## 1 Introduction  
Rockfalls are common geological hazards in mountainous areas that are characterized by rapid, sudden, and highly destructive conditions that often threaten the safety of nearby infrastructure (such as bridges, roads, and railways) and residents [1]. Therefore, it is necessary to evaluate the occurrence probability of rockfall hazards and predict their trajectories when designing protective structures. Research on rockfall movement characteristics has mainly focused on the movement trajectory, kinetic energy (and its evolution), and block stop position [2]. The coefficient-of-restitution (COR), trajectory, velocity, and kinetic energy are key parameters used to characterize rockfall movements, and they are directly considered in the design of protective countermeasures [3, 4]. These parameters can provide a basis for selecting protective structures and their optimal location, size, and strength [5]. Due to the scale, the propagation process of rockfalls is dominated by different physical processes. Fragmental rockfalls are often analyzed as the movement of a single rigid body, which moves under the action of gravity and discontinuously interacts with the substrate [6]. However, the falling of rock mass is usually regarded as a particle flow with a lumped mass to maintain fairly continuous contact with the bedrock for dynamic analysis [7, 8, 9, 10]. The boundary between fragmental rockfalls and rock mass fall is transitional. The propagation process of rockfalls is usually hybrid-analyzed [11]. Therefore, the study of rockfall movement characteristics is particularly important for rockfall risk assessment, prediction, and prevention [6]. Many methods, such as theoretical calculations [6, 12], laboratory experiments [13, 14, 15], field experiments [16, 17, 18] and numerical simulations [8, 19, 20], have been adopted to study the movement characteristics of rockfalls. The jump in the trajectory of the falling rock is only due to the irregular shape of the block and its rotation. In complex rockfall motion simulations, COR is mainly used to describe trajectory rebounds, such as movement COR (\(R_{\rm v}\)), tangential COR (\(R_{\rm t}\)), and normal COR (\(R_{\rm n}\)). These parameters are especially important because they reflect the energy dissipation throughout the impact process and affect the accuracy of rockfall trajectory prediction [3]. However, due to the above reasons, it is still difficult to accurately calculate the trajectory of a rockfall. Therefore, it is necessary to comprehensively study the dynamic rockfall process from the initial instability to movement until stopping. Due to the complex contact transformations among blocks of various shapes and slopes in complex terrain [11], a suitable discontinuous dynamic numerical method is needed to analyze the rockfall movement process. Many discontinuous numerical methods can be adopted to simulate the movement process of rockfalls, such as the three-dimensional discrete element method (3D-DEM) [9; 21], three-dimensional discontinuous deformation analysis (3D-DDA) [11; 19], and numerical-manifold (NMM) [22], general particle dynamics (GPD) [23], peridynamics (PD) [24], and nonsmooth multibody systems dynamics methods [25]. Theoretically, the DEM uses an explicit time integration approach, but DDA and the NMM use implicit time integration. The unnecessary global matrix generation in each calculation step in explicit time integration increases the calculation speed in DEM relative to DDA and NMM, especially when there are numerous blocks [9]. The mechanical behavior of energy dissipation is involved when simulating discontinuous problems such as landslides and rockfalls with DEM. As an approach to alleviate unnecessary vibration caused in a dynamic system, damping is used to characterize the energy dissipation in DEM simulation. Researchers have conducted extensive research on the damping of DEM. [PERSON] et al. proposed that there is less quantitative research on damping in the form of energy dissipation in numerical methods [26].