## 3 Results  
Based on numerical simulations of six hazardous rock masses (WY1-WY6; see Figure 8) and spatial profiles of kinetic energy, velocity, and bounce height for WY3 and WY6 (see Figure 9), the rockfall process exhibits a three-stage dynamic evolution: (1) an initial free-fall stage, characterized by gravity-driven acceleration and energy accumulation; (2) a transport-rebound stage, involving high-elasticity impacts between blocks and slope surfaces, where sliding, bouncing, and rolling are coupled, and kinetic and potential energy alternate cyclically, resulting in localized energy peaks; and (3) a deceleration-deposition stage, in which friction and contact damping gradually dissipate energy as the block enters a gentler slope zone, transitioning from bouncing and rolling to slow sliding until its velocity falls below a critical threshold and it comes to rest. To assess the potential threat of rockfalls to residents near the slope toe of the Lujiawan resettlement area, six rockfall sources were classified into risk levels based on the energy classes of flexible barriers defined in EAD 340059-00-0106 [30] (Class A: \(\leq\) 500 kJ/ \(\leq\) 10 m/s; Class B: \(\leq\) 1000 kJ/ \(\leq\) 20 m/s; Class C: \(\leq\) 2000 kJ/ \(\leq\) 30 m/s; Class D: \(\geq\) 2000 kJ/ \(\geq\) 30 m/s). A Monte Carlo uncertainty analysis was performed, incorporating \(\pm\)10% variation in kinetic energy and \(\pm\)15% in bounce height. Additionally, a sensitivity analysis was conducted to evaluate the impact of a 20% increase in moisture content, which could raise kinetic energy by 5-10% and extend flight distance by 3-8%. Based on these analyses, the following mitigation strategies are proposed:  
WY1 (3 \(\times\) 10\({}^{5}\) kJ, 8 m/s, 6 m) is located at the boundary between Class A and Class B. Its energy dissipates rapidly upon entering the gentler slope section, showing no significant potential for further travel. A low- to medium-energy flexible barrier (Class A/B, Level1-2) is recommended at the slope toe-to-downstream transition zone, supplemented with surface drainage measures to intercept blocks early and dissipate residual energy on site. WY2 (2.3 \(\times\) 10\({}^{6}\) kJ, 41.7 m/s, 25 m) exceeds the upper threshold of Class C and presents the highest risk among all sources. Elevated moisture content may further increase its kinetic energy and extend its travel distance. High-energy flexible barriers (Class D/E, Level \(\geq\)3-4) are recommended at the slope outlet and within 200 m downstream, supplemented with energy-dissipating trenches or retaining structures. A sufficient buffer zone should be reserved to absorb peak energy and mitigate high-velocity impacts. WY2 should be prioritized in hazard mitigation planning. WY3 (1.55 \(\times\) 10\({}^{6}\) kJ, 34.8 m/s, 18 m) is also classified as high risk (Class C). Although its energy attenuates before reaching the slope toe, the block retains sufficient momentum to potentially overtop the barrier. As with WY2, high-energy barriers (Level \(\geq\) 3) should be installed at the slope outlet and critical toe locations, supplemented by toe reinforcement and surface drainage. WY3 is recommended as the second-highest priority for mitigation. WY4 (8 \(\times\) 10\({}^{4}\) kJ, 5 m/s, 3 m) exhibits the highest stability, with both kinetic energy and velocity well within Class A thresholds and no risk of airborne movement. A low-profile Class A barrier (Level 1)--such as a short flexible net or stone bund--is sufficient, particularly when combined with existing drainage or retaining structures. High-energy protection is not required. Figure 8: Rockfall trajectory diagrams for all 600 simulated trajectories (100 per zone) aggregated across WY1–WY6: (**a**) WY1–WY6 Rockfall Kinetic Energy Trajectory; (**b**) WY1–WY6 Rockfall Velocity Trajectory; (**c**) WY1–WY6 Rockfall Bounce Height Trajectory. WY5 (8.9 \(\times\) 10\({}^{5}\) kJ, 22 m/s, 12 m) falls between Class B and Class C and is considered a moderate-risk source.