## 3 Results
### The Interactive Effects of Main Controlling Factors on \(R_{\rm n}\)
#### 3.4.4 The Interaction of Slope Surface Material and Initial Velocity  
Figure 15 shows \(R_{\rm n}\) decreases with \(A_{\rm slope}\) and \(v\) increase. This decrease is 62.74%, which is lower than the combined independent effect of the two factors (64.87%). The  
Figure 14: The interactive effects of falling rock shape and slope angle on \(R_{\rm n}\): (a) Three-dimensional surface plot showing the variation in \(R_{\rm n}\) with different \(\eta\) and \(\theta\). The color scale indicates the corresponding \(R_{\rm n}\), with blue representing high \(R_{\rm n}\) and red representing low \(R_{\rm n}\). The plot highlights the positive interaction effect on \(R_{\rm n}\), with higher \(R_{\rm n}\) observed for more spherical falling rocks and smaller slope angles; (b) Contour plot illustrating the same data in two dimensions, providing a clearer view of the interaction. The contour lines represent different \(R_{\rm n}\) values, and the feature points on the plot indicate combinations of \(\eta\) and \(\theta\) that correspond to notable changes in \(R_{\rm n}\). interaction between slope surface material and initial velocity was slightly weaker than the independent superimposed effects. The effect of initial velocity on \(R_{\rm n}\) significantly depends on \(A_{\rm slope}\). For low-level \(A_{\rm slope}\), high bounces occur, causing a 58.56% reduction in \(R_{\rm n}\) (from blue to red) as \(v\) decreases. However, high-level \(A_{\rm slope}\) results in low bounces, leading to a 27.14% reduction in \(R_{\rm n}\) (from orange to red). In this case, the effect of slope surface material on \(R_{\rm n}\) is less than half of that observed for low-level \(A_{\rm slope}\). Low-level \(A_{\rm slope}\) exhibits strong deformation recovery, reducing the collision kinetic energy dissipation. Therefore, \(R_{\rm n}\) is higher at low-level \(v\). However, as \(v\) rises, the impact energy dissipation increases, resulting in a significant decrease in \(R_{\rm n}\). High-level \(A_{\rm slope}\) has weak deformation recovery, leading to higher collision kinetic energy dissipation and lower \(R_{\rm n}\). With \(v\) increases, more collision kinetic energy is converted into plastic deformation energy dissipation, reducing the effect of the initial velocity on \(R_{\rm n}\). Similarly, the correlation between slope surface material and \(R_{\rm n}\) changes significantly with \(v\). At low-level \(v\), weak collisions occur, leading to a 48.86% decrease in \(R_{\rm n}\) (from blue to orange) as \(A_{\rm slope}\) increases. In contrast, at high-level \(v\), heavy collisions occur, causing only a small 10.09% reduction in \(R_{\rm n}\) (red remains constant). In this case, the effect of initial velocity on \(R_{\rm n}\) is negligible. Under low-level \(v\), the collision kinetic energy is small, and the slope surface material determines the energy dissipation. The deformation recovery of low-level \(A_{\rm slope}\) reduces the energy dissipation, resulting in high \(R_{\rm n}\). The deformation recovery of high-level \(A_{\rm slope}\) is weakened, and the increase in plastic deformation energy dissipation leads to a decrease in \(R_{\rm n}\). Under high-level \(v\), the collision kinetic energy increases, and the ratio of unrecoverable energy dissipation, such as impact and friction energy, rises. Initial velocity dominates the energy dissipation, reducing the influence of slope surface material on \(R_{\rm n}\). Given the above, high-level \(v\) significantly reduces the effect of slope surface material on \(R_{\rm n}\). Conversely, high-level \(A_{\rm slope}\) also diminishes the effect of initial velocity on \(R_{\rm n}\). The interaction suggests that the effect of initial velocity on \(R_{\rm n}\) (\(-\)48.86%\(\sim\)\(-\)10.09%) is more pronounced than that of slope surface material (\(-\)58.56%\(\sim\)\(-\)27.14%).