## 1 Introduction  
Rockfalls, along with other large-scale mass movements such as landslides and debris flows, represent significant geohazards that pose considerable risks to infrastructure, transportation networks, and human safety in mountainous regions [1,2]. The movements refer to events involving extensive area coverage and high volume of displaced material, typically affecting multiple structures or large sections of land. These types of hazards are often characterized by their high energy release and rapid movement, making their accurate prediction critical for disaster management. Effective risk management for these hazards requires accurate prediction models that can simulate rockfall behavior, and \(R_{\text{n}}\) plays a key role in such models. \(R_{\text{n}}\) is a key parameter in rockfall dynamics, which quantifies the amount of kinetic energy retained after collision between falling rock and slope surface [3, 4, 5]. Specifically, \(R_{\text{n}}\) is defined as the ratio of the relative velocity along the normal direction before and after impact. \(R_{\text{n}}\) reflects how elastic or inelastic the collision is, and it plays an essential role in modeling the rebound and trajectory prediction of the falling rock after collision. While \(R_{\text{n}}\) is influenced by various factors, its accurate estimation is crucial for improving hazard risk assessments related to rockfall events. In this study, the term \"rockfall\" is used in two distinct contexts: (1) \"rockfall\" refers to \"falling rock\" itself, which is the object of study in terms of its movement and behavior during impact; (2) \"rockfall\" can also refer to the event or the area affected by the rockfall, including the slope surface over which the rock moves or the region where the collision takes place. In these contexts, we use terms like \"rockfall\" or \"slope surface\" to distinguish the process from the rock block itself. \(R_{\text{n}}\) is widely applied in the framework of the lumped mass method for simulating block dynamics, but its accurate estimation remains challenging [6,7]. \(R_{\text{n}}\) is influenced by several factors, each of which affects the energy dissipation and rebound behavior during rockfall collisions. These factors include (1) slope angle: the angle of the slope influences the impact velocity and the directional forces acting on the falling rock, affecting its kinetic energy retention; (2) slope surface material: different slope surface materials (e.g., concrete and turf) have varying frictional properties and energy absorption capacities, influencing how much energy is dissipated during collision; (3) falling rock shape: the geometry and roughness of the rock affect its contact area with the surface, which influences the energy dissipation and how the rock rebounds; and (4) initial velocity: the speed at which the rock is released influences the impact force and the subsequent energy dissipation. High initial velocities generally result in more inelastic collisions, leading to greater energy loss. The interactions among these factors complicate the estimation of \(R_{\text{n}}\), making it difficult to predict precisely. The rockfall collision mechanisms refer to the physical processes and energy exchange that occur when falling rock collides with the slope surface. These mechanisms involve elastic and inelastic interactions, where the rock's kinetic energy is partially conserved (elastic) or dissipated (inelastic) through friction, deformation, and compression. In the context of this study, the term also encompasses the contact dynamics between the rockfall and slope surface material, which are influenced by factors such as surface roughness, material hardness, and the angle of impact. These mechanisms are essential for understanding how the rock will rebound after collision, which in turn helps predict the rock's post-impact trajectory and kinetic behavior.