## 4 Discussion  
Analysis of the experimental test results shows that falling rock shape is a main controlling factor affecting \(R_{\text{n}}\). Low-level \(\eta\) experiences minimal local deformation due to  
Figure 18: The recording of falling rock movement process in field experiments.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Estimation Methods**} & \multicolumn{3}{c}{**Falling Rock Shape**} & \multicolumn{3}{c}{**The Error Compared with the Experiment/\%**} \\ \cline{2-5}  & **Sphere** & **Prism** & \\ \hline on-site experiment & 0.459 & 0.413 & 0 & 0 \\ multi-factor interaction model & 0.474 & 0.399 & 3.27 & 3.39 \\ non-interaction model & 0.574 & 0.474 & 25.05 & 14.77 \\ [PERSON] [13] & 0.275 & / & 40.09 & / \\ [PERSON] [22] & / & 0.116 & / & 71.91 \\ [PERSON] [23] & 0.387 & / & 15.68 & / \\ \hline \hline \end{tabular}
\end{table}
Table 5: The estimation and comparison.  
the small contact areas and concentrated impact force. As \(A_{\text{slope}}\), \(v\), and \(\theta\) increase, energy dissipation increases, leading to a decrease in \(R_{\text{n}}\). High-level \(\eta\) involves large contact areas and significant local deformation energy dissipation. The energy dissipation is primarily controlled by falling rock shape. The influence of slope surface material and initial velocity on \(R_{\text{n}}\) weakens. As \(\theta\) increases, the normal velocity component increases, raising the ratio of local deformation energy dissipation. However, energy dissipation decreases, and \(R_{\text{n}}\) increases due to the shorter movement distance. As \(\eta\) increases, frictional and plastic deformation energy dissipation rises, weakening the effects of slope surface material, initial velocity, and slope angle on \(R_{\text{n}}\). This suggests that falling rock shape dominates the changes in \(R_{\text{n}}\) as \(\eta\) increases.  
The effect of falling rock shape on \(R_{\text{n}}\) is influenced by its regulation of contact patterns and post-collision dynamic behavior: (1) Difference in contact pattern: Regular shape (sphere) primarily exhibits point-face contact, where normal energy is concentrated and dissipated in a controllably, promoting high \(R_{\text{n}}\). Irregular shapes (cube, prism, and triangular block) lead to increased normal energy dissipation due to mixed line/face-face contacts, inducing tangential movements (sliding or rolling) that significantly reduce \(R_{\text{n}}\). The discrepancies weaken the \(R_{\text{n}}\) sensitivity to other main controlling factors by altering the contact stress distribution. (2) Nonlinear dynamic behavior: Regular falling rock movement is dominated by bouncing, and its energy dissipation is approximately linear with respect to the initial conditions. Irregular rockfall triggers uneven energy dissipation and random trajectories due to complex movements such as sliding and rolling. This nonlinear behavior amplifies the shape effect in multi-factor interaction.  
In falling rock disaster prevention and control engineering, falling rock shape plays a critical role in determining the contact areas between the rockfall and the slope surface. Based on geological feature analysis and potential kinetic risk coefficient assessment, active energy dissipation and intervention strategies, such as on-site fragmentation or migration, should be considered. The adoption of flexible protection network-slope shape synergistic control technology could alleviate the local stress concentration and energy concentration effects induced by irregular falling rocks.