratio of 1:1.5 and a height of 5 m under 10 h of continuous heavy rainfall, as well as the slope stability performance at various time intervals during the rainfall event. In the initial stages of rainfall, the stability factor exhibits significant variation, but the rate of change begins to decrease as time progresses. After 4 h of continuous rainfall, the slope stability factor starts to stabilize.  
Based on the simulation results, the single-step slope with a height of 5 m and a slope ratio of 1:1.5 does not experience failure under these conditions. However, during continuous rainfall, its stability decreases sharply. This can be attributed to the infiltration of rainwater into the soil, which gradually increases the soil's water content and reduces matric suction. Matric suction plays a critical role in maintaining the stability of unsaturated soils. As matric suction decreases, the effective stress within the soil diminishes, leading to a reduction in soil strength and, consequently, a decrease in slope stability.  
Changes in Slope Stability at Different Step Heights with the Same Slope Ratio Under Continuous Rainfall  
To investigate the stability variations of single-step slopes with different heights under the same slope ratio during continuous rainfall, Figure 5 presents the stability calculation  
Figure 4: Ratio 1:1.5 calculation results of stability of slope with a height of 5 m: (**a**) stability calculation results diagram; (**b**) slope 10 h calculation results diagram.  
Figure 3: Model of the slope of the dump.  
contour maps for single-step slopes with a height of 10 m and slope ratios of 1:1.5 and 1:1.75. Figure 6 shows the variation curves of the safety factors over 10 h of continuous rainfall for slope ratios of 1:1.5 and 1:1.75 at different time intervals.  
Based on the simulation results, the single-step slope with a height of 10 m and a slope ratio of 1:1.5 begins to fail after 7 h of rainfall, with slope damage occurring. After 8 h of rainfall, the safety factor approaches its minimum value, reaching only 0.9. However, under the same conditions, when the slope ratio is reduced to 1:1.75, the safety factor reaches its lowest point of 1.11 after 8 h of rainfall, showing a significant improvement compared to the 1:1.5 slope ratio, and the slope remains stable. This indicates that steeper slopes lead to lower slope stability.  
The choice of slope ratio affects the geometric shape of the slope, and the geometry is directly related to the distribution and potential sliding surfaces. For steeper slopes, the self-weight strain per unit area increases, leading to higher shear strain in the soil or rock, which reduces the strength of the slope material. A steeper slope also tends to shorten the natural drainage paths, increasing the likelihood of water retention within the soil or rock, leading to higher pore water pressure, which further reduces shear strength. On the other hand, gentler slope ratios typically enhance slope stability. A gentler slope distributes stresses more evenly, reducing shear forces along the potential sliding surface, and thereby lowering the risk of landslides. Additionally, a gentler slope often improves the natural drainage capacity for rainwater or groundwater, decreasing the accumulation of pore water pressure and helping maintain the strength of the soil.  
Figure 5: Stability calculation results of slope height 10 m.: (**a**) slope ratio 1:1.5, (**b**) slope ratio 1:1.75.  
Figure 6: The 10 h safety factor variation curve over time: (**a**) slope ratio 1:1.5; (**b**) slope ratio 1:1.75.