, Volume 12, Issue 4, pp 757–772 | Cite as

Probabilistic estimation of rockfall height and kinetic energy based on a three-dimensional trajectory model and Monte Carlo simulation

  • Renato Macciotta
  • C. Derek Martin
  • David M. Cruden
Original Paper


Railways across the Canadian Cordillera have long histories of losses associated with ground hazards. The hazards most frequently reported are rockfalls, which are ubiquitous along the steep rock cuts required to accommodate the railway alignment. Several hazard control measures can be adopted in rockfall areas. However, when rockfall frequencies cannot be controlled, protective structures may be necessary to decrease rockfall-related risks to tolerable levels. Designs of protective structures require knowing rockfall trajectory heights and kinetic energies. This information is difficult to obtain even at locations where comprehensive rockfall records are kept. We present a method to calculate rockfall trajectory heights and velocities based on three-dimensional, lumped mass, rockfall simulations. Rockfall source location, model parameters and model calibration are also discussed. In this regard, the model should be calibrated against observed values of rockfall heights and velocities, and the design parameters should be validated before proceeding with the design of rockfall mitigation measures. The method is illustrated with the analysis of a section of a railway along the Canadian Cordillera. Furthermore, a probabilistic approach is adopted to calculate rockfall trajectory heights and velocities when intersecting the railway alignment. This is consistent with the natural variability of rockfall trajectories and falling block volumes. We illustrate the use of probability distributions of rockfall velocities and volumes to calculate the distribution of kinetic energy at three locations along the study section. The calculated rockfall trajectory heights are also presented in probabilistic terms and discussed. The rockfall kinetic energy distributions are used to assess the type of protective structures that could be required for further reduction of risk levels.


Rockfall Ground hazard Probabilistic analysis Trajectory modelling 



Funding for this study was provided by the Railway Ground Hazard Research Program (RGHRP) and the Canadian Railway Research Laboratory (CaRRL). The authors acknowledge the Canadian National Railway Company (CN) for providing the information needed for the study and Dr. T. Keegan from Klohn Crippen Berger Ltd. for his insights about the rockfall hazards along the study area.


  1. Agliardi F, Crosta GB (2003) High resolution three-dimensional numerical modeling of rockfalls. Int J Rock Mech Mining Sci 40:455–471CrossRefGoogle Scholar
  2. Azzoni A, de Freitas MH (1995) Experimentally gained parameters, decisive for rock fall analysis. Rock Mech Rock Eng 28(2):111–124CrossRefGoogle Scholar
  3. Bunce CM, Cruden DM, Morgenstern NR (1997) Assessment of the hazard from rock fall on a highway. Can Geotech J 34:344–356CrossRefGoogle Scholar
  4. Chiessi V, D’Orefice M, Scarascia Mugnozza G, Vitale V, Cannese C (2010) Geological, geomechanical and geostatistical assessment of rockfall hazard in San Quirico Village (Abruzzo, Italy). Geomorphology 119:117–161CrossRefGoogle Scholar
  5. Crosta GB, Agliardi F (2003) A methodology for physically based rockfall hazard assessment. Nat Hazards Earth Syst Sci 3:407–422CrossRefGoogle Scholar
  6. Cruden MD, Varnes JD (1996) Landslide types and processes. Landslides: investigation and mitigation, transportation research board (National Research Council). National Academy Press, Washington, D.C., pp 36–75Google Scholar
  7. Dorren LKA (2003) A review of rock fall mechanics and modeling approaches. Prog Phys Geogr 27(1):69–87CrossRefGoogle Scholar
  8. Dussauge-Peisser C, Helmstetter A, Grasso JR, Hantz D, Desvarreux P, Jeannin M, Giraud A (2002) Probabilistic approach to rock fall hazard assessment: potential of historical data analysis. Nat Hazards Earth Syst Sci 2:15–26CrossRefGoogle Scholar
  9. Evans SG, Hungr O (1993) The assessment of rockfall hazard at the base of talus slopes. Can Geotech J 30:620–636CrossRefGoogle Scholar
  10. Fookes PG, Sweeney M (1976) Stabilization and control of local rock falls and degrading rock slopes. Q J Eng Geol 9:37–55CrossRefGoogle Scholar
  11. Giani GP, Giacomini A, Migliazza M, Segalini A (2004) Experimental and theoretical studies to improve rock fall analysis and protection work design. Rock Mech Rock Eng 37(5):369–389CrossRefGoogle Scholar
  12. Gigli G, Morelli S, Fornera S, Casagli N (2014) Terrestrial laser scanner and geomechanical surveys for the rapid evaluation of rock fall susceptibility scenarios. Landslides 11:1–14CrossRefGoogle Scholar
  13. Guzzetti F, Crosta G, Detti R, Agliardi F (2002) STONE: a computer program for the three-dimensional simulation of rock-falls. Comput Geosci 28(9):1079–1093CrossRefGoogle Scholar
  14. Guzzetti F, Reichenbach P, Ghigi S (2004) Rockfall hazard and risk assessment along a transportation corridor in the Nera Valley, Central Italy. Environ Manag 34(2):191–208CrossRefGoogle Scholar
  15. Hantz D, Vengeon JM, Dussauge-Peisser C (2003) An historical, geomechanical and probabilistic approach to rock-fall hazard assessment. Nat Hazards Earth Syst Sci 3:693–701CrossRefGoogle Scholar
  16. Harp EL, Dart RL, Reichenbach P (2011) Rock fall simulation at Timpanogos Cave National Monument, American Fork Canyon, Utah, USA. Landslides 8:373–379CrossRefGoogle Scholar
  17. Hoek E (2007) Practical rock engineering, 2007 electronic edition, RocScience, Accessed 1 June 2013
  18. Hungr O, Evans SG, Hazzard J (1999) Magnitude and frequency of rock falls and rock slides along the main transportation corridors of southwestern British Columbia. Can Geotech J 36:224–238CrossRefGoogle Scholar
  19. Hutchinson JN (1988) Morphological and geotechnical parameters of landslides in relation to geology and hydrogeology, state-of-the-art report. In: Bonnard C (ed) Proceedings of the fifth international symposium on landslides, Lausanne, vol 1. A.A. Balkema, Rotterdam, pp 3–35Google Scholar
  20. Jones CL, Higgins JD, Andrew RD (2000) Colorado rockfall simulation program version 4.0 (for Windows). Colorado Department of Transportation, Colorado Geological SurveyGoogle Scholar
  21. Lan H, Martin CD, Lim CH (2007) Rock fall analyst: a GIS extension for three-dimensional and spatially distributed rock fall hazard modeling. Comput Geosci 33:262–279CrossRefGoogle Scholar
  22. Lan H, Martin CD, Zhou C, Lim CH (2010) Rock fall hazard analysis using LiDAR and spatial modeling. Geomorphology 118:213–223CrossRefGoogle Scholar
  23. Leroi E (2005) Global rockfalls risk management process in ‘La Désirade’ Island (French West Indies). Landslides 2:358–365CrossRefGoogle Scholar
  24. Macciotta R, Martin CD (2013). Role of 3D topography in rock fall trajectories and model sensitivity to input parameters. In: Pyrak-Nolte LJ, Chan A, Dershowitz W, Morris J, Rostami J (eds) 47th US rock mechanics/geomechanics symposium, San Francisco, California, USA, 23–26 June. pp. 1–9Google Scholar
  25. Macciotta R, Cruden DM, Martin CD, Morgenstern NR (2011) Combining geology, morphology and 3D modelling to understand the rock fall distribution along the railways in the Fraser River Valley, between Hope and Boston Bar. In: Eberhardt E, Stead D (eds) Slope stability 2011. Proceedings of the 2011 international symposium on rock slope stability in open pit mining and civil engineering. 18–21 September 2011. Canadian Rock Mechanics Association, VancouverGoogle Scholar
  26. Macciotta R, Cruden DM, Martin CD, Morgenstern NR, Petrov M (2013) Spatial and temporal aspects of slope hazards along a railroad corridor in the Canadian Cordillera. In: Dight P (ed) Slope stability 2013: international symposium on slope stability in open pit mining and civil engineering, Brisbane, Australia, pp. 1171–1186Google Scholar
  27. McTaggart KC, Thompson RM (1967) Geology of part of the Northern Cascades in Southern British Columbia. Can J Earth Sci 4:1199–1228CrossRefGoogle Scholar
  28. Paronuzzi P (1989) Probabilistic approach for design optimization of rockfall protective barriers. Q J Eng Geol 22:175–183CrossRefGoogle Scholar
  29. Peckover FL, Kerr JWG (1977) Treatment and maintenance of rock slopes on transportation routes. Can Geotech J 14(4):487–507CrossRefGoogle Scholar
  30. Perret S, Dolf F, Kienholz H (2004) Rockfalls into forests: analysis and simulation of rockfall trajectories—considerations with respect to mountainous forests in Switzerland. Landslides 1:123–130CrossRefGoogle Scholar
  31. Piteau DR (1977) Regional slope stability controls and related engineering geology of the Fraser Canyon, British Columbia. In: Coates DR (ed) Landslides—reviews in engineering geology, GSA, vol. 3, pp. 85–111Google Scholar
  32. Ritchie AM (1963) Evaluation of rockfall and its control. Highw Res Board Rec 17:13–28Google Scholar
  33. Rolland C, Prakash N, Benjamen A (1999) A multi-model view of process modelling. Requir Eng 4(4):169–187CrossRefGoogle Scholar
  34. Salciarini D, Tamagnini C, Conversini P (2009) Numerical approaches for rockfall analysis: a comparison. In: Anderssen RS, Braddock RD, Newham LTH (eds) Proceedings of the 18th world IMACS/MODSIM congress, Cairns, Australia, 13–17 July 2009. pp. 2706–2712Google Scholar
  35. Spang RM, Rautenstrauch RW (1988) Empirical and mathematical approaches to rockfall protection and their practical applications. In: Bonnard C (ed) Proceedings of the fifth international symposium on landslides, vol 2. A.A. Balkema, Rotterdam, pp 1237–1243Google Scholar
  36. Stevens W (1998) RocFall: a tool for probabilistic analysis, design of remedial measures and prediction of rockfalls. M.A.Sc. Dissertation, Department of Civil Engineering, University of Toronto, Ontario, CanadaGoogle Scholar
  37. Ushiro T, Shinohara S, Tanida K, Yagi N (2000) A study on the motion of rockfalls on slopes. In: Proceedings of the 5th symposium on impact problems in civil engineering. Japan Society of Civil Engineers, pp. 91–96Google Scholar
  38. Varnes DJ (1978) Slope movement types and processes. In: Schuster RL, Krizek RJ (eds) Landslides, analysis and control. Transportation Research Board, National Research Council, Washington, D.C. Special Report 176. pp. 11–33Google Scholar
  39. Wang X, Frattini P, Crosta GB, Zhang L, Agliardi F, Lari S, Yang Z (2013) Uncertainty assessment in quantitative rockfall risk assessment. Landslides. doi: 10.1007/s10346-013-0447-8 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Renato Macciotta
    • 1
  • C. Derek Martin
    • 2
  • David M. Cruden
    • 3
  1. 1.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  2. 2.Canadian Rail Research Laboratory, Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  3. 3.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada

Personalised recommendations