# Study on the Influence of Rock Shape on Rolling Distance
## 1 Introduction  
China is a mountainous country with mountainous regions covering 1/3 of the country's total land area. These mountainous areas are particularly prone to geological hazards, with rockfall disasters being a prominent concern. In 2022 alone, China experienced 1366 cases of landslide disasters, representing 24.14% of the total geological disasters in the nation. These events pose a substantial threat to the safety of lives and property, as depicted in Figures 1 and 2. Rockfall is the process and phenomenon in which rock masses of various sizes detach from their source areas and accumulate at the base of slopes through falling, bouncing, rolling, sliding, and other movements [1]. For areas within mountainous regions, including residential areas, transportation routes, pipelines, bridges, and more, a crucial component of rockfall hazard assessment involves delineating hazardous zones beneath rock walls. Determining the distance traveled by rockfall is essential for evaluating these hazard zones [2]. In the investigation and study of diverse rockfall-prone areas, it is evident that factors impacting the rolling distance of rockfall encompass many characteristics: terrain conditions, such as slope angle, release height, slope surface roughness, and vegetation coverage [3; 4; 5; 6; 7]; the geomechanical properties of the slope, including particle size, void ratio, moisture, and hardness [8; 9]; the three-dimensional nature of slopes, including lateral, vertical, valley, and channel dimensions [10]; and the roughness of the slope surface, including the size and shape of the surface coverings [11; 12]. Moreover, the properties of the rockfall itself, including its size, shape, and lithology, are intimately linked to the rollingdistance [13; 14; 15]. Notably, the size and shape of the rockfall, along with their interaction with the slope surface during rolling, are recognized as pivotal factors influencing the rolling distance [8; 16; 17]. By quantifying these influential factors and incorporating them into calculation models, we can predict the rolling distance of rockfall [18; 19; 20]. distance. Within a kinematic framework, [PERSON] et al. [2] introduced a mathematical model for rolling distance, considering the influence of self-rotation of rockfall. Currently, research on the impact of rockfall characteristics, including shape, size, and slope surface hardness, on rolling distance is relatively scarce [26; 27; 28; 29]. Primary research methods encompass model experiments [30; 31], case analysis [24], and numerical simulations [32; 33; 34]. In this context, [PERSON] et al. [30] discovered that rockfall's own shape notably influences rolling distance, with near-spherical and gently inclined rockfall covering greater distances. They also proposed that the trajectory of rockfall can be predicted based on its shape and size. [PERSON] et al. [35] introduced a method for generating intricate geometric shapes through 3D reconstruction, which was utilized to investigate the impact of rock block shape and size on motion and energy conversion. [PERSON] et al. [36] employed orthogonal experimental methods to assess the sensitivity of factors influencing the horizontal movement distance of rockfall. They developed a predictive system for rockfall movement that incorporates factors like slope height, slope angle, and mass. [PERSON] et al. [37], by analyzing field test data, quantified the influence of rockfall shape and mass on lateral spreading and longitudinal displacement. They highlighted that rockfall shape significantly affects its motion characteristics. Additionally, [PERSON] et al. [38] observed that spherical rockfall, in comparison to irregularly shaped rockfall, exhibits a longer rolling distance. [PERSON] et al. [39] highlighted that energy loss during the rolling process of rolling bodies primarily results from rolling frictional resistance, and the magnitude of this resistance relies on the shape, material, and surface characteristics of the rolling body.