Paper contribution

From nominal energy to capacity curves: a probabilistic framework for reliability-based design of flexible rockfall barriers

Valerio De Biagi; Maddalena Marchelli; Francesco Pimpinella

Proceedings
EUROCK 2026
Pages
181-186
Submitted
28 January 2026
Accepted
15 June 2026
Published
12 August 2026

Summary

Abstract

Flexible rockfall barriers are widely adopted passive protection systems in mountainous regions, yet their design still relies on deterministic criteria based on Maximum Energy Level (MEL) and Service Energy Level (SEL) tests. These standardized procedures provide a single nominal energy value, which does not reflect the variability of real impact scenarios nor the stochastic nature of barrier performance. This limitation hinders the integration of reliability-based principles into design, a cornerstone of modern structural engineering. This work merges a probabilistic framework to estimate the mechanical performance of flexible rockfall barriers under a wide range of impact scenarios into the RockStop software, integrating the resulting capacity curve within the software and enabling its practical use in design workflows. The framework derives capacity curves for flexible rockfall barriers and is built upon a generalized multi-component analytical model, developed by the authors, that simulates barrier response under arbitrary impact conditions by assembling analytical representations of each component (net, wire ropes, posts, energy dissipators). A Monte Carlo simulation scheme propagates uncertainties in geometry, mechanical properties, impact position, and component variability, generating a probabilistic description of the barrier’s energy absorption capacity. Results show that highly eccentric impacts can significantly alter the nominal capacity. The integration of trajectory outputs, combined with the barrier capacity curve, in RockStop enables site-specific assessment of all possible actions and their frequency, allowing the calculation of failure probability for both newly installed and existing barriers. This framework marks a major advancement toward risk-informed design by enabling the integration of reliability-based safety formats for rockfall barriers, supporting comprehensive lifecycle performance assessment, and providing a robust basis for quantifying residual risk after mitigation.

Contributors

Authors

  1. Valerio De Biagi Politecnico di Torino, Italy ORCID 0000-0003-1866-9362
  2. Maddalena Marchelli Politecnico di Torino, Italy ORCID 0000-0002-9919-2916
  3. Francesco Pimpinella Politecnico di Torino, Italy

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References

  1. Bourrier F, Baroth J, Lambert S (2016) Accounting for the variability of rock detachment conditions in designing rockfall protection structures. Natural Hazards 81(1):365–385. https://doi.org/10.1007/s11069-015-2084-0
  2. Coulibaly JB, Chanut MA, Lambert S, Nicot F (2019) Toward a generic computational approach for flexible rockfall barrier modeling. Rock Mechanics and Rock Engineering 52(11):4475–4496. https://doi.org/10.1007/s00603-019-01878-6
  3. De Biagi V, Marchelli M, Peila D (2020) Reliability analysis and partial safety factors approach for rockfall protection structures. Engineering Structures 213:100553. https://doi.org/10.1016/j.engstruct.2020.110553
  4. De Biagi V, Marchelli M (2025) A new tool to quantify the failure probability of rockfall net fences. In: Rocscience International Conference 2025 (RIC 2025), 451–459. Atlantis Press. https://doi.org/10.2991/978-94-6463-402-5_45
  5. EOTA (2018) EAD 340059 00 0106 Falling Rock Protection Kits. European Organisation for Technical Assessment, Brussels
  6. Macciotta R (2019) Review and latest insights into rock fall temporal variability associated with weather. Proceedings of the Institution of Civil Engineers – Geotechnical Engineering 172(6):556–568. https://doi.org/10.1680/jgeen.18.00224
  7. Marchelli M, De Biagi V (2019) Optimization methods for the evaluation of the parameters of a rockfall fractal fragmentation model. Landslides, 16(7), 1385-1396. https://doi.org/10.1007/s10346-019-01182-y
  8. Marchelli M, De Biagi V, Peila D (2020) Reliability based design of protection net fences: Influence of rockfall uncertainties through a statistical analysis. Geosciences 10:280. https://doi.org/10.3390/geosciences10070280
  9. Marchelli M, De Biagi V, Peila D (2021) Reliability based design of rockfall passive systems height. International Journal of Rock Mechanics and Mining Sciences 139:104664. https://doi.org/10.1016/j.ijrmms.2021.104664
  10. ONR (2021) ONR 24810 Technical protection against rockfall. Austrian Standards Institute, Vienna
  11. Peila D, Ronco C (2009) Design of rockfall net fences and the new ETAG 027 European guideline. Natural Hazards and Earth System Sciences, 9(4), 1291-1298. https://doi.org/10.5194/nhess-9-1291-2009
  12. Pimpinella, F., Marchelli, M., Lanter, A., & De Biagi, V. (2024). Numerical back-analysis of impacted rockfall barriers steel posts: discussion on the effectiveness of the system. In 14th International Symposium on Landslides 2024, Chambery, 8-12 July 2024
  13. Pimpinella F, Marchelli M, De Biagi V (2025) A generalized multi component analytical method to study the performance of a rockfall barrier under a generic impact condition. Computers and Geotechnics 188:107602. https://doi.org/10.1016/j.compgeo.2025.107602
  14. Pimpinella F, Marchelli M, De Biagi V (2025) Towards a probabilistic description of the mechanical performance of rockfall retaining systems. Engineering Structures (submitted)
  15. UNI (2018) UNI 11211 4: Rockfall protective measures – Part 4: Definitive and executive design. UNI, Milano
  16. UNI (2021) UNI 11211 2: Rockfall protective measures – Part 2: Preliminary intervention programme. UNI, Milano
  17. Yu Z, Luo L, Liu C, Guo L, Qi X, Zhao L (2021) Dynamic response of flexible rockfall barriers with different block shapes. Landslides 18(7):2621–2637. https://doi.org/10.1007/s10346-021-01658-w