## 1 Introduction
From this, it can be seen that conducting physical experiments on rock rolling using laboratory equipment is an effective approach to studying the influence of shape factors on their rolling characteristics. [PERSON] et al. [25] investigated the fracture mechanism of rock blocks and emphasized that the degree of fracture is closely linked to the mechanical properties of the rockfall, rather than being significantly associated with the size of the rockfall. Therefore, in the case of rockfalls with poor mechanical properties in karst areas [26; 27], calculations should consider the potential occurrence of fractures during the rolling process. Numerical simulation can be categorized into rockfall software simulation and code for developing rockfall simulation. [PERSON] et al. [28] proposed a rock collapse trajectory analysis model based on the framework of multi-body dynamics and non-smooth contact dynamics, capable of simulating rock collapse and rockfall events involving rock blocks of various shapes on different characteristic slopes in full 3D. The trajectory analysis model suggested by [PERSON] et al. [29] can simulate rockfalls with different sphericity and convexity. [PERSON] et al. [30] calibrated existing 2D rock collapse prediction models, achieving accurate predictions of the farthest impact range of rockfall. [PERSON] et al. [31] imported a three-dimensional geological model into simulation software (RAMMS) to obtain the motion trajectory of rockfalls. [PERSON] et al. [32] utilized the energy tracking method (ETM) to study the impact of rock fragmentation on its motion trajectory, pointing out that the fragmentation process is accompanied by energy loss, resulting in a decrease in rolling speed. In summary, the shape and size of a rockfall are key factors influencing its rolling speed and determining its moment of inertia. These factors, in turn, affect its rotation behavior in the air and upon contact with the ground. The rolling resistance of a rockfall arises from mutual contact with the slope during the rolling process, and the nature of this contact varies with different shapes of rockfalls and the slope. Therefore, different shapes of falling rocks exhibit significant differences in overcoming rolling resistance during the rolling process. The rolling motion of falling rocks is one of their movement characteristics on the slope, primarily controlled by the slope gradient--rolling dominates on steeper slopes, while sliding dominates on gentler slopes [33]. Through investigation and analysis of the slope gradient in historical rock collapse events, it was found that the slopes in areas prone to rockfall disasters are mainly concentrated above 45\({}^{\circ}\)[34]. It can be seen that it is necessary to study and quantify the relationship between rockfall shape and rolling resistance, to explore the rolling characteristics of falling rocks on slopes, to supplement the quantitative parameters of the influence of rockfall shape on rolling velocity, on the basis of the existing calculation formula. It is difficult to establish an ideal calculation model with a single research method when considering the influence of the shape of a falling rock on its rolling speed. Therefore, in the follow-up research, model test research and theoretical analysis can be combined to obtain the movement of different shapes of fallen rocks on the slope. Finally, according to the test results, the influence mechanism of rockfall shape on its rolling characteristics is analyzed and, on this basis, the influence of other factors is combined to establish a calculation model. Currently, there are two commonly used methods for establishing models of the motion speed of rolling rocks: the concentrated mass method and the rigid body method. The concentrated mass method concentrates the mass of a continuously distributed object to a single point, assuming the object only has mass without stiffness parameters. Thissimplifies the analysis of the object's motion and is suitable for cases with simple shapes and uniformly distributed mass [35].