# Study on the Influence of Rock Shape on Rolling Distance
## 3 Analysis of Experimental Results
### Relationship between Rock Shape and Rolling Distance  
To delve deeper into how rock shape affects rolling distance, scatter plots were generated using experimental results. These plots depict the rolling distances of test blocks with various shapes on different rolling surface materials and at varying speeds, as displayed in the figures below. Upon examination of Figures 9-11, a positive correlation between the rolling distance and the number of edges in the two-dimensional cross-section shape of the test block during rolling is evident. This discovery aligns with the conclusions reached by [PERSON] et al. [47] through the utilization of rockfall software rockfall 5.0. In the case of test blocks rolling on a surface, if the rolling torque generated by kinetic energy is lower than the opposing rolling torque arising from gravity and the resistance attributed to the test block's shape and the characteristics of the rolling surface, the test block ceases to roll. The resisting rolling torque due to gravity relies on the test block's shape, as depicted in Figure 12. Owing to variations in shape, the side length of the cross-section shape of the twelve-edged prism F, oriented perpendicular to the rolling surface, is smaller than that of the four-edged prism D with the same volume. This implies that under identical conditions, test block F demands less force to surmount the rolling resistance than test block D, leading to a greater rolling distance for test block F. Consequently, it can be inferred that the number of edges in the two-dimensional cross-section shape of the test block, perpendicular to the rolling surface, exhibits a negative correlation with rolling resistance. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Rolling Surface** & **Test Block** & **Speed** & \multicolumn{4}{c}{**Test Rolling Distance (m)**} & \multicolumn{1}{c}{**Average**} & \multicolumn{1}{c}{**Standard**} & \multicolumn{1}{c}{**Coefficient of**} \\
**Material** & **Number** & **(m/s)** & **S\({}_{1}\)** & **S\({}_{2}\)** & **S\({}_{3}\)** & **S\({}_{4}\)** & **S\({}_{5}\)** & **S\({}_{6}\)** & **S\({}_{7}\)** \\ \hline \  
Figure 11: Experimental results of test blocks rolling on artificial turf. Figure 10: Experimental results of test blocks rolling on ceramic tile backing. Figure 9: Experimental results of test blocks rolling on wood. The rolling resistance dependent on the test block's shape is quantified by a coefficient known as the delayed rolling factor (\(RF\)). \(RF\) is defined as the ratio of the distance from the rolling stone's center of mass to the ground (\(li\)) to the distance from the instantaneous center to the center of mass and perpendicular to the ground (\(d\)):  
\[RF=\frac{d}{li} \tag{1}\]  
Variations in shape lead to distinct behaviors during rolling. In the case of cubic test block A, where the long and short axes have equal lengths, the rolling resistance when rolling about these axes is identical. Consequently, there is a greater potential for offset and axis transition during rolling. The occurrence of offset or axis transition implies that the test block must overcome a sudden increase in rolling resistance during the transition, as illustrated in Figure 13. This substantially depletes the rolling kinetic energy of test block A, leading to a reduction in its rolling distance and an increase in offset distance. Experimental observations revealed that test blocks with a length-to-width ratio exceeding two rarely undergo axis transition during rolling. For instance, test blocks B and C exhibit slight lateral swaying during rolling, but due to their rotational inertia, they exhibit stability, reducing the likelihood of toppling or altering their rolling axis. At very low rolling speeds, when rotational inertia is insufficient to maintain stability, test blocks may tilt and come to a halt.