Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4475–4496 | Cite as

Toward a Generic Computational Approach for Flexible Rockfall Barrier Modeling

  • Jibril B. CoulibalyEmail author
  • Marie-Aurélie Chanut
  • Stéphane Lambert
  • François Nicot
Original Paper


Flexible rockfall barriers are protection structures used to mitigate rockfall hazards in mountainous areas. The complex nonlinear mechanical behavior of these structures under impacts requires powerful modeling tools to perform structural analysis. In this article, a generic computational approach to rockfall barriers analysis is introduced. First, the generic formulation and numerical implementation in the GENEROCK software are detailed. Then, two barrier models are considered and validated against experimental full-scale tests on two different technologies. This numerical investigation permits insightful numerical investigation of the barriers’ behavior. Exploratory numerical simulations are eventually performed to highlight the strengths and generality of the proposed approach. The influence of the curtain effect modeling in simulation results is presented. The effects of repeated impacts on rockfall barriers are investigated and present new insight into barrier behavior and management practices. Stochastic modeling methods are also used to study the propagation of uncertainty and variability of the structure itself in its dynamic response.


Rockfall barrier Generic approach GENEROCK Curtain effect Ring net Stochastic modeling 

List of Symbols

\(\mathbf {A}\)

Stochastic input variables


Young’s modulus


Energy level


Probability density function


Activation force of energy dissipating devices


Earth gravitational acceleration


Second moment of area of post

\(K_1, K_2, K_3\)

Elastic, elastoplastic and blockage stiffness of energy dissipating devices


Length of post


Side length of boulder


Mass of boulder


Critical buckling load of post


Deficiency probability


Height ratio


Height ratio threshold

\(\mathbf {x}^*\)

Design point

\(\varvec{\alpha }\)

Importance factor

\({\varDelta }E_{\mathrm{p}}\)

Potential energy variation

\(\delta _{\mathrm{s}}\)

Stroke of energy dissipating devices

\({\varDelta }z\)

Altitude variation

\(\mu _{F_{\mathrm{y}}}\)

Mean of activation forces

\(\sigma _{F_{\mathrm{y}}}\)

Standard deviation of activation forces


Time step


Discrete element method


First-order reliability method



The authors would like to express their sincere thanks to the French National Project C2ROP (Chutes de Blocs, Risques Rocheux et Ouvrages de Protection, ) for having supported this work and for fostering the development of the GENEROCK software potential applications.


  1. Andrew RD, Fry DA, Bookwalter RE (1998) Field testing and evaluation of various rock fall control system. Chama ValleyProductions, LLC, Chama ValleyGoogle Scholar
  2. Arpin BD (2013) Development of standardized testing procedures for flexible rockfall fence systems. Master’s thesis, Colorado School of Mines, GoldenGoogle Scholar
  3. Bertrand D, Trad A, Limam A, Silvani C (2012) Full-scale dynamic analysis of an innovative rockfall fence under impact using the discrete element method: from the local scale to the structure scale. Rock Mech Rock Eng 45(5):885–900Google Scholar
  4. Bourrier F, Lambert S, Baroth J (2015) A reliability-based approach for the design of rockfall protection fences. Rock Mech Rock Eng 48(1):247–259CrossRefGoogle Scholar
  5. CAN (2018) Travaux spéciaux: accès difficile, risques naturels, maritime et fluvial. CAN - Le Relut, 26270 Mirmande, France. Accessed 4 June 2019
  6. Castanon-Jano L, Blanco-Fernandez E, Castro-Fresno D, Ballester-Muñoz F (2017) Energy dissipating devices in falling rock protection barriers. Rock Mech Rock Eng 50(3):603–619CrossRefGoogle Scholar
  7. Castanon-Jano L, Blanco-Fernandez E, Castro-Fresno D, Ferreño D (2018) Use of explicit fem models for the structural and parametrical analysis of rockfall protection barriers. Eng Struct 166:212–226. CrossRefGoogle Scholar
  8. Cazzani A, Mongiovì L, Frenez T (2002) Dynamic finite element analysis of interceptive devices for falling rocks. Int J Rock Mech Mining Sci 39:303–321CrossRefGoogle Scholar
  9. Chanut MA, Dubois L, Matot B, Nicot F (2012) Comportement dynamique des écrans de filets sous impact: un modèle générique d’écrans. In: Journées Nationales de Géotechnique et de Géologie de l’Ingénieur, JNGG, Bordeaux, France, 4–6 JulyGoogle Scholar
  10. Chanut MA, Coulibaly JB, Lambert S, Nicot F (2018) Numerical investigation of rockfall barrier under realistic on-site impacts. In: International symposium rock slope stability 2018. 13–15 November, Chambery, France. Accessed 4 June 2019
  11. Coulibaly JB (2017) Modélisation numérique discrète du comportement mécanique sous impact des structures d’écrans de filets pare-pierres. PhD thesis, University Grenoble-Alpes, Grenoble, France (in French) Google Scholar
  12. Coulibaly JB, Chanut MA, Lambert S, Nicot F (2017a) Non-linear discrete mechanical model of steel rings. J Eng Mech 143(9):04017087CrossRefGoogle Scholar
  13. Coulibaly JB, Chanut MA, Galandrin C, Olmedo I, Lambert S, Nicot F (2017b) Generic modeling of flexible rockfall barriers: from components characterization to full-scale numerical simulations. In: 6th Interdisciplinary workshop on rockfall protection, RocExs 2017, Barcelona, Spain, 22–24 May. ISBN: 978-84-946909-4-5Google Scholar
  14. Coulibaly JB, Chanut MA, Lambert S, Nicot F (2018) Sliding cable modeling: An attempt at a unified formulation. Int J Solids Struct 130–131:1–10CrossRefGoogle Scholar
  15. de Miranda S, Gentilini C, Gottardi G, Govoni L, Mentani A, Ubertini F (2015) Virtual testing of existing semi-rigid rockfall protection barriers. Eng Struct 85:83–94. CrossRefGoogle Scholar
  16. Duffy JD, Haller B (1993) Field tests of flexible rockfall barriers. In: Conference on transportation facilities through difficult terrain, Aspen-Snowmass, CO, USA, 8–10 August. pp 465–473. ISBN: 90-5410-343-4Google Scholar
  17. EOTA (2013) ETAG 27—Guideline for European technical approval of falling rock protection kits. European organization for technical approvals. BrusselsGoogle Scholar
  18. Erhart T (2012) Pulley mechanism for muscle or tendon movements along bones and around joints. In: LS-DYNA forum, DYNAmore, Ulm, Germany, 9–10 October. Accessed 4 June 2019
  19. Escallón J, Wendeler C, Chatzi E, Bartelt P (2014) Parameter identification of rockfall protection barrier components through an inverse formulation. Eng Struct 77:1–16CrossRefGoogle Scholar
  20. Escallón JP, Wendeler C (2013) Numerical simulations of quasi-static and rockfall impact tests of ultra-high strength steel wire-ring nets using abaqus/explicit. In: 2013 SIMULIA community conference, Vienna, Austria, 23–24 May. Accessed 4 June 2019
  21. Escallón JP, Boetticher V, Wendeler C, Chatzi E, Bartelt P (2015) Mechanics of chain-link wire nets with loose connections. Eng Struct 101:68–87CrossRefGoogle Scholar
  22. Gentilini C, Govoni L, de Miranda S, Gottardi G, Ubertini F (2012) Three-dimensional numerical modelling of falling rock protection barriers. Comput Geotech 44:58–72CrossRefGoogle Scholar
  23. Gentilini C, Gottardi G, Govoni L, Mentani A, Ubertini F (2013) Design of falling rock protection barriers using numerical models. Eng Struct 50:96–106. CrossRefGoogle Scholar
  24. Gerber W, Böll A (2006) Type-testing of rockfall barriers—comparative results. In: International symposium interpraevent, Munich, Germany, 3–4 April, pp 189–198. Accessed 4 June 2019
  25. Gerber W, Grassl H, Böll A, Ammann W (2001) Flexible rockfall barriers—development, standardisation and type-testing in switzerland. In: International Conference on Landslides—causes, impacts and countermeasures. Davos, Switzerland, pp 515–524Google Scholar
  26. Gottardi G, Govoni L (2010) Full-scale modelling of falling rock protection barriers. Rock Mech Rock Eng 43:261–274CrossRefGoogle Scholar
  27. Grassl H (2002) Experimentelle und numerische modellierung des dynamischen tragund verformungsverhaltens von hochflexiblen schutzsystemen gegen steinschlag. PhD Thesis, ETH Zurich, ZurichGoogle Scholar
  28. Grassl H, Volkwein A, Anderheggen E, Ammann J (2002) Steel-net rockfall protection—experimental and numerical simulation. WIT Trans Built Environ 63:11Google Scholar
  29. Hambleton JP, Buzzi O, Giacomini A, Spadari M, Sloan SW (2013) Perforation of flexible rockfall barriers by normal block impact. Rock Mech Rock Eng 46(3):515–526CrossRefGoogle Scholar
  30. Heiss C (2004) Characteristics of the testing of rock fall protection kits on transversal test sites on example “Steirischer Erzberg”. In: International Symposium Interpraevent, Riva del Garda, Italy, pp 49–58Google Scholar
  31. Hincz K (2009) Nonlinear analysis of cable net structures suspended from arches with block and tackle suspension system, taking into account the friction of the pulleys. Int J Space Struct 24(3):143–152CrossRefGoogle Scholar
  32. Lambert S, Nicot F (eds) (2011) Rockfall engineering. Wiley, New YorkGoogle Scholar
  33. Lemaitre J, Chaboche JL (1990) Mechanics of solid materials. Cambridge University Press, Cambridge.
  34. Luciani A, Todaro C, Peila D (2017) Maintenance and risk management of rockfall protection net fences through numerical study of damage influence. Frattura ed Integrità Strutturale 12(43):241–250. CrossRefGoogle Scholar
  35. McCauley MT, Works BW, Naramore SA (1985) Rockfall Mitigation. California Department of Transportation, SacramentoGoogle Scholar
  36. Mentani A, Giacomini A, Buzzi O, Govoni L, Gottardi G, Fityus S (2016a) Numerical modelling of a low-energy rockfall barrier: new insight into the bullet effect. Rock Mech Rock Eng 49(4):1247–1262. CrossRefGoogle Scholar
  37. Mentani A, Govoni L, Gottardi G, Lambert S, Bourrier F, Toe D (2016b) A new approach to evaluate the effectiveness of rockfall barriers. Procedia Eng 158:398–403. VI Italian conference of researchers in geotechnical engineering, CNRIG2016—Geotechnical engineering in multidisciplinary research: from microscale to regional scale, Bologna, Italy, 22–23 September 2016CrossRefGoogle Scholar
  38. Mentani A, Govoni L, Giacomini A, Gottardi G, Buzzi O (2018) An equivalent continuum approach to efficiently model the response of steel wire meshes to rockfall impacts. Rock Mech Rock Eng. CrossRefGoogle Scholar
  39. Moon T, Oh J, Mun B (2014) Practical design of rockfall catchfence at urban area from a numerical analysis approach. Eng Geol 172:41–56CrossRefGoogle Scholar
  40. Muraishi H, Sano S (1999) Full-scale rockfall test of ring net barrier and components. In: Seminar on Rockfall Tests and Standardization, Davos, SwitzerlandGoogle Scholar
  41. Muraishi H, Samizo M, Sugiyama T (2005) Development of a flexible low-energy rockfall protection fence. Q Rep Railway Tech Res Inst 46(3):161–166Google Scholar
  42. Nicot F, Cambou B, Mazzoleni G (2001a) Design of rockfall restraining nets from a discrete element modelling. Rock Mech Rock Eng 34(2):99–118CrossRefGoogle Scholar
  43. Nicot F, Cambou B, Mazzoleni G (2001b) From a constitutive modelling of metallic rings to the design of rockfall restraining nets. Int J Numer Anal Methods Geomech 25(1):49–70CrossRefGoogle Scholar
  44. Olmedo I, Robit P, Bertrand D, Galandrin C, Coulibaly JB, Chanut MA (2017) Extended experimental studies on rockfall flexible fences. In: RocExs 2017—6th Interdisciplinary Workshop on Rockfall ProtectionGoogle Scholar
  45. Peila D, Pelizza S, Sassudelli F (1998) Evaluation of behavior of rockfall restraining nets by full scale tests. Rock Mech Rock Eng 31(1):1–24CrossRefGoogle Scholar
  46. Smith DD, Duffy JD (1990) Field tests and evaluation of rockfall restraining nets. Tech. rep., California Department of Transportation, Sacramento, California (USA), cA/TL-90/05Google Scholar
  47. Spadari M, Giacomini A, Buzzi O, Hambleton JP (2012) Prediction of the bullet effect for rockfall barriers: a scaling approach. Rock Mech Rock Eng 45(2):131–144CrossRefGoogle Scholar
  48. Toe D, Mentani A, Govoni L, Bourrier F, Gottardi G, Lambert S (2018) Introducing meta-models for a more efficient hazard mitigation strategy with rockfall protection barriers. Rock Mech Rock Eng 51(4):1097–1109. CrossRefGoogle Scholar
  49. Tran PV, Maegawa K, Fukada S (2013) Experiments and dynamic finite element analysis of a wire-rope rockfall protective fence. Rock Mech Rock Eng 46(5):1183–1198. CrossRefGoogle Scholar
  50. Volkwein A (2004) Numerische simulation von flexiblen steinschlagschutzsystemen. PhD thesis, ETH Zurich, ZurichGoogle Scholar
  51. Volkwein A (2005) Numerical simulation of flexible rockfall protection systems. In: International conference on computing in civil engineering, ASCE, Cancun, Mexico, 12–15 July.
  52. Volkwein A, Schellenberg K, Labiouse V, Agliardi F, Berger F, Bourrier F, Dorren LKA, Gerber W, Jaboyedoff M (2011) Rockfall characterisation and structural protection—a review. Nat Hazards Earth Syst Sci 11(9):2617–2651. CrossRefGoogle Scholar
  53. Zhou B, Accorsi ML, Leonard JW (2004) Finite element formulation for modeling sliding cable elements. Comput Struct 82(2–3):271–280CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Geological Hazards Team, Cerema Centre-EstBron CedexFrance
  2. 2.Univ. Grenoble Alpes, Irstea, ETNAGrenobleFrance

Personalised recommendations