, Volume 17, Issue 1, pp 49–59 | Cite as

Reliability-based design for debris flow barriers

  • Federico VagnonEmail author
  • Anna Maria Ferrero
  • Leandro R. Alejano
Original Paper


In the European Union since 2010, the design of any type of structures must comply with EN-1997 Geotechnical Design (CEN 2004) (EC7) referring to engineering projects in the rock mechanics field. However, the design of debris flow countermeasures in compliance with EC7 requirements is not feasible: EC7 uses partial safety factors for design calculations, but safety factors are not provided for phenomena such as debris flows and rock falls. Consequently, how EC7 can be applied to the design of debris flow barriers is not clear, although the basic philosophy of reliability-based design (RBD), as defined in EN1990 (CEN 2002) and applicable to geotechnical applications, may be a suitable approach. However, there is insufficient understanding of interactions between debris flows and structures to support RBD application to debris flow barrier design, as full-scale experimental data are very limited and difficult to obtain. Laboratory data are available but they are governed by scale effects that limit their usefulness for full-scale problems. The article describes an analysis, using the first-order reliability method (FORM), of two different datasets, one obtained through laboratory experiments and the other reflecting historical debris flow events in the Jiangjia Ravine (China). Statistical analysis of laboratory data enabled a definition of the statistical distributions of the parameters that primarily influence debris flow and barrier interactions. These statistical distributions were then compared to the field data to explore the links between flume experiments and full-scale problems. This paper reports a first attempt to apply RBD to debris flow countermeasures, showing how the choice of the target probability of failure influences the barrier design resistance value. An analysis of the factors governing debris flows highlights the applicability and limitations of EN1990 and EN1997 in the design of these rock engineering structures.


Eurocode 7 (EC7) Reliability index First-order reliability method (FORM) Partial safety factor Debris flow Mitigation design 



We gratefully acknowledge Ailish M. J. Maher for the language polishing of the final version of the manuscript.


  1. Ang HS, Tang WH (1984) Probability concepts in engineering planning and design. Decision, Risk and Reliability, vol 2. Wiley, New YorkGoogle Scholar
  2. Armanini A, Scotton P (1992) Experimental analysis on the dynamic impact of a debris flow on structures. In Proceedings of the International Symposium Interpraevent, Bern, Switzerland, 107–116Google Scholar
  3. Austrian Standard Rule ONR 24800 (2009) Protection works for torrent control—terms and their definitions as well as classification. Austrian Institute for Standardisation, Wien, Austria (in German)Google Scholar
  4. Austrian Standard Rule ONR 24802 (2011) Protection works for torrent control–design and structures. Austrian Institute for Standardisation, Wien, Austria (in German)Google Scholar
  5. Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. Wiley, Chichester. West Sussex, England: HobokenGoogle Scholar
  6. Callisto L (2010) A factored strength approach for the limit states design of geotechnical structures. Can Geotech J 47:1011–1023CrossRefGoogle Scholar
  7. Ditlevsen O (1981) Uncertainty modelling: with applications to multidimensional civil engineering systems. McGraw-Hill, New YorkGoogle Scholar
  8. Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron 126(4):307–316CrossRefGoogle Scholar
  9. EN 1990 (2002) Eurocode—basis of structural design. CEN, BrusselsGoogle Scholar
  10. EN 1997-1 (2004) Eurocode 7: geotechnical design—part 1: general rules. CEN, BrusselsGoogle Scholar
  11. Haldar A, Mahadevan S (1999) Probability, reliability and statistical methods in engineering design. Wiley, New YorkGoogle Scholar
  12. Harrison JP (2014) Eurocode 7 and rock engineering: current problems and future opportunities. In Proceedings of EUROCK European regional symposium—rock engineering and rock mechanics: structures in and on rock masses, Vigo, Spain, 1531–1537Google Scholar
  13. Hasofer AM, Lind NC (1974) An exact and invariant second-moment code format. J Mech Div ASCE 100(1):111–121Google Scholar
  14. Helsen MM, Koop PJM, Van Steijn H (2002) Magnitude-frequency relationship for debris flows of the fan of the Chalance torrent, Valgaudemar (French Alps). Earth Surf Process Landf 27(12):1299–1307CrossRefGoogle Scholar
  15. Hong Y, Wang JP, Li DQ, Cao ZJ, Ng CWW, Cui P (2015) Statistical and probabilistic analyses of impact pressure and discharge of debris flow from 139 events during 1961 and 2000 at Jiangjia Ravine, China. Eng Geol 187:122–134CrossRefGoogle Scholar
  16. Huang HW, Wen SC, Zhang J, Chen FY, Martin JR, Wang H (2018) Reliability analysis of slope stability under seismic condition during a given exposure time. Landslides 15(11):2303–2313CrossRefGoogle Scholar
  17. Hubl J, Suda J, Proske D, et al. (2009) Debris flow impact estimation. In Proceedings of the 11th international symposium on water management and hydraulic engineering, 37–148Google Scholar
  18. Hungr O, Morgan GC, Kellerhals R (1984) Quantitative analysis of debris torrent hazard for design of remedial measures. Can Geotech J 21:663–667CrossRefGoogle Scholar
  19. Jakob M, Hungr O (2005) Debris-flow hazards and related phenomena. Springer-Verlag, Berlin HeidelbergGoogle Scholar
  20. Kang ZC, Cui P, Wei FQ, He SF (2006) Data collection of observation of debris flows in Jiangjia Ravine, Dongchuan Debris Flow Observation and Research Station (1961–1984). Science Press, BeijingGoogle Scholar
  21. Kang ZC, Cui P, Wei FQ, He SF (2007) Data collection of observation of debris flows in Jiangjia Ravine, Dongchuan Debris Flow Observation and Research Station (1995–2000). Science Press, BeijingGoogle Scholar
  22. Lamas L, Perucho A, Alejano LR (2014) Some key issues regarding application of Eurocode 7 to rock engineering design. In Proceedings of EUROCK European regional symposium—rock engineering and rock mechanics: structures in and on rock masses, Vigo, Spain, 1459–1465Google Scholar
  23. Li DQ, Xiao T, Cao ZJ, Zhou CB, Zhang LM (2016) Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation. Landslides 13(2):293–303CrossRefGoogle Scholar
  24. Low BK, Phoon KK (2015) Reliability-based design and its complementary role to Eurocode 7 design approach. Comput Geotech 65:30–44CrossRefGoogle Scholar
  25. Low BK, Tang WH (1997) Efficient reliability evaluation using spreadsheet. J Eng Mech ASCE 123:749–752CrossRefGoogle Scholar
  26. Low BK, Tang WH (2004) Reliability analysis using object-oriented constrained optimization. Struct Saf 26:69–89CrossRefGoogle Scholar
  27. Low BK, Tang WH (2007) Efficient spreadsheet algorithm for first-order reliability method. J Eng Mech ASCE 133(12):1378–1387CrossRefGoogle Scholar
  28. Madsen HO, Krenk S, Lind NC (1986) Methods of structural safety. Prentice-Hall, Englewood CliffsGoogle Scholar
  29. Marchi L, D’Agostino V (2004) Estimation of debris-flow magnitude in the eastern Italian Alps. Earth Surf Process Landf 29:207–220CrossRefGoogle Scholar
  30. McGuire MP, VandenBerge DR (2017) Interpretation of shear strength uncertainty and reliability analyses of slopes. Landslides 14(6):2059–2072CrossRefGoogle Scholar
  31. Melchers RE (1999) Structural reliability analysis and prediction, 2nd edn. Wiley, New YorkGoogle Scholar
  32. Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):484–494CrossRefGoogle Scholar
  33. Sun HW, Lam TTM, Tsui HM, Hong Kong Geotechnical Engineering Office (2005) Design basis for standardised modules of landslide debris-resisting barriers. Geotechnical Engineering Office, Civil Engineering and Development DepartmentGoogle Scholar
  34. Vagnon F, Segalini A (2016) Debris flow impact estimation on a rigid barrier. Nat Hazards Earth Syst Sci 16:1691–1697. CrossRefGoogle Scholar
  35. Vagnon F, Segalini A, Ferrero AM (2015) Studies of flexible barriers under debris flow impact: an application to an Alpine Basin. In Proceedings of 1st world multidisciplinary earth sciences symposium, 15: 165–172CrossRefGoogle Scholar
  36. Vagnon F, Ferrero AM, Segalini A (2016a) EC7 design approach for debris flow flexible barriers: applicability and limitations. In: Proceedings of EUROCK 2016 ISRM international symposium—rock mechanics and rock engineering: from the past to the future. CappadociaGoogle Scholar
  37. Vagnon F, Ferrero AM, Segalini A, Pirulli M (2016b) Experimental study for the design of flexible barriers under debris flow impact. In Aversa et al. (Eds) Landslides and engineered slopes. Experience, theory and practice. Associazione Geotecnica Italiana, RomeGoogle Scholar
  38. Vagnon F, Ferrero AM, Umili G, Segalini A (2017) A factor strength approach for the design of rock fall and debris flow barriers. Geotech Geol Eng 6:2663–2675. CrossRefGoogle Scholar
  39. Vagnon F, Bonetto SMR, Ferrero AM, Migliazza MR, Umili G (2020) Rock-engineering design and NTC 2018: some open questions. Geotech Res Land Protect Dev:519–528. Google Scholar
  40. Zhang J, Xiong G (1997) Data collection of kinematic observation of debris flows in Jiangjia Ravine, Dongchuan, Yunnan (1987–1994). Science Press, BeijingGoogle Scholar
  41. Zhao L, Zuo S, Lin Y, Li L, Zhang Y (2016) Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory. Landslides 13:711–724CrossRefGoogle Scholar
  42. Zhou GGD, Ng CWW (2010) Dimensional analysis of natural debris flows. Can Geotech J 47(7):719–729CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Earth ScienceUniversity of TurinTurinItaly
  2. 2.Department of Natural Resources and Environmental EngineeringUniversity of VigoVigoSpain

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