## 3 Results
### The Interactive Effects of Main Controlling Factors on \(R_{\rm n}\)  
#### 3.4.1 The Interaction of Falling Rock Shape and Slope Surface Material  
Figure 12 shows \(R_{\rm n}\) decreases with \(\eta\) and \(A_{\rm slope}\) increase. This decrease is 61.96%, which is lower than the combined independent effect of the two factors (74.83%). The interaction between falling rock shape and slope surface material is significantly weakened.  
The effect of falling rock shape on \(R_{\rm n}\) varies with \(A_{\rm slope}\). For low-level \(A_{\rm slope}\), high bounces occur, resulting in a 62.96% decrease in \(R_{\rm n}\) (from blue to red) as \(\eta\) decreases. However, with high-level \(A_{\rm slope}\), low bounces occur, leading to a 25.89% 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 that of low-level \(A_{\rm slope}\). Low-level \(A_{\rm slope}\) exhibits high deformation recovery, effectively restoring deformation energy dissipation and converting more kinetic energy into rebound kinetic energy. Combined with low-level \(\eta\), energy dissipation is reduced, resulting in higher \(R_{\rm n}\). With high-level \(\eta\), the increased contact area leads to higher friction energy dissipation, causing a significant decrease in \(R_{\rm n}\). However, the weak deformation recovery of high-level \(A_{\rm slope}\) results in greater plastic deformation energy dissipation and lower \(R_{\rm n}\). Consequently, the influence of falling rock shape on \(R_{\rm n}\) diminishes.  
Additionally, the correlation between slope surface material and \(R_{\rm n}\) varies with \(\eta\). For low-level \(\eta\), fewer contact areas cause a 48.67% reduction in \(R_{\rm n}\) (from blue to orange) as \(A_{\rm slope}\) changes. In contrast, for high-level \(\eta\), more contact areas leads to only a 2.69% reduction in \(R_{\rm n}\) (red remains constant), making the effect of slope surface material on \(R_{\rm n}\) negligible. Low-level \(\eta\) has concentrated impact force and small contact area, and the ratio of friction energy dissipation is small. The material deformation recovery is weakened as \(A_{\rm slope}\) rises, resulting in energy dissipation increases and \(R_{\rm n}\) decreases. In contrast, high-level \(\eta\) has dispersed impact force and a large contact area, and the ratio of friction energy  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Explanatory Variables** & **Estimating Coefficients** & **Standard Error** & \(t\)**Values** & \(p\)**Values** (Pr \textgreater{consumption is large. Falling rock shape dominates the energy dissipation, diminishing the influence of slope surface material on \(R_{\rm n}\). Therefore, the change in \(A_{\rm slope}\) under high-level \(\eta\) has less effect on \(R_{\rm n}\).  
In summary, high-level \(\eta\) significantly reduces the effect of slope surface material on \(R_{\rm n}\). However, high-level \(A_{\rm slope}\) also diminishes the effect of falling rock shape on the coefficient. The interaction suggests that the effect of falling rock shape on \(R_{\rm n}\) (\(-48.67\%\)-\(2.69\%\)) is more pronounced than that of slope surface material (\(-62.96\%\)--\(-25.89\%\)). When interacting with high-level \(\eta\), the slope surface material has a little significant effect on \(R_{\rm n}\).