## 1 Introduction  
Rocks involved in collapses and landslides exhibit characteristics such as high destructiveness, suddenness, scattered distribution, and complex and unpredictable trajectories [1,2]. They represent a primary geological hazard in the mountainous regions of China. In 2022 alone, China witnessed 1366 incidents of rockfall disasters, constituting 24.14% of the total geological disasters in the country and posing a severe threat to the safety of people's lives and property. Figures 1 and 2 illustrate the devastation caused by rockfalls. In the design of protection against rockfall, it is crucial to accurately calculate the characteristics of rockfall movement. The shape of the falling rock is a pivotal factor in determining its rotation and collision behavior, playing a key role in energy consumption and trajectory alterations during the rolling process. Different rockfall shapes result in varying moments of inertia, impacting the rotation behavior of the rockfall upon contact with the slope [3]. These dynamics significantly influence the extent of the hazard and contribute to the design of effective protection measures against rockfall. Data related to the rockfall's position, velocity, rotation, energy, and impact force are utilized to ascertain the influence range and hazard degree of the rockfall. Consequently, this enables the determination of optimized designs for rockfall protection. The current research methods related to the characteristics of rockfall movement mainly include theoretical derivation [4], model experiments [5; 6; 7; 8], numerical simulations [9; 10; 11; 12], and mathematical probability models for data analysis and statistics of historical rock collapse events [13; 14; 15]. Theoretical derivation typically relies on kinematic principles and contact mechanics to derive the trajectory of a falling rock. For instance, [PERSON] [16] formulated equations for calculating motion characteristics such as rockfall velocity and displacement. [PERSON] et al. [17] established a model for the oblique throwing and impact of falling rocks, allowing for the calculation of movement distance and impact force. [PERSON] et al. [18] considered the influence of the rotational inertia of rockfalls, dividing the motion into five stages and providing calculation formulas for each stage. On the basis of considering geometric similarity, physical similarity, and material similarity, indoor model experiments will scale down the actual site in the model device. Through designing indoor experiments, the motion of falling rocks was simulated using test blocks of different shapes, assuming that there were no collisions or fractures during the rolling process. The rolling characteristics of test blocks with different shapes were observed, and the influence of shape on their rolling characteristics was studied. Among these studies, [PERSON] et al. [19] highlighted, based on indoor test results, that rolling resistance is not solely a result of contact behavior during the rolling process, but is also influenced by the shape of rockfalls. Figure 1: Rockfall into a residential building. Figure 2: Rockfall at Guilin Dlecai Mountain. [PERSON] et al. [20] emphasized that the shape effect serves as a significant source of rolling resistance for rockfalls. [PERSON] et al. [21] clarified, based on model test results, that the sphericity of rockfalls is a crucial shape parameter affecting rolling characteristics. [PERSON] et al. [22] pointed out that the rotational speed of a block is a function of its rotational inertia on the cross-section where it moves. [PERSON] et al. [23] discovered through experiments that the rolling distance and velocity of rockfalls are positively correlated with their volume. [PERSON] et al. [24] used the ratio of rock block volume to its minimum circumscribed circle volume as a parameter to describe its shape characteristics, and proposed a rolling speed calculation model including the shape parameter of rockfall based on indoor experimental data.