## 3 Results and Analysis
### Sediment Production Process  
As shown in Figure 3, an evident rise in the sediment yield rate occurs with an increase in the rainfall intensity for the same slope gradient. For instance, at a slope gradient of 40\({}^{\circ}\), the peak sediment yield rates attained at rainfall intensities of 50, 80, and 110 mm/h are 0.81, 1.47, and 3.07 g/s, respectively, with corresponding average sediment yield rates of 0.24, 0.81, and 2.25 g/s, respectively. When the rainfall intensity elevates from 50 to 80 mm/h, the peak sediment yield rate experiences an 81% surge, and the average sediment yield rate increases by 235%. Similarly, when the rainfall intensity grows from 80 to 110 mm/h, the peak sediment yield rate undergoes a 107% rise, and the average sediment yield rate increases by 178%.  
Under uniform rainfall intensity, a minor elevation in the slope gradient leads to a slight rise in the sediment yield rate. The most significant increment in peak sediment yield rate with increasing slope is detected under the rainfall intensity of 110 mm/h, with a substantial surge observed as the slope gradient escalates from 30\({}^{\circ}\) to 40\({}^{\circ}\). Conversely, the most trivial rise in peak sediment yield rate occurs at the rainfall intensity of 80 mm/h, with only a modest increase detected as the slope gradient increases from 10\({}^{\circ}\) to 20\({}^{\circ}\). The maximal increment in the average sediment yield rate transpires when the rainfall intensity is 110 mm/h, with a notable rise observed as the slope gradient increases. When the slope gradient increases from 30\({}^{\circ}\) to 40\({}^{\circ}\), the average sediment yield rate undergoes a substantial escalation of 269%. In contrast, the most minor augmentation in average sediment yield rate is recorded when the rainfall intensity is 80 mm/h; with only a modest increment of 8% detected as the slope gradient elevates from 10\({}^{\circ}\) to 20\({}^{\circ}\). For insignificant slope gradients and rainfall intensities, the effect of slope gradient on sediment yield rate is not apparent. However, as the slope gradient and rainfall intensity increase, the sediment yield rate also rises, with the slightest growth rate observed under the slope gradient of 20\({}^{\circ}\) and the rainfall intensity of 80 mm/h. Based on these observations, it can be speculated that a critical point exists at or near these conditions.  
Elevating either the rainfall intensity or slope gradient induces an augmentation in sediment yield to a certain extent. Raising the slope gradient diminishes the stability of the slope. Meanwhile, alterations in rainfall intensity modify the intensity and erosive force of slope flow, with augmented runoff leading to heightened sediment yield. The simultaneous effect of increased slope and rainfall intensity accelerates the slope erosion process, giving rise to rills and depressions on the slope surface and collapses in areas with the most severe erosion. Augmentations in both rainfall intensity and slope gradient also abbreviate the time taken to reach the peak sediment yield.  
Under the same slope gradient, the sediment yield rate initially rises with the intensifying rainfall intensity, subsequently declines, and ultimately stabilizes. This occurs because as the slope surface experiences erosion, forming rills, the quantity of sediment transported escalates. When the slope morphology is disrupted, a sudden collapse triggers a massive volume of sediment to be carried away by the slope flow, reaching the peak sediment yield rate. Following the initial significant damage, the slope morphology rapidly achieves stability; during this phase, the slope flow is inadequate to inflict secondary damage on the slope, causing the sediment yield rate to diminish and stabilize.