Hazard Assessment of Unstable Rock Mass Collapse in Hydropower Station Areas Based on Spatial Motion Characteristics

Hazard Assessment of Unstable Rock Mass Collapse in Hydropower Station Areas Based on Spatial Motion Characteristics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Hazard Assessment of Unstable Rock Mass Collapse in Hydropower Station Areas Based on Spatial Motion Characteristics Hong YANG, Luyuan Jiao, Zinan Zou, Chen Zhao, Mowen Xie, Xin LI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7822779/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Pumped-storage power stations are typically built in steep, mountainous terrain, where rock-slope collapse threatens critical infrastructure including powerhouses and dams. Conventional assessments seldom consider the full 3-D kinematics of unstable rock masses. To fill this gap, we present a spatial-motion-based method for evaluating slope-collapse hazard at hydropower sites. Using the planned lower reservoir area of a pumped-storage station in southwestern China as a case study, unmanned-aerial-vehicle photogrammetry was employed to obtain the spatial distribution, geometric features, and topographic attributes of unstable rock masses. These data were used to generate a high-resolution DTM and an orthophoto mosaic.RocPro3D simulated the 3-D trajectories of falling rocks. A comprehensive evaluation model integrating four indicators—rock-mass stability, rockfall kinetic energy, bounce height, and trajectory density—was established to classify hazard levels and propose corresponding protection measures. This assessment framework enables spatially quantitative characterization of hazard parameters and provides a scientific basis for slope-collapse mitigation design in hydropower engineering. Hydropower slope Rockfall hazards Rockfall motion simulation Hazard assessment Passive protection Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 0 Introduction Rockfalls on slopes represent a common engineering geological hazard, marked by frequent occurrence, limited visibility, and sudden onset. As China’s energy infrastructure expands rapidly into southwestern mountainous regions, unstable rock masses on slopes near hydropower projects pose serious threats to infrastructure and resource development safety [ 1 ] . A rockfall occurs when unstable rock detaches from its parent formation and, under gravity, undergoes free-fall, rolling, and sliding along exposed slopes. This process releases substantial kinetic energy, endangering people, vehicles, infrastructure, and hydraulic facilities along its path [ 2 ] . Rockfall hazard assessment in areas with concentrated unstable rock masses is essential for disaster early warning and engineering protection. Rockfall hazard assessment quantifies both the likelihood of instability and the potential severity of damage within unstable rock masses [ 3 ] . Early hazard assessments mainly considered topography and geological features, often neglecting interactions between unstable rock masses and slopes. This approach lacked accuracy in evaluating rockfall risks under complex topography and variable geological conditions. Subsequently, researchers placed greater emphasis on rockfall kinematic characteristics, including motion mechanisms, hazard extent, and intensity. For example, Lan et al. [ 4 ] combined LiDAR and GIS for spatial modelling to assess rockfall hazards along a Canadian railway. Tang Hongmei et al. [ 5 – 8 ] applied grey system theory, fuzzy mathematics, the Analytic Hierarchy Process, and GIS to build a multi-factor evaluation model. Wu Zhongpeng et al. [ 9 ] used the Monte Carlo method in Matlab to estimate the probability of instability at Fanjiayan, Weining County, Guizhou Province, under various conditions, thereby evaluating local rockfall hazards. These approaches incorporated rockfall motion and accumulation characteristics, thereby improving the scientific rigour of hazard analysis. With advances in numerical analysis, rockfall simulations now enable visualisation of movement and calculation of key parameters during motion. Two-dimensional tools such as Rockfall are widely used in engineering to quickly obtain parameters such as rebound height, contact energy, and velocity distribution within predefined profiles [ 10 ] . However, these methods treat rockfall–slope interactions as planar problems. Due to the spatial limitations of predefined profiles, they introduce subjective biases in path simulation. Recently, advances in unmanned aerial vehicle (UAV) technology and geographic information systems (GIS) have highlighted the advantages of UAV photogrammetry for investigating geological hazards on steep slopes. Its wide field of view, high precision, and absence of spatial constraints allow acquisition of high-resolution digital terrain models, enabling prediction of three-dimensional movement domains and collision characteristics of unstable rock masses [ 11 ] . Researchers such as Dupire et al. [ 12 ] , and Li You [ 13 ] used Rockfall Analyst to reproduce the kinematic characteristics of unstable rock masses in the Alpine foothills, collapsed blocks near railway tunnels in southwestern China, and the landslide at Sanguanmiao Village in the Wenchuan earthquake zone. Compared with two-dimensional simulations, three-dimensional numerical models better capture how terrain heterogeneity influences rockfall collision parameters, enabling more accurate prediction of hazardous processes and impact zones. The Rockfall Analyst software employed by the aforementioned scholars is a rockfall motion simulation tool developed on the ArcGIS platform. While it offers 3D visualization capabilities, its simulation parameters—such as rock release intervals and azimuth spacing—require manual presetting and lack dynamic adjustment mechanisms. This makes it difficult to accurately reflect the randomness of rockfall trajectories across complex terrain and topography. RocPro3D, grounded in rigid-body dynamics theory, accounts for the dynamic interactions between unstable rock masses and slopes during motion. This includes physical processes such as collision, friction, ricochet, and energy dissipation. Compared to traditional two-dimensional simplified models, RocPro3D's three-dimensional numerical model effectively captures the localized regulatory effects of terrain spatial heterogeneity on rock block motion parameters (such as reflection angles, velocity attenuation, and rebound height). This enables more realistic reproduction of the motion trajectories, energy evolution, and final deposition distribution during rockfall disaster processes, significantly enhancing the accuracy and reliability of predicting disaster impact areas. At present, detailed investigation of unstable rock sources on steep slopes and hazard analysis for hydraulic structures remain challenging. This study integrates three-dimensional kinematic characteristics of unstable rock masses into hazard assessment. Focusing on hydropower project areas in Southwest China, it applies UAV photogrammetry to investigate slope hazards, builds high-precision three-dimensional models, and simulates the spatial movement of unstable rock collapses. By integrating parameters such as kinetic energy, rebound height, and trajectory of unstable rock masses, a multi-factor evaluation model is developed. The model uses GIS techniques to assess collapse hazards and evaluate mitigation measures, providing a scientific basis for early warning and engineering management of slope hazards. 1 Development Characteristics of Rockfall Hazards 1.1 Overview of the Project Area Lower reservoirs of pumped-storage power stations, which require large-scale water storage, are typically created by damming mountainous terrain. The lower reservoir site of a pumped-storage power station in the Jinsha River Basin, China, is characterised by steep terrain on both banks, with a maximum relative elevation difference of 710 m. The lower to middle slope sections generally have gradients of 30–40°, while the upper sections are steeper, forming multiple tiers of cliffs. The lithology mainly consists of sedimentary rocks, Quaternary colluvial deposits, and Jurassic strata. These units are widely distributed within multi-cyclic fluvial–lacustrine deposits, showing distinct mud–sand interbedding, as illustrated in Fig. 1 . Unstable rock masses develop along sandstone escarpments, forming banded clusters approximately 20–30 m thick, with small- to medium-sized rock bodies. The surface rock mass on ridges and escarpments is fractured, often unloaded and relaxed, readily forming concentrated unstable rock zones. The dominant joint system includes two sets of orthogonal conjugate joints and one set of gently dipping joints parallel to the slope, dividing the rock mass into columnar unstable blocks. Due to rapid weathering and erosion of mudstone, differential weathering at the mudstone–sandstone interface leads to localised basal exposure, gradually reducing support and inducing overturning–pull-out instability, as illustrated in Fig. 2 . The study area shows typical alternating gully–valley landforms, with collapse deposits of unstable rock masses widely distributed in gullies and valley floors. These blocks are generally tens of centimetres in diameter, with some reaching several metres locally. 1.2 Spatial Distribution of Rockfall Sources Using a progressive survey approach of general–detail–verification for unstable rock masses, extensive multi-dimensional and multi-scale imagery of the project area was obtained with a DJI Mavic 3E drone (including oblique photography, orthophotos, close-range panoramic videos, and infrared thermal imaging) combined with detailed field investigations. This approach enabled detailed surveys of the quantity, scale, failure types, and locations of unstable rock masses, thereby identifying collapse risk sources. The UAV-based investigation process for unstable rock sources is illustrated in Fig. 3. A total of 44 unstable rock masses were identified: 23 on the left bank and 21 on the right bank. These included 2 large-scale and 16 medium-scale unstable rock masses, 21 clusters of unstable rock blocks, and 5 isolated block groups. Specifically, 22 unstable rock masses were located on reservoir slopes, 15 on dam shoulder slopes, and 8 on plant building slopes. The distribution of unstable rock masses and key project structures is shown in Fig. 3. 1.3 Stability Classification of Unstable Rock Masses Field engineering–geological investigations revealed that unstable rock masses in the project area predominantly exhibit toppling and falling failure modes. Based on these failure types, stability was classified using the limit equilibrium method into four categories: stable, basically stable, marginally stable, and unstable [ 14 ] , as shown in Table 1. Table.1 Stability classification of unstable rock masses Stability Classification Hazardous Rock Body ID Stable R-Z-8 Basically Stable L-Z-3 L-Z-6 R-D-2 R-WSQ-1 R-WSQ-4 R-WSQ-5 R-WSQ-9 R-Z-1 R-Z-3 R-Z-6 Marginally Stable L-WSQ-1 L-WSQ-2 L-WSQ-3 L-WSQ-4 L-WSQ-5 L-WSQ-6 L-WSQ-7 L-WSQ-8 L-WSQ-9 L-WSQ-10 L-WSQ-11 L-WSQ-12 L-Z-2 L-Z-4 L-Z-7 L-Z-8 R-D-1 R-G-1 R-Z-2 R-Z-4 R-Z-7 R-WSQ-2 R-WSQ-3 R-WSQ-6 R-WSQ-7 R-WSQ-8 Unstable L-G-1 L-G-2 L-G-3 L-Z-1 L-Z-5 R-G-2 R-Z-5 Numbering Principle: Bank–Type–Index; L = Left Bank, R = Right Bank, WSQ = Small to Medium Hazardous Rock Cluster, Z = Medium-Sized Hazardous Rock Mass, D = Large Hazardous Rock Mass, G = Isolated Boulder Group 2 Spatial Kinematic Characteristics of Unstable Rock Masses RocPro3D employs probabilistic methods to calculate three-dimensional movement trajectories of unstable rock blocks, accounting for irregular variations in block geometry, geotechnical properties, and topography. By simulating rockfall descent and collapse processes of unstable rock masses, RocPro3D enables analysis of block energy, velocity, rebound height, and final deposition points [ 17 ] . 2.1 High-Resolution Terrain Modelling Topography is a key factor governing the dynamics of unstable rock blocks, and high-precision terrain modelling is essential to ensure the reliability of motion trajectory simulations. Driven by gravity, the motion of unstable rock blocks involves a distinct conversion between potential and kinetic energy. Post-collision rebound height, motion direction, and energy dissipation characteristics are controlled by the geometric configuration of the collision surface (e.g., slope gradient, aspect, and local curvature). High-resolution digital elevation models (DEM) and digital orthophoto maps (DOM) of the project area were obtained through unmanned aerial vehicle (UAV) surveying. After data processing steps such as point cloud filtering, coordinate system transformation, and terrain feature enhancement, a three-dimensional digital terrain model (DTM) consistent with the actual surface morphology was constructed. This DTM was employed in subsequent rockfall motion simulations to improve the reliability of the results, as illustrated in Fig. 4 . 2.2 Selection and Calibration of Computational Parameters In probabilistic simulations, key variables—including the initial spatial coordinates, potential height, mass parameters, and geotechnical material properties of unstable rock masses—were represented as probability distributions. This approach realistically captures the heterogeneity and randomness of unstable rock masses, enabling a more scientifically grounded assessment of hazards in the project area under limited data conditions. Considering the spatial variability of detachment surfaces of unstable rock masses, this probabilistic approach employs Monte Carlo simulation techniques to numerically reconstruct multi-angle collapse scenarios. This enables systematic evaluation of the spatial distribution of rock movement trajectories and their energy evolution patterns under different detachment orientations. The computational parameters encompass both fundamental rock mass characteristics and geotechnical medium properties. The former primarily includes the quantity, location, shape, dimensions, density, and initial velocity of rock masses. The latter comprises collision parameters (normal and tangential restitution coefficients), friction parameters, and the transition angle between rolling and flying motion. The selection criteria for rockfall motion simulation parameters are detailed in Table 2. Table.2 Basis for selection of rockfall motion simulation parameters Project Name Description Computational Settings Simulation Method Hazardous Rock Mass Parameters: Considering Initial Position and Mass Geotechnical Medium Parameters: Considering Restitution Coefficients(R n 和R t )and Friction Coefficient༈k༉ Block Definition Rigid Body (Including Rolling Motion) Number of Simulations Number of Simulations for Single Hazardous Rock Mass: 50 Number of Simulations for Hazardous Rock Clusters: 50, 100, and 200 (Depending on Cluster Size) Grid Size 5×5m Rock Mass Location Field Survey Measurements Geometry Cylindrical or Spherical Shape Dimensions Real-Scene 3D Model Measurements Density 2500kg/m³ Initial Conditions Free Fall under Self-Weight Based on field geological survey data, the lithology of the study area was classified into eight types, as illustrated in Fig. 5 . The geotechnical medium parameters were determined through inverse calibration analysis. By comparing simulated collapse deposits with actual field survey results, key parameters were iteratively calibrated to establish reasonable values consistent with the geological conditions of the study area, as presented in Table 3. Table.3 Selection table of characteristic parameters of geotechnical media Geological Type Code Normal Restitution Coefficient (R n ) Tangential Restitution Coefficient (R t ) Friction Coefficient (k) Transition Angle β (°) J 2 S 0.54 0.89 0.43 24 J 2 XS 0.55 0.90 0.45 25 J 1-2 Z 0.55 0.90 0.45 25 J 1 Z 0.56 0.91 0.46 27 T 3 Xj 0.56 0.91 0.46 27 Q 4 col + dl 0.39 0.83 0.66 36 Q 4 pl + col 0.4 0.85 0.65 35 Q 4 dl + el 0.38 0.82 0.67 38 2.3 Analysis of Rockfall Kinematic Behaviour Rock masses located far from the project area or exhibiting high stability, and thus posing minimal threat, were excluded from the analysis. Movement simulations were conducted on the 37 identified unstable rock masses, with the results presented in Fig. 6 . The results indicate that rock mass movement paths predominantly follow gully channels and accumulate at valley bottoms. Upstream rockfalls often terminate within the reservoir area, posing limited threats to the project, whereas isolated boulders above the downstream plant and dam structure present direct hazards to hydraulic facilities. The project area was divided into grid cells measuring 5 m × 5 m. The number of rockfall trajectories within each grid cell, together with the kinetic energy and rebound height of rockfalls at a 95% confidence level, were statistically analysed. The grid-based rockfall trajectory density map (Fig. 7 (a)), generated from three-dimensional simulation outputs, illustrates the probability of different areas being impacted by rockfalls during the collapse of unstable rock masses with potential instability risks. The trajectory density recorded within each grid cell is quantified as a spatial probability indicator. A higher cumulative trajectory density within a grid cell indicates a greater likelihood of impact from falling rock masses. The rockfall energy map (Fig. 7 (b)) and rebound height map (Fig. 7 (c)) illustrate the intensity characteristics of rockfalls during unstable rock mass collapse, as well as the potential damage levels to vulnerable structures. 3 Hazard Assessment of Rockfall Risks in the Project Area 3.1 Methodological Framework and Evaluation Factor Selection Once dislodged, unstable rock masses often undergo high-velocity sliding along slopes, carrying immense kinetic energy that poses significant threats to personnel safety and critical infrastructure in the project area. To scientifically delineate the potential impact zones and inform the optimisation of engineering protection systems, a refined hazard assessment was conducted. In the small-scale, multi-constrained, disaster-prone environment of hydropower project zones, traditional hazard assessment methods based on static factor weighting exhibit two major shortcomings: (1) they fail to quantitatively characterise the energy evolution during rock mass movement, and (2) their spatial resolution is insufficient to support engineering-level protection design. To address these issues, this study proposes an evaluation method based on the rasterisation of dynamic parameters. Using rock mass stability as the core evaluation indicator, key parameters such as kinetic energy, rebound height, and trajectory density were calculated for each grid cell through numerical simulations. This process ultimately produced a high-precision three-dimensional hazard assessment model for rockfall movement. Table 4 presents the selection and grading of evaluation factors for the three-dimensional hazard assessment model. Within the rockfall hazard assessment model, the weighting of evaluation factors follows these principles: (1) rock mass stability (S) serves as the prerequisite for rockfall initiation, directly determining the probability of instability; (2) rockfall trajectory density (N) characterises the spatial distribution of hazards, with denser trajectories indicating broader threatened areas; (3) rockfall energy (E) reflects the destructive force of impacts, quantifiable using the kinetic energy formula E = 1/2 mv²; and (4) rebound height (H) determines the efficacy of protective structures, with excessive rebound potentially causing barrier failure.The weights of the hazard assessment parameters are shown in Table 5. Formula for Rasterised Hazard Index ( D ): $$\:D={\omega\:}_{1}S+{\omega\:}_{2}N+{\omega\:}_{3}E+{\omega\:}_{4}H$$ where \(\:{\omega\:}_{1}\) denotes the weighting factor; S represents stability, N denotes trajectory density, E signifies rockfall energy, and H indicates rebound height. Table.4 Selection and classification of evaluation factors Evaluation Factor Value Range Classification Level Hazard Level Stability (S) Basically Stable 1 Very Low Marginally Stable 3 Medium Unstable 5 Very High Trajectory Density (N) 0–1 1 Very Low 1–8 2 Low 8–20 3 Medium 20–50 4 High > 50 5 Very High Impact Energy (E) 0-2000KJ 1 Very Low 2000-5000KJ 2 Low:A single-layer protective net can effectively intercept. 5000-50000KJ 3 Medium:Multiple protective nets can effectively intercept. 50000-500000KJ 4 High:Multiple protective nets cannot intercept; active protection is required. > 500000KJ 5 Very High:Protective structures cannot intercept. Rebound Height (H) 0-1m 1 Very Low 1-5m 2 Low:A single-layer protective net can effectively intercept. 5-10m 3 Medium:Multiple protective nets can effectively intercept. 10-30m 4 High:Multiple protective nets cannot intercept; active protection is required. > 30m 5 Very High:Protective structures cannot intercept. Table.5 Weighting of risk assessment parameters Indicators Weighting Factor Stability 0.4 Number of Rockfalls 0.2 Rockfall Kinetic Energy 0.2 Rebound Height 0.2 Dynamic parameters of rockfall motion were extracted from grid cells, including peak impact energy, maximum rebound height, and trajectory density. Raw parameter data were converted into graded scores ranging from 1 to 5 according to the established standardised classification system. A spatially weighted overlay analysis was employed for multi-factor comprehensive evaluation, with the weighting of each indicator determined through formula-based calculation. The comprehensive evaluation results were classified into five risk levels using the equidistant method, as shown in Table 6. The rockfall hazard classification map (Fig. 8 ) illustrates the spatial distribution of different risk levels within the study area. The left bank of the dam shoulder slope and the left bank of the plant building constitute high-risk zones requiring particular attention, whereas the right bank slope predominantly exhibits medium to low risk. This evaluation method enables scientific disaster risk assessment through quantitative analysis of rockfall movement characteristics, providing a decision-making basis for subsequent disaster prevention and mitigation design. Table.6 Hazard classification criteria Score Hazard Level 0–1 Very Low Risk 1–2 Low Risk 2–3 Medium Risk 3–4 High Risk 4–5 Very High Risk 3.2 Rockfall Prevention Strategies Based on Hazard Zoning Based on the results of the rockfall hazard classification, a tiered prevention and control strategy was developed for the power station project [ 15 , 16 ] . The primary above-ground structures in the project area include the earth-rock dam, surface plant (switching station), spillway and drainage tunnels, and diversion tunnel inlets and outlets. The left bank of the dam face area is predominantly classified as a low-to-medium risk zone, where single- and multi-layer protective netting is installed along the dam face. The right bank of the dam face area is classified as a medium-to-high risk zone. Proactive protection measures (e.g., anchoring or clearance) are recommended for unstable rock masses above high-risk areas, with multi-layer protective netting installed along roads above the slope protection. The rockfill dam body area presents low risk, with single-layer protective netting recommended across the entire slope protection zone. The right bank of the surface plant is a low-risk zone, where single-layer protective netting is recommended around the plant perimeter. The road area on the left bank is a medium-to-high risk zone, requiring single- or multi-layer protective netting segmented by hazard level. The diversion tunnel inlets and outlets are medium-risk zones, requiring multi-layer protective netting. The slopes of the spillway and overflow channel pose no rockfall hazard. By dynamically matching protective measures through zoned and graded approaches, a balance between safety and economy was achieved. Priority control focused on the high-risk zone on the dam's left bank, the diversion tunnel inlets and outlets, and the area beneath the left-bank road, while protection in non-risk zones was simplified to optimise costs. 3.3 Reliability Evaluation of Passive Rockfall Protection Systems Slopes within the project area exhibit vertical drops of approximately 500–700 m, with widely distributed small- to medium-sized unstable rock masses. Passive protection is the primary method for intercepting minor rockfalls from these slopes. Reliability analysis and optimisation of passive protection net deployment are critical to effective slope management [ 17 , 18 ] . The L-WSQ-6 rockfall zone consists of a large cluster of small unstable rock masses located above the left-bank surface plant and dam, along the water conveyance pipeline route, as illustrated in Fig. 9 . This zone is prone to collective collapses triggered by construction activities. To evaluate the effectiveness of passive protection net deployment, the interception capacity of passive protection nets in this rockfall zone was analysed. Based on the motion simulation results, the unstable rock mass was positioned approximately 150 m above the surface powerhouse, with an elevation difference of about 70 m relative to the rockfall zone. The passive protection net was specified with a protection capacity of 5000 kJ and an installation height of 2.3 m. With the interception probability of the passive protection net set to 100%, the maximum allowable diameter of the unstable rock mass was determined to be 2.4 m. The simulation results and the energy distribution upon impact with the passive protection net are shown in Fig. 10 . Table 7 presents statistical parameters for rock impacts on the passive protection net, with a maximum impact energy of 4918 kJ and a maximum rebound height of 1.748 m. These calculations provide reference values for determining the optimal installation height of passive protection nets. Table.7 Kinematic parameters of unstable rock masses Kinematic Parameters Minimum Maximum Mean Standard Deviation Energy (kJ) 1707 4918 3586 751.8 Velocity (m/s) 14.32 36.86 21.78 7.228 Rebound Height (m) 0.79 1.748 1.078 0.207 Time (s) 18.92 23.79 21.37 1.283 4 Discussion This study employs a combination of UAV photogrammetry and numerical simulation to analyze the kinematic characteristics of unstable rock masses post-failure. It establishes a “static + kinematic” collapse hazard assessment model, providing a foundation for passive rockfall protection measures. This methodology significantly enhances the reliability of rockfall mitigation plans and is applicable to addressing rockfall hazards in high-mountain canyon regions. Surveys of historical rockfall distributions reveal that fallen rocks are concentrated in gully channels, gentle slopes, and slope bases. Five typical rockfall accumulation zones identified through simulation results were verified to validate the reliability of the rockfall motion simulation. Close-range field surveys and UAV inspections of these areas are shown in Fig. 11 . Areas 1 and 2 feature scattered boulders along the slope gully, representing remnants of earlier collapses (Fig. 11 (a,b)). Areas 3, 4, and 5 exhibit substantial boulder accumulations in the valley bottom, with occasional boulders scattered along the gully edges (Fig. 11 (c,d,e)). Most fallen rocks range from tens of centimeters to several meters in diameter. Field investigations showed high consistency with the rockfall accumulation zones identified through numerical simulations, confirming the active historical collapse phenomena in these areas. The investigation reveals that the volume of unstable rock masses in the source area is significantly larger than that of fallen rocks in the accumulation zone, indicating substantial fragmentation of unstable rocks during descent triggered by slope collisions. This study simulates medium-to-large unstable rock masses as intact rigid bodies, disregarding fragmentation effects during motion. Consequently, the calculated rebound heights and impact energies are relatively conservative, and predictions of movement trajectories and impact ranges remain incomplete. Current research on rockfall processes predominantly focuses on overall motion characteristics, with insufficient attention given to the mechanisms governing volumetric changes during motion. Previous studies have indicated that significant fragmentation during motion is a common phenomenon in high-elevation rockfalls [ 19 ] . Rockfall fragmentation is fundamentally a complex process of energy conversion and dissipation, its extent controlled by multiple factors including slope surface roughness and the mechanical properties of contacting materials. However, systematic theoretical elucidation of the quantitative relationship between fragmentation behavior and these physical parameters, as well as its regulatory mechanism on motion trajectories, remains lacking. Research indicates that fragmentation during motion not only significantly influences the velocity evolution and spatial distribution of rockfall bodies but also critically controls the final deposition morphology and grain size sorting structure of rock piles [ 20 ] . To deepen understanding of this process, scholars have conducted a series of studies using physical model experiments and discrete element numerical simulations. For instance, Bowman [ 21 ] discovered a linear correlation between normalized travel distance and potential energy rate; Ruiz-Carulla [ 22 ] .proposed a fractal-based collapse fragmentation model and established an energy criterion for the disintegration process. Furthermore, studies have confirmed a significant positive correlation between fragmentation degree and stress growth rate [ 23 , 24 ] . Analysis of rockfall energy distribution indicates [ 25 – 27 ] that energy consumption during rock fragmentation is relatively low, with most potential energy being converted into kinetic energy of fragmented blocks. Currently, large-scale rockfall motion simulations lack concise, effective key parameters for characterizing fragmentation effects that can be readily applied to practical engineering. There is an urgent need to develop improved kinematic models that incorporate fragmentation mechanisms to reasonably characterize the processes of mass redistribution and energy reallocation within rock masses during motion. This approach will enhance the spatial prediction accuracy of rockfall hazards, providing a more scientific and reliable theoretical basis for slope rockfall risk assessment and passive protection engineering design. 5 Conclusion (1) By integrating UAV photogrammetry with three-dimensional numerical simulation, this study investigated rockfall sources and analysed rockfall trajectories in the project area of a pumped-storage power station in southwestern China. A multi-factor hazard assessment model was then developed by synthesising key rockfall movement parameters, including unstable rock mass stability, rockfall kinetic energy, rebound height, and trajectory characteristics, enabling refined characterisation of rockfall hazard risks. (2) Based on hazard grading outcomes, a scientifically designed, zone-specific, and dynamically matched protection scheme was formulated. Through the control strategy of “reinforcing high-risk areas, optimising medium- to low-risk zones, and simplifying risk-free sections,” priority was given to safeguarding high-risk areas while reducing redundant protection in low-risk areas, thereby achieving coordinated optimisation of engineering safety and economic efficiency. (3) The reliability of passive protection nets was evaluated. When operating with a 5000 kJ energy absorption capacity and installed at a height of 2.3 m, positioning the net 70 m below the unstable rock mass can intercept rock blocks with diameters less than 2.4 m. (4) Integrating static and kinematic parameters facilitates the transition from “static parameter analysis” to “dynamic process simulation” in rockfall hazard assessment. The resulting three-dimensional visualisation assists decision-makers in rapidly identifying high-risk areas, optimising disaster prevention resource allocation, and supporting intelligent geological hazard management. Declarations Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (42477167),the National Key R&D Program of China (2023YFC3081400). Author contributions H. Yang: Conceptualization, Methodology, Experimental validation, Writing-original draft preparation. L.Y. Jiao : Writing-review and editing. Z.N. Zou: On-site data collection. C.Zhao: UAV data acquisition, processing, and analysis .M.W. Xie: Investigation, Supervision,Project administration, Funding acquisition. Data curation. All authors have read and agreed to the published version of the manuscript. X.Li: Article Format Revision Data Availability Statement The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. Competing interests The authors declare no competing interests. Consent to Publish declaration We confirm that we have read the journal policies and we are submitting our manuscript in accordance with journal policies. All the authors gave their consent for publication of the results. Ethics and Consent to Participate declarations Not applicable, this study did not involve human participants or animal subjects. Clinical trial number Not applicable. References Renato Macciotta. Slope risk management in light of uncertainty and environmental variability-202l Canadian Geotechnical Colloquium, Canadian Geotechnical Journal,2023,.60112): 1777–91. https://doi.org/10.1139/cgj-2022-0626 Rahmati O, Yousefi S, Kalantari Z et al. 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Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Dec, 2025 Reviews received at journal 10 Dec, 2025 Reviewers agreed at journal 10 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 03 Dec, 2025 Reviewers agreed at journal 10 Nov, 2025 Reviewers invited by journal 10 Nov, 2025 Editor assigned by journal 03 Nov, 2025 Submission checks completed at journal 03 Nov, 2025 First submitted to journal 03 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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L-WSQ-6\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7822779/v1/8d540f1bad54200e5aa79534.png"},{"id":96285309,"identity":"48104401-b63d-4939-9e96-06fa9cdb12b3","added_by":"auto","created_at":"2025-11-19 11:57:02","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1097516,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInterception effect of protective net\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e（a） Location of protective netting installation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e（b） Impact energy distribution of protective net\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7822779/v1/e5c6f1fe72ac7d72fabfa3b3.png"},{"id":96365083,"identity":"f32c45af-0217-4ff8-8cb7-e36fd1da71ab","added_by":"auto","created_at":"2025-11-20 10:09:58","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":2297842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVerification of rocks deposition zone: (a) potential rocks accumulation zones delineated; (b) rocks accumulation in Zone 1 slope gully; (c) Rocks accumulation in zone 2 slope gully; (d) rocks accumulation in zone 3 valley bottom; (e) rocks accumulation in zone 4 slope and valley bottom;\u003c/strong\u003e \u003cstrong\u003e(f)rocks accumulation in zone 5 valley bottom.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7822779/v1/b8bcc8158674fdd6b49b440b.png"},{"id":96369304,"identity":"6738c21f-8078-45aa-aab2-522b5842d950","added_by":"auto","created_at":"2025-11-20 10:20:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":14703116,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7822779/v1/89f0c021-3ed7-4539-b527-3f4e8e261d0a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hazard Assessment of Unstable Rock Mass Collapse in Hydropower Station Areas Based on Spatial Motion Characteristics","fulltext":[{"header":"0 Introduction","content":"\u003cp\u003eRockfalls on slopes represent a common engineering geological hazard, marked by frequent occurrence, limited visibility, and sudden onset. As China\u0026rsquo;s energy infrastructure expands rapidly into southwestern mountainous regions, unstable rock masses on slopes near hydropower projects pose serious threats to infrastructure and resource development safety \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. A rockfall occurs when unstable rock detaches from its parent formation and, under gravity, undergoes free-fall, rolling, and sliding along exposed slopes. This process releases substantial kinetic energy, endangering people, vehicles, infrastructure, and hydraulic facilities along its path \u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e. Rockfall hazard assessment in areas with concentrated unstable rock masses is essential for disaster early warning and engineering protection.\u003c/p\u003e\u003cp\u003eRockfall hazard assessment quantifies both the likelihood of instability and the potential severity of damage within unstable rock masses \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e. Early hazard assessments mainly considered topography and geological features, often neglecting interactions between unstable rock masses and slopes. This approach lacked accuracy in evaluating rockfall risks under complex topography and variable geological conditions. Subsequently, researchers placed greater emphasis on rockfall kinematic characteristics, including motion mechanisms, hazard extent, and intensity. For example, Lan et al. \u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e combined LiDAR and GIS for spatial modelling to assess rockfall hazards along a Canadian railway. Tang Hongmei et al. \u003csup\u003e[\u003cspan additionalcitationids=\"CR6 CR7\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e applied grey system theory, fuzzy mathematics, the Analytic Hierarchy Process, and GIS to build a multi-factor evaluation model. Wu Zhongpeng et al. \u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e used the Monte Carlo method in Matlab to estimate the probability of instability at Fanjiayan, Weining County, Guizhou Province, under various conditions, thereby evaluating local rockfall hazards. These approaches incorporated rockfall motion and accumulation characteristics, thereby improving the scientific rigour of hazard analysis.\u003c/p\u003e\u003cp\u003eWith advances in numerical analysis, rockfall simulations now enable visualisation of movement and calculation of key parameters during motion. Two-dimensional tools such as Rockfall are widely used in engineering to quickly obtain parameters such as rebound height, contact energy, and velocity distribution within predefined profiles \u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e. However, these methods treat rockfall\u0026ndash;slope interactions as planar problems. Due to the spatial limitations of predefined profiles, they introduce subjective biases in path simulation.\u003c/p\u003e\u003cp\u003eRecently, advances in unmanned aerial vehicle (UAV) technology and geographic information systems (GIS) have highlighted the advantages of UAV photogrammetry for investigating geological hazards on steep slopes. Its wide field of view, high precision, and absence of spatial constraints allow acquisition of high-resolution digital terrain models, enabling prediction of three-dimensional movement domains and collision characteristics of unstable rock masses \u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e. Researchers such as Dupire et al. \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e, and Li You \u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e used Rockfall Analyst to reproduce the kinematic characteristics of unstable rock masses in the Alpine foothills, collapsed blocks near railway tunnels in southwestern China, and the landslide at Sanguanmiao Village in the Wenchuan earthquake zone. Compared with two-dimensional simulations, three-dimensional numerical models better capture how terrain heterogeneity influences rockfall collision parameters, enabling more accurate prediction of hazardous processes and impact zones. The Rockfall Analyst software employed by the aforementioned scholars is a rockfall motion simulation tool developed on the ArcGIS platform. While it offers 3D visualization capabilities, its simulation parameters\u0026mdash;such as rock release intervals and azimuth spacing\u0026mdash;require manual presetting and lack dynamic adjustment mechanisms. This makes it difficult to accurately reflect the randomness of rockfall trajectories across complex terrain and topography. RocPro3D, grounded in rigid-body dynamics theory, accounts for the dynamic interactions between unstable rock masses and slopes during motion. This includes physical processes such as collision, friction, ricochet, and energy dissipation. Compared to traditional two-dimensional simplified models, RocPro3D's three-dimensional numerical model effectively captures the localized regulatory effects of terrain spatial heterogeneity on rock block motion parameters (such as reflection angles, velocity attenuation, and rebound height). This enables more realistic reproduction of the motion trajectories, energy evolution, and final deposition distribution during rockfall disaster processes, significantly enhancing the accuracy and reliability of predicting disaster impact areas.\u003c/p\u003e\u003cp\u003eAt present, detailed investigation of unstable rock sources on steep slopes and hazard analysis for hydraulic structures remain challenging. This study integrates three-dimensional kinematic characteristics of unstable rock masses into hazard assessment. Focusing on hydropower project areas in Southwest China, it applies UAV photogrammetry to investigate slope hazards, builds high-precision three-dimensional models, and simulates the spatial movement of unstable rock collapses. By integrating parameters such as kinetic energy, rebound height, and trajectory of unstable rock masses, a multi-factor evaluation model is developed. The model uses GIS techniques to assess collapse hazards and evaluate mitigation measures, providing a scientific basis for early warning and engineering management of slope hazards.\u003c/p\u003e"},{"header":"1 Development Characteristics of Rockfall Hazards","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e1.1 Overview of the Project Area\u003c/h2\u003e\u003cp\u003eLower reservoirs of pumped-storage power stations, which require large-scale water storage, are typically created by damming mountainous terrain. The lower reservoir site of a pumped-storage power station in the Jinsha River Basin, China, is characterised by steep terrain on both banks, with a maximum relative elevation difference of 710 m. The lower to middle slope sections generally have gradients of 30\u0026ndash;40\u0026deg;, while the upper sections are steeper, forming multiple tiers of cliffs.\u003c/p\u003e\u003cp\u003eThe lithology mainly consists of sedimentary rocks, Quaternary colluvial deposits, and Jurassic strata. These units are widely distributed within multi-cyclic fluvial\u0026ndash;lacustrine deposits, showing distinct mud\u0026ndash;sand interbedding, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Unstable rock masses develop along sandstone escarpments, forming banded clusters approximately 20\u0026ndash;30 m thick, with small- to medium-sized rock bodies. The surface rock mass on ridges and escarpments is fractured, often unloaded and relaxed, readily forming concentrated unstable rock zones.\u003c/p\u003e\u003cp\u003eThe dominant joint system includes two sets of orthogonal conjugate joints and one set of gently dipping joints parallel to the slope, dividing the rock mass into columnar unstable blocks. Due to rapid weathering and erosion of mudstone, differential weathering at the mudstone\u0026ndash;sandstone interface leads to localised basal exposure, gradually reducing support and inducing overturning\u0026ndash;pull-out instability, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe study area shows typical alternating gully\u0026ndash;valley landforms, with collapse deposits of unstable rock masses widely distributed in gullies and valley floors. These blocks are generally tens of centimetres in diameter, with some reaching several metres locally.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e1.2 Spatial Distribution of Rockfall Sources\u003c/h2\u003e\u003cp\u003eUsing a progressive survey approach of general\u0026ndash;detail\u0026ndash;verification for unstable rock masses, extensive multi-dimensional and multi-scale imagery of the project area was obtained with a DJI Mavic 3E drone (including oblique photography, orthophotos, close-range panoramic videos, and infrared thermal imaging) combined with detailed field investigations. This approach enabled detailed surveys of the quantity, scale, failure types, and locations of unstable rock masses, thereby identifying collapse risk sources. The UAV-based investigation process for unstable rock sources is illustrated in Fig.\u0026nbsp;3.\u003c/p\u003e\u003cp\u003eA total of 44 unstable rock masses were identified: 23 on the left bank and 21 on the right bank. These included 2 large-scale and 16 medium-scale unstable rock masses, 21 clusters of unstable rock blocks, and 5 isolated block groups. Specifically, 22 unstable rock masses were located on reservoir slopes, 15 on dam shoulder slopes, and 8 on plant building slopes. The distribution of unstable rock masses and key project structures is shown in Fig.\u0026nbsp;3.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e1.3 Stability Classification of Unstable Rock Masses\u003c/h2\u003e\u003cp\u003eField engineering\u0026ndash;geological investigations revealed that unstable rock masses in the project area predominantly exhibit toppling and falling failure modes. Based on these failure types, stability was classified using the limit equilibrium method into four categories: stable, basically stable, marginally stable, and unstable \u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e, as shown in Table\u0026nbsp;1.\u003c/p\u003e\u003cp\u003eTable.1 Stability classification of unstable rock masses\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStability Classification\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eHazardous Rock Body ID\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eR-Z-8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eBasically Stable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-Z-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eL-Z-6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR-D-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR-WSQ-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eR-WSQ-4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR-WSQ-5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR-WSQ-9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR-Z-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR-Z-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eR-Z-6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e\u003cp\u003eMarginally Stable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-WSQ-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eL-WSQ-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eL-WSQ-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eL-WSQ-4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eL-WSQ-5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-WSQ-6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eL-WSQ-7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eL-WSQ-8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eL-WSQ-9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eL-WSQ-10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-WSQ-11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eL-WSQ-12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eL-Z-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eL-Z-4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eL-Z-7\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-Z-8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR-D-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR-G-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR-Z-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eR-Z-4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eR-Z-7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR-WSQ-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR-WSQ-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eR-WSQ-6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eR-WSQ-7\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eR-WSQ-8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eUnstable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL-G-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eL-G-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eL-G-3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eL-Z-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eL-Z-5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eR-G-2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e\u003cp\u003eR-Z-5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eNumbering Principle: Bank\u0026ndash;Type\u0026ndash;Index; L\u0026thinsp;=\u0026thinsp;Left Bank, R\u0026thinsp;=\u0026thinsp;Right Bank, WSQ\u0026thinsp;=\u0026thinsp;Small to Medium Hazardous Rock Cluster, Z\u0026thinsp;=\u0026thinsp;Medium-Sized Hazardous Rock Mass, D\u0026thinsp;=\u0026thinsp;Large Hazardous Rock Mass, G\u0026thinsp;=\u0026thinsp;Isolated Boulder Group\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"2 Spatial Kinematic Characteristics of Unstable Rock Masses","content":"\u003cp\u003eRocPro3D employs probabilistic methods to calculate three-dimensional movement trajectories of unstable rock blocks, accounting for irregular variations in block geometry, geotechnical properties, and topography. By simulating rockfall descent and collapse processes of unstable rock masses, RocPro3D enables analysis of block energy, velocity, rebound height, and final deposition points \u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.1 High-Resolution Terrain Modelling\u003c/h2\u003e\u003cp\u003eTopography is a key factor governing the dynamics of unstable rock blocks, and high-precision terrain modelling is essential to ensure the reliability of motion trajectory simulations. Driven by gravity, the motion of unstable rock blocks involves a distinct conversion between potential and kinetic energy. Post-collision rebound height, motion direction, and energy dissipation characteristics are controlled by the geometric configuration of the collision surface (e.g., slope gradient, aspect, and local curvature).\u003c/p\u003e\u003cp\u003eHigh-resolution digital elevation models (DEM) and digital orthophoto maps (DOM) of the project area were obtained through unmanned aerial vehicle (UAV) surveying. After data processing steps such as point cloud filtering, coordinate system transformation, and terrain feature enhancement, a three-dimensional digital terrain model (DTM) consistent with the actual surface morphology was constructed. This DTM was employed in subsequent rockfall motion simulations to improve the reliability of the results, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Selection and Calibration of Computational Parameters\u003c/h2\u003e\u003cp\u003eIn probabilistic simulations, key variables\u0026mdash;including the initial spatial coordinates, potential height, mass parameters, and geotechnical material properties of unstable rock masses\u0026mdash;were represented as probability distributions. This approach realistically captures the heterogeneity and randomness of unstable rock masses, enabling a more scientifically grounded assessment of hazards in the project area under limited data conditions. Considering the spatial variability of detachment surfaces of unstable rock masses, this probabilistic approach employs Monte Carlo simulation techniques to numerically reconstruct multi-angle collapse scenarios. This enables systematic evaluation of the spatial distribution of rock movement trajectories and their energy evolution patterns under different detachment orientations.\u003c/p\u003e\u003cp\u003eThe computational parameters encompass both fundamental rock mass characteristics and geotechnical medium properties. The former primarily includes the quantity, location, shape, dimensions, density, and initial velocity of rock masses. The latter comprises collision parameters (normal and tangential restitution coefficients), friction parameters, and the transition angle between rolling and flying motion. The selection criteria for rockfall motion simulation parameters are detailed in Table\u0026nbsp;2.\u003c/p\u003e\u003cp\u003eTable.2 Basis for selection of rockfall motion simulation parameters\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProject\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eName\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003eComputational Settings\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSimulation Method\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHazardous Rock Mass Parameters: Considering Initial Position and Mass\u003c/p\u003e\u003cp\u003eGeotechnical Medium Parameters: Considering Restitution Coefficients(R\u003csub\u003en\u003c/sub\u003e和R\u003csub\u003et\u003c/sub\u003e)and Friction Coefficient༈k༉\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBlock Definition\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRigid Body (Including Rolling Motion)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of Simulations\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eNumber of Simulations for Single Hazardous Rock Mass: 50\u003c/p\u003e\u003cp\u003eNumber of Simulations for Hazardous Rock Clusters: 50, 100, and 200 (Depending on Cluster Size)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGrid Size\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u0026times;5m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eRock Mass\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLocation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eField Survey Measurements\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGeometry\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCylindrical or Spherical Shape\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDimensions\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eReal-Scene 3D Model Measurements\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDensity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2500kg/m\u0026sup3;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eInitial Conditions\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFree Fall under Self-Weight\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eBased on field geological survey data, the lithology of the study area was classified into eight types, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The geotechnical medium parameters were determined through inverse calibration analysis. By comparing simulated collapse deposits with actual field survey results, key parameters were iteratively calibrated to establish reasonable values consistent with the geological conditions of the study area, as presented in Table\u0026nbsp;3.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eTable.3 Selection table of characteristic parameters\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eof geotechnical media\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGeological Type Code\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNormal Restitution Coefficient (R\u003csub\u003en\u003c/sub\u003e)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTangential Restitution Coefficient (R\u003csub\u003et\u003c/sub\u003e)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eFriction Coefficient (k)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eTransition Angle β (\u0026deg;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJ\u003csub\u003e2\u003c/sub\u003eS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJ\u003csub\u003e2\u003c/sub\u003eXS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJ\u003csub\u003e1-2\u003c/sub\u003eZ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJ\u003csub\u003e1\u003c/sub\u003eZ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e27\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eT\u003csub\u003e3\u003c/sub\u003eXj\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e27\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ\u003csub\u003e4\u003c/sub\u003e\u003csup\u003ecol\u0026thinsp;+\u0026thinsp;dl\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e36\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ\u003csub\u003e4\u003c/sub\u003e\u003csup\u003epl\u0026thinsp;+\u0026thinsp;col\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ\u003csub\u003e4\u003c/sub\u003e\u003csup\u003edl\u0026thinsp;+\u0026thinsp;el\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e38\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Analysis of Rockfall Kinematic Behaviour\u003c/h2\u003e\u003cp\u003eRock masses located far from the project area or exhibiting high stability, and thus posing minimal threat, were excluded from the analysis. Movement simulations were conducted on the 37 identified unstable rock masses, with the results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The results indicate that rock mass movement paths predominantly follow gully channels and accumulate at valley bottoms. Upstream rockfalls often terminate within the reservoir area, posing limited threats to the project, whereas isolated boulders above the downstream plant and dam structure present direct hazards to hydraulic facilities.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe project area was divided into grid cells measuring 5 m \u0026times; 5 m. The number of rockfall trajectories within each grid cell, together with the kinetic energy and rebound height of rockfalls at a 95% confidence level, were statistically analysed. The grid-based rockfall trajectory density map (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a)), generated from three-dimensional simulation outputs, illustrates the probability of different areas being impacted by rockfalls during the collapse of unstable rock masses with potential instability risks. The trajectory density recorded within each grid cell is quantified as a spatial probability indicator. A higher cumulative trajectory density within a grid cell indicates a greater likelihood of impact from falling rock masses. The rockfall energy map (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b)) and rebound height map (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(c)) illustrate the intensity characteristics of rockfalls during unstable rock mass collapse, as well as the potential damage levels to vulnerable structures.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Hazard Assessment of Rockfall Risks in the Project Area","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Methodological Framework and Evaluation Factor Selection\u003c/h2\u003e\u003cp\u003eOnce dislodged, unstable rock masses often undergo high-velocity sliding along slopes, carrying immense kinetic energy that poses significant threats to personnel safety and critical infrastructure in the project area. To scientifically delineate the potential impact zones and inform the optimisation of engineering protection systems, a refined hazard assessment was conducted. In the small-scale, multi-constrained, disaster-prone environment of hydropower project zones, traditional hazard assessment methods based on static factor weighting exhibit two major shortcomings: (1) they fail to quantitatively characterise the energy evolution during rock mass movement, and (2) their spatial resolution is insufficient to support engineering-level protection design. To address these issues, this study proposes an evaluation method based on the rasterisation of dynamic parameters. Using rock mass stability as the core evaluation indicator, key parameters such as kinetic energy, rebound height, and trajectory density were calculated for each grid cell through numerical simulations. This process ultimately produced a high-precision three-dimensional hazard assessment model for rockfall movement. Table\u0026nbsp;4 presents the selection and grading of evaluation factors for the three-dimensional hazard assessment model.\u003c/p\u003e\u003cp\u003eWithin the rockfall hazard assessment model, the weighting of evaluation factors follows these principles: (1) rock mass stability (S) serves as the prerequisite for rockfall initiation, directly determining the probability of instability; (2) rockfall trajectory density (N) characterises the spatial distribution of hazards, with denser trajectories indicating broader threatened areas; (3) rockfall energy (E) reflects the destructive force of impacts, quantifiable using the kinetic energy formula E\u0026thinsp;=\u0026thinsp;1/2 mv\u0026sup2;; and (4) rebound height (H) determines the efficacy of protective structures, with excessive rebound potentially causing barrier failure.The weights of the hazard assessment parameters are shown in Table\u0026nbsp;5.\u003c/p\u003e\u003cp\u003eFormula for Rasterised Hazard Index (\u003cem\u003eD\u003c/em\u003e):\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:D={\\omega\\:}_{1}S+{\\omega\\:}_{2}N+{\\omega\\:}_{3}E+{\\omega\\:}_{4}H$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e denotes the weighting factor; S represents stability, N denotes trajectory density, E signifies rockfall energy, and H indicates rebound height.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTable.4 Selection and classification of evaluation factors\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEvaluation Factor\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eValue Range\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eClassification Level\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHazard Level\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eStability (S)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBasically Stable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMarginally Stable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnstable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eTrajectory Density (N)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u0026ndash;1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u0026ndash;8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u0026ndash;20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e20\u0026ndash;50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026gt;\u0026thinsp;50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eImpact Energy (E)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0-2000KJ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2000-5000KJ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLow:A single-layer protective net can effectively intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5000-50000KJ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium:Multiple protective nets can effectively intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50000-500000KJ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh:Multiple protective nets cannot intercept; active protection is required.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026gt;\u0026thinsp;500000KJ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High:Protective structures cannot intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eRebound Height (H)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0-1m\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery Low\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1-5m\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLow:A single-layer protective net can effectively intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5-10m\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedium:Multiple protective nets can effectively intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10-30m\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHigh:Multiple protective nets cannot intercept; active protection is required.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026gt;\u0026thinsp;30m\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVery High:Protective structures cannot intercept.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eTable.5 Weighting of risk assessment parameters\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndicators\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eWeighting Factor\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStability\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber of Rockfalls\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRockfall Kinetic Energy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRebound Height\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eDynamic parameters of rockfall motion were extracted from grid cells, including peak impact energy, maximum rebound height, and trajectory density. Raw parameter data were converted into graded scores ranging from 1 to 5 according to the established standardised classification system. A spatially weighted overlay analysis was employed for multi-factor comprehensive evaluation, with the weighting of each indicator determined through formula-based calculation. The comprehensive evaluation results were classified into five risk levels using the equidistant method, as shown in Table\u0026nbsp;6. The rockfall hazard classification map (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e) illustrates the spatial distribution of different risk levels within the study area. The left bank of the dam shoulder slope and the left bank of the plant building constitute high-risk zones requiring particular attention, whereas the right bank slope predominantly exhibits medium to low risk. This evaluation method enables scientific disaster risk assessment through quantitative analysis of rockfall movement characteristics, providing a decision-making basis for subsequent disaster prevention and mitigation design.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTable.6 Hazard classification criteria\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eScore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHazard Level\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u0026ndash;1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVery Low Risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u0026ndash;2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLow Risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u0026ndash;3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMedium Risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u0026ndash;4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHigh Risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u0026ndash;5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVery High Risk\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Rockfall Prevention Strategies Based on Hazard Zoning\u003c/h2\u003e\u003cp\u003eBased on the results of the rockfall hazard classification, a tiered prevention and control strategy was developed for the power station project \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. The primary above-ground structures in the project area include the earth-rock dam, surface plant (switching station), spillway and drainage tunnels, and diversion tunnel inlets and outlets. The left bank of the dam face area is predominantly classified as a low-to-medium risk zone, where single- and multi-layer protective netting is installed along the dam face. The right bank of the dam face area is classified as a medium-to-high risk zone. Proactive protection measures (e.g., anchoring or clearance) are recommended for unstable rock masses above high-risk areas, with multi-layer protective netting installed along roads above the slope protection. The rockfill dam body area presents low risk, with single-layer protective netting recommended across the entire slope protection zone.\u003c/p\u003e\u003cp\u003eThe right bank of the surface plant is a low-risk zone, where single-layer protective netting is recommended around the plant perimeter. The road area on the left bank is a medium-to-high risk zone, requiring single- or multi-layer protective netting segmented by hazard level. The diversion tunnel inlets and outlets are medium-risk zones, requiring multi-layer protective netting. The slopes of the spillway and overflow channel pose no rockfall hazard.\u003c/p\u003e\u003cp\u003eBy dynamically matching protective measures through zoned and graded approaches, a balance between safety and economy was achieved. Priority control focused on the high-risk zone on the dam's left bank, the diversion tunnel inlets and outlets, and the area beneath the left-bank road, while protection in non-risk zones was simplified to optimise costs.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Reliability Evaluation of Passive Rockfall Protection Systems\u003c/h2\u003e\u003cp\u003eSlopes within the project area exhibit vertical drops of approximately 500\u0026ndash;700 m, with widely distributed small- to medium-sized unstable rock masses. Passive protection is the primary method for intercepting minor rockfalls from these slopes. Reliability analysis and optimisation of passive protection net deployment are critical to effective slope management\u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e. The L-WSQ-6 rockfall zone consists of a large cluster of small unstable rock masses located above the left-bank surface plant and dam, along the water conveyance pipeline route, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e. This zone is prone to collective collapses triggered by construction activities.\u003c/p\u003e\u003cp\u003eTo evaluate the effectiveness of passive protection net deployment, the interception capacity of passive protection nets in this rockfall zone was analysed. Based on the motion simulation results, the unstable rock mass was positioned approximately 150 m above the surface powerhouse, with an elevation difference of about 70 m relative to the rockfall zone. The passive protection net was specified with a protection capacity of 5000 kJ and an installation height of 2.3 m. With the interception probability of the passive protection net set to 100%, the maximum allowable diameter of the unstable rock mass was determined to be 2.4 m. The simulation results and the energy distribution upon impact with the passive protection net are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eTable 7 presents statistical parameters for rock impacts on the passive protection net, with a maximum impact energy of 4918 kJ and a maximum rebound height of 1.748 m. These calculations provide reference values for determining the optimal installation height of passive protection nets. \u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003e\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003eTable.7 Kinematic parameters of unstable rock masses\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKinematic Parameters\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMinimum\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMaximum\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eStandard Deviation\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy (kJ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1707\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4918\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3586\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e751.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVelocity (m/s)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e14.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e36.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e21.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e7.228\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRebound Height (m)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.748\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.078\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.207\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTime (s)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e18.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e23.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e21.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.283\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThis study employs a combination of UAV photogrammetry and numerical simulation to analyze the kinematic characteristics of unstable rock masses post-failure. It establishes a \u0026ldquo;static\u0026thinsp;+\u0026thinsp;kinematic\u0026rdquo; collapse hazard assessment model, providing a foundation for passive rockfall protection measures. This methodology significantly enhances the reliability of rockfall mitigation plans and is applicable to addressing rockfall hazards in high-mountain canyon regions.\u003c/p\u003e\u003cp\u003eSurveys of historical rockfall distributions reveal that fallen rocks are concentrated in gully channels, gentle slopes, and slope bases. Five typical rockfall accumulation zones identified through simulation results were verified to validate the reliability of the rockfall motion simulation. Close-range field surveys and UAV inspections of these areas are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e. Areas 1 and 2 feature scattered boulders along the slope gully, representing remnants of earlier collapses (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a,b)). Areas 3, 4, and 5 exhibit substantial boulder accumulations in the valley bottom, with occasional boulders scattered along the gully edges (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e(c,d,e)). Most fallen rocks range from tens of centimeters to several meters in diameter. Field investigations showed high consistency with the rockfall accumulation zones identified through numerical simulations, confirming the active historical collapse phenomena in these areas.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe investigation reveals that the volume of unstable rock masses in the source area is significantly larger than that of fallen rocks in the accumulation zone, indicating substantial fragmentation of unstable rocks during descent triggered by slope collisions. This study simulates medium-to-large unstable rock masses as intact rigid bodies, disregarding fragmentation effects during motion. Consequently, the calculated rebound heights and impact energies are relatively conservative, and predictions of movement trajectories and impact ranges remain incomplete. Current research on rockfall processes predominantly focuses on overall motion characteristics, with insufficient attention given to the mechanisms governing volumetric changes during motion.\u003c/p\u003e\u003cp\u003ePrevious studies have indicated that significant fragmentation during motion is a common phenomenon in high-elevation rockfalls\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. Rockfall fragmentation is fundamentally a complex process of energy conversion and dissipation, its extent controlled by multiple factors including slope surface roughness and the mechanical properties of contacting materials. However, systematic theoretical elucidation of the quantitative relationship between fragmentation behavior and these physical parameters, as well as its regulatory mechanism on motion trajectories, remains lacking. Research indicates that fragmentation during motion not only significantly influences the velocity evolution and spatial distribution of rockfall bodies but also critically controls the final deposition morphology and grain size sorting structure of rock piles\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. To deepen understanding of this process, scholars have conducted a series of studies using physical model experiments and discrete element numerical simulations. For instance, Bowman\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e discovered a linear correlation between normalized travel distance and potential energy rate; Ruiz-Carulla\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e.proposed a fractal-based collapse fragmentation model and established an energy criterion for the disintegration process. Furthermore, studies have confirmed a significant positive correlation between fragmentation degree and stress growth rate\u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e. Analysis of rockfall energy distribution indicates\u003csup\u003e[\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003ethat energy consumption during rock fragmentation is relatively low, with most potential energy being converted into kinetic energy of fragmented blocks.\u003c/p\u003e\u003cp\u003eCurrently, large-scale rockfall motion simulations lack concise, effective key parameters for characterizing fragmentation effects that can be readily applied to practical engineering. There is an urgent need to develop improved kinematic models that incorporate fragmentation mechanisms to reasonably characterize the processes of mass redistribution and energy reallocation within rock masses during motion. This approach will enhance the spatial prediction accuracy of rockfall hazards, providing a more scientific and reliable theoretical basis for slope rockfall risk assessment and passive protection engineering design.\u003c/p\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003e(1) By integrating UAV photogrammetry with three-dimensional numerical simulation, this study investigated rockfall sources and analysed rockfall trajectories in the project area of a pumped-storage power station in southwestern China. A multi-factor hazard assessment model was then developed by synthesising key rockfall movement parameters, including unstable rock mass stability, rockfall kinetic energy, rebound height, and trajectory characteristics, enabling refined characterisation of rockfall hazard risks.\u003c/p\u003e\u003cp\u003e(2) Based on hazard grading outcomes, a scientifically designed, zone-specific, and dynamically matched protection scheme was formulated. Through the control strategy of \u0026ldquo;reinforcing high-risk areas, optimising medium- to low-risk zones, and simplifying risk-free sections,\u0026rdquo; priority was given to safeguarding high-risk areas while reducing redundant protection in low-risk areas, thereby achieving coordinated optimisation of engineering safety and economic efficiency.\u003c/p\u003e\u003cp\u003e(3) The reliability of passive protection nets was evaluated. When operating with a 5000 kJ energy absorption capacity and installed at a height of 2.3 m, positioning the net 70 m below the unstable rock mass can intercept rock blocks with diameters less than 2.4 m.\u003c/p\u003e\u003cp\u003e(4) Integrating static and kinematic parameters facilitates the transition from \u0026ldquo;static parameter analysis\u0026rdquo; to \u0026ldquo;dynamic process simulation\u0026rdquo; in rockfall hazard assessment. The resulting three-dimensional visualisation assists decision-makers in rapidly identifying high-risk areas, optimising disaster prevention resource allocation, and supporting intelligent geological hazard management.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u0026nbsp;\u003c/strong\u003eThe authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (42477167),the National Key R\u0026amp;D Program of China (2023YFC3081400).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e \u003cstrong\u003eH. Yang:\u003c/strong\u003e Conceptualization, Methodology, Experimental validation, Writing-original draft preparation. \u003cstrong\u003eL.Y. Jiao\u003c/strong\u003e \u003cstrong\u003e:\u003c/strong\u003e Writing-review and editing.\u003cstrong\u003e\u0026nbsp;Z.N. Zou:\u003c/strong\u003e On-site data collection.\u003cstrong\u003e\u0026nbsp;C.Zhao:\u003c/strong\u003e UAV data acquisition, processing, and analysis\u003cstrong\u003e.M.W. Xie:\u003c/strong\u003e Investigation, Supervision,Project administration, Funding acquisition. Data curation. All authors have read and agreed to the published version of the manuscript.\u003cstrong\u003eX.Li:\u003c/strong\u003e Article Format Revision\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u0026nbsp;\u003c/strong\u003eThe datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u0026nbsp;\u003c/strong\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish declaration\u0026nbsp;\u003c/strong\u003eWe confirm that we have read the journal policies and we are submitting our manuscript in accordance with journal policies. All the authors gave their consent for publication of the results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics and Consent to Participate declarations\u003c/strong\u003e Not applicable, this study did not involve human participants or animal subjects.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e Not applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eRenato Macciotta. 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Extremely energetic rockfalls J Geophys Research: EarthSurface. 2018;123:2392\u0026ndash;421. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/2017JF004327\u003c/span\u003e\u003cspan address=\"10.1029/2017JF004327\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Hydropower slope, Rockfall hazards, Rockfall motion simulation, Hazard assessment, Passive protection","lastPublishedDoi":"10.21203/rs.3.rs-7822779/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7822779/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePumped-storage power stations are typically built in steep, mountainous terrain, where rock-slope collapse threatens critical infrastructure including powerhouses and dams. Conventional assessments seldom consider the full 3-D kinematics of unstable rock masses. To fill this gap, we present a spatial-motion-based method for evaluating slope-collapse hazard at hydropower sites. Using the planned lower reservoir area of a pumped-storage station in southwestern China as a case study, unmanned-aerial-vehicle photogrammetry was employed to obtain the spatial distribution, geometric features, and topographic attributes of unstable rock masses. These data were used to generate a high-resolution DTM and an orthophoto mosaic.RocPro3D simulated the 3-D trajectories of falling rocks. A comprehensive evaluation model integrating four indicators\u0026mdash;rock-mass stability, rockfall kinetic energy, bounce height, and trajectory density\u0026mdash;was established to classify hazard levels and propose corresponding protection measures. This assessment framework enables spatially quantitative characterization of hazard parameters and provides a scientific basis for slope-collapse mitigation design in hydropower engineering.\u003c/p\u003e","manuscriptTitle":"Hazard Assessment of Unstable Rock Mass Collapse in Hydropower Station Areas Based on Spatial Motion Characteristics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-19 11:56:57","doi":"10.21203/rs.3.rs-7822779/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-19T11:20:32+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-10T10:24:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"42756295883626249270965727652979014879","date":"2025-12-10T06:50:41+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-07T09:40:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7132290337575424449042410308838550302","date":"2025-12-03T13:07:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"195699140775139618865116711442282300807","date":"2025-11-10T06:15:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-10T05:36:10+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-04T04:05:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-03T09:35:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Applied Sciences","date":"2025-11-03T09:31:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8b58ce70-2310-4318-b0f7-1b7ae7e2652c","owner":[],"postedDate":"November 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-02-12T15:39:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-19 11:56:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7822779","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7822779","identity":"rs-7822779","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}