# Experimental Study on Rockfall Mechanism of Platy Rock on a Complex Slope
## 3 Experimental Results and Analysis
### The Analysis of Restitution Coefficient  
The coefficient of restitution can express in terms of velocities or energies, indicating the amount of velocity or energy dissipated during the ground collision [2,17,19,22,32]:  
\[R_{n}=\frac{|v_{m}|}{|v_{bm}|},\ R_{t}=\frac{|v_{rt}|}{|v_{bt}|}\,\ R=\frac{E_{r}}{E_{ b}}=\frac{m(v_{m}^{2}+v_{rt}^{2})+I(\omega_{r})^{2}}{m(v_{bn}^{2}+v_{bt}^{2})+I( \omega_{b})^{2}} \tag{1}\]  
where \(v\) and \(\omega\) are the translational and rotational velocity respectively, \(m\) is the mass and \(I\) is the moment of inertia about the center of the platy rock. The subscripts \"\(r\)\" and \"\(b\)\" characterize the velocity or energy before and after the collision, respectively. Considering that the movement process of the platy rock during the collision is more complex and the duration is very short, it is difficult to accurately capture the immediate velocity before and after the collision, and the error is very large. Therefore, to facilitate the analysis, the author defines the coefficient of restitution as the ratio of the average velocity of the rebound stage after the collision to the average velocity of the compression stage before the collision, that is:  
\[\overline{R}=\frac{\overline{E_{r}}}{\overline{E_{b}}},\ \overline{R_{n}}=\frac{ \overline{v_{m}}}{\overline{v_{bm}}},\ \overline{R_{t}}=\frac{\overline{v_{rt}}}{\overline{v_{bt}}} \tag{2}\]  
In the above formula, \(R,R_{n},R_{t}\) are the restitution coefficients, the normal coefficient of restitution and the tangent coefficient of restitution, respectively. \(\overline{E_{r}},\overline{v_{m}},\overline{v_{rt}}\) are the average energy dissipated, the normal average velocity and the tangent average velocity of the platy rock after the collision, respectively. \(\overline{E_{b}},\overline{v_{bm}},\overline{v_{bt}}\) are the average energy dissipated, the normal average velocity and the tangent average velocity before the collision, respectively. Among the 303 collisions, there were 86 times for \(R>1\). Of these, there were 14 times for \(R_{n}>1\) and 72 times for \(R_{t}>1\). This article has carried on thorough research on the 86 times for \(R>1\) and related causes were investigated. The experiment found that the motion type of platy rock before and after the collision was a combination of one or more motion types in Figure 10. These collisions have mainly occurred in the area of DE (slope angle \(i=30^{\circ}\)) and EF (slope angle \(i=0^{\circ}\)) with slow slope (as shown in Figure 9d). Figure 11 shows that under the condition of the same slope, the movement type of platy rock before and after the collision was an important reason for the occurrence of \(R_{n}>1\). In the fourteen times of collisions with \(R_{n}>1\), there were six types of motion before and after collision respectively and all of them include flip motion. There were two times of collisions in the EF area (\(i=0^{\circ}\)) and twelve times of collisions in the DE area (\(i=30^{\circ}\)). In the EF area, the movement types have changed before and after the collision. The average value \(R_{n}\) was different for different movement types. The same characteristics have also held in the DE area. Figure 12 shows that under the condition of same slope, the movement type of platy rock before and after the collision is also an important reason for the occurrence of \(R_{t}>1\). In the 72 times of collisions with \(R_{t}>1\), there were 41 times of collisions in the EF area (\(i=0^{\circ}\)) and 31 times of collisions  
Figure 11: Movement type of platy rock and normal restitution coefficient. Figure 10: The basic type of motion of the platy rock. in the DE area (\(i=30^{\circ}\)). In the EF area, there were thirteen types of motion before the collision and nine types of them include flip motion. The proportion was 69.2%. The average value \(R_{t}\) was different in various movement types. However, there were 12 types of motion after the collision and all of them include flip motion. The average value \(R_{t}\) was also different in various movement types.