Paper contribution

A probabilistic fragmentation-based rockfall model for open-pit and natural slopes

Maddalena Marchelli; Marco Paganone

Proceedings
EUROCK 2026
Pages
175-180
Submitted
28 January 2026
Accepted
15 June 2026
Published
12 August 2026

Summary

Abstract

Accurate prediction of rockfall propagation is critical for designing safe slopes in open-pit mines as well as in other engineered or natural environments. Fragmentation during impact significantly alters runout distances, energy dissipation, and the hazard footprint, yet most trajectory models neglect this phenomenon or treat it empirically. This study applies RockFRAG, a novel probabilistic 2D lumped-mass model, developed by the author and implemented in a code, that explicitly incorporates fragmentation processes informed by laboratory experiments accounting for impact energy, block shape and rock-mass structure through probabilistic fragment trajectories. Applied to synthetic open‑pit bench profiles, fragmentation‑aware and intact‑block simulations are compared across different bench configurations, showing that neglecting fragmentation is not inherently conservative: depending on face angle and bench geometry, breakage can either extend runout and increase pit‑floor arrival probability, or promote earlier arrest through fracture‑energy dissipation. These geometry‑dependent, non‑monotonic effects cannot be captured by non‑fragmenting assumptions and lead to significant differences in runout envelopes and impact conditions. These findings underscore the need to account for fragmentation in runout‑based design checks and bench performance evaluation. A probabilistic treatment is essential to cover uncertainty in fragment behaviour and slope interaction, enabling risk‑informed design beyond deterministic assumptions, with implications extending to mountainous environments where impact‑induced breakage commonly influences runout variability and the performance of protective measures.

Contributors

Authors

  1. Maddalena Marchelli Politecnico di Torino, Italy ORCID 0000-0002-9919-2916
  2. Marco Paganone Department of Planning, Water Resources and Land Use, Autonomous Region of Valle d'Aosta, Aosta, Italy

Index terms

Keywords

Full text

Attachments

Works cited

References

  1. Alejano LR, Pons B, Bastante F, Alonso E, Stockhausen H (2007) Slope geometry design as a means for controlling rockfalls in quarries. International Journal of Rock Mechanics and Mining Sciences 44(6):903–921. 10.1016/j.ijrmms.2007.02.001
  2. Bourrier F, Toe D, Garcia B, Baroth J, Lambert S (2021) Experimental investigations on complex block propagation for the assessment of propagation models quality. Landslides 18(2):639–654. 10.1007/s10346-020-01517-6
  3. Darling P (Ed.) (2011)SME mining engineering handbook (Vol. 1), 3rd edn. Society for Mining, Metallurgy, and Exploration, Englewood, Colorado.
  4. Ferrari F, Thoeni K, Giacomini A, Lambert C (2016) A rapid approach to estimate the rockfall energies and distances at the base of rock cliffs. Georisk 10(3):179–199. 10.1080/17499518.2016.1139729
  5. Gili JA, Ruiz-Carulla R, Matas G, Moya J, Prades A, Corominas J, ... &Mavrouli O (2022). Rockfalls: analysis of the block fragmentation through field experiments. Landslides, 19(5), 1009-1029. 10.1007/s10346-021-01837-9
  6. Li L, & Lan H (2015). Probabilistic modeling of rockfall trajectories: a review. Bulletin of Engineering Geology and the Environment, 74(4), 1163-1176. 10.1007/s10064-015-0718-9
  7. Macciotta R, Altamirano F, Gibbins L, Espezua M, Fernández R, &Maguiña J (2021). Rock fall hazard analysis for in-pit operations potentially impacting external sensitive areas. Mining, 1(2), 135-154. 10.3390/mining1020009
  8. Matas G, Lantada N, Corominas J, Gili JA, Ruiz-Carulla R, Prades A (2020) Simulation of full-scale rockfall tests with a fragmentation model. Geosciences 10(5):168. 10.3390/geosciences10050168
  9. Marchelli M, Peila D, Giacomini A (2023) Rockfall in open pit mines: management of the pit geometry and protection measures design. International Journal of Rock Mechanics and Mining Sciences 170:105551. 10.1016/j.ijrmms.2023.105551
  10. Marchelli M, Guccione DE, Giacomini A, Buzzi O (2025) Fragmentation patterns and trajectories during rockfall: influence of discontinuities and impact conditions through drop tests. Rock Mechanics and Rock Engineering: 1–33. 10.1007/s00603-025-04937-3
  11. Marchelli M (2026). A new probabilistic rockfall trajectory model incorporating fragmentation, rock mass quality and block shape variability. International Journal of Rock Mechanics and Mining Sciences, 206, 106624
  12. McNabb JC, Potter JJ, Restrepo JA, Warren SN, Ryan TM, &Luxbacher KD (2025, June). Quantifying Topographic Influences on Rockfall Trajectories in Open Pit Mines Using Stochastic Rockfall Modeling. In ARMA US Rock Mechanics/Geomechanics Symposium (p. D021S002R006)
  13. Read J, Stacey P (2009) Guidelines for open pit slope design. CSIRO Publishing, Clayton.
  14. Ruiz-Carulla R, Corominas J, Gili JA, Matas G, Lantada N, Moya J, ... & Puig C (2020). Analysis of fragmentation of rock blocks from real-scale tests. Geosciences, 10(8), 308. 10.3390/geosciences10080308
  15. Wang X, Frattini P, Crosta GB, Zhang L, Agliardi F, Lari S, Yang, Z. (2014). Uncertainty assessment in quantitative rockfall risk assessment. Landslides, 11(4), 711-722. 10.1007/s10346-013-0447-8