, Volume 16, Issue 12, pp 2353–2367 | Cite as

Modelling rockfall impact with scarring in compactable soils

  • Guang LuEmail author
  • Andrin Caviezel
  • Marc Christen
  • Sophia E. Demmel
  • Adrian Ringenbach
  • Yves Bühler
  • Claire E. Dinneen
  • Werner Gerber
  • Perry Bartelt
Original Paper


An accurate modelling of rockfall runout continues to be a demanding challenge within the geotechnical and hazards engineering community. Most existing rockfall dynamic programs apply effective restitution coefficients to model the energy dissipation during the rock-ground interaction. Recent experimental measurements, however, reveal the limitations of effective restitution coefficients, especially to account for scarring with frictional rebound in soft compactable soils. This study proposes a three-dimensional, non-smooth computational mechanic approach to model dissipative rock-ground interactions in soft compactable soils. The ground is mathematically divided into a soft, compactable scarring layer and a hard rebound layer. The model considers the plastic deformation of the ground with rotating rocks of general, non-spherical shape. The simulated rockfall energy dissipation is validated at both the single impact and multi-impact levels using induced 780-kg rockfall experiments performed at Chant Sura, Switzerland, in 2018. Overall, the numerical results are in good quantitative agreement with the experimental measurements. Ongoing improvements of the scar drag model are to integrate rotational drag into the rock energy dissipation term, and to calibrate the drag parameters in depths using repetitive rockfall experiments spanning a greater range of rock shapes and masses.


Rockfall Scarring drag Non-smooth mechanics Computational modelling Simulation 


  1. Albert I, Sample JG, Morss AJ, Rajagopalan S, Barabási AL, Schiffer P (2001) Granular drag on a discrete object: shape effects on jamming. Phys Rev E 64:061303CrossRefGoogle Scholar
  2. Asteriou P, Tsiambaos G (2018) Effect of impact velocity, block mass and hardness on the coefficients of restitution for rockfall analysis. Int J Rock Mech Min Sci 106:41–50CrossRefGoogle Scholar
  3. Asteriou P, Saroglou H, Tsiambaos G (2012) Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis. Int J Rock Mech Min Sci 54:103–113CrossRefGoogle Scholar
  4. Bartelt P, Gerber W, Christen M, Bühler Y (2016) Modeling rockfall trajectories with non-smooth contact/impact mechanics. In: Koboltschnig G (ed) Proc., 13th Congress INTERPRAEVENT, International Research Society INTERPRAEVENT, Luzern, Switzerland, pp 203–211Google Scholar
  5. Blasio FVD, Dattola G, Crosta GB (2018) Extremely energetic rockfalls. J Geophys Res Earth Surf 123:2392–2421CrossRefGoogle Scholar
  6. Bourrier F, Berger F, Tardif P, Dorren L, Hungr O (2012) Rockfall rebound: comparison of detailed field experiments and alternative modelling approaches. Earth Surf Process Landf 37:656–665CrossRefGoogle Scholar
  7. Caviezel A, Gerber W (2018) Brief communication: measuring rock decelerations and rotation changes during short-duration ground impacts. Nat Hazards Earth Syst Sci 18:3145–3151CrossRefGoogle Scholar
  8. Caviezel A, Bühler Y, Lu G, Christen M, Bartelt P (2018a) Experimental validation of numerical rockfall trajectory models. In: Cardoso AS, Borges JL, Costa PA, Gomes AT, Marques JC, Vieira CS (eds) Proc., 9th European Conference on Numerical Methods in Geotechnical Engineering, Faculty of Engineering, University of Porto, Taylor & Francis, Porto, Portugal, pp 875–883Google Scholar
  9. Caviezel A, Schaffner M, Cavigelli L, Niklaus P, Bühler Y, Bartelt P, Magno M, Benini L (2018b) Design and evaluation of a low-power sensor device for induced rockfall experiments. IEEE Trans Instrum Meas 67:767–779CrossRefGoogle Scholar
  10. Caviezel A, Demmel SE, Ringenbach A, Bühler Y, Lu G, Christen M, Dinneen CE, Eberhard LA, von Rickenbach D, Bartelt P (2019) Reconstruction of three-dimensional rockfall trajectories using remote sensing and rock-based accelerometers and gyroscopes. Earth Surf Dyn 7:199–210CrossRefGoogle Scholar
  11. Christen M, Bühler Y, Bartelt P, Leine R, Glover J, Schweizer A, Graf C, McArdell BW, Gerber W, Deubelbeiss Y, Feistl T, Volkwein A (2012) Integral hazard management using a unified software environment: numerical simulation tool “ramms” for gravitational natural hazards. In: Koboltschnig G, Hübl J, Braun J (eds) Proc., 12th Congress INTERPRAEVENT, International Research Society INTERPRAEVENT, Grenoble, France, pp 77–86Google Scholar
  12. Corona C, Lopez-Saez J, Favillier A, Mainieri R, Eckert N, Trappmann D, Stoffel M, Bourrier F, Berger F (2017) Modeling rockfall frequency and bounce height from three-dimensional simulation process models and growth disturbances in submontane broadleaved trees. Geomorphology 281:66–77CrossRefGoogle Scholar
  13. Dorren LKA (2016) Rockyfor3D (v5.2) revealed – transparent description of the complete 3D rockfall model. ecorisQ paper ( 32p
  14. Effeindzourou A, Thoeni K, Giacomini A, Wendeler C (2017) Efficient discrete modelling of composite structures for rockfall protection. Comput Geotech 87:99–114CrossRefGoogle Scholar
  15. Gang L, Hu XW, Du YJ, Fu JK, Mei XF (2018) A collision fragmentation model for predicting the distal reach of brittle fragmentable rock initiated from a cliff. Bull Eng Geol Environ 78:579–592Google Scholar
  16. Gao G, Meguid MA (2018) On the role of sphericity of falling rock clusters − insights from experimental and numerical investigations. Landslides 15:219–232CrossRefGoogle Scholar
  17. Gerber W (2019) Naturgefahr Steinschlag: Erfahrungen und Erkenntnisse. WSL-Bericht, BirmensdorfGoogle Scholar
  18. Gischig VS, Hungr O, Mitchell A, Bourrier F (2015) Pierre3d: a 3d stochastic rockfall simulator based on random ground roughness and hyperbolic restitution factors. Can Geotech J 52:1360–1373CrossRefGoogle Scholar
  19. Gratchev I, Saeidi S (2018) The effect of surface irregularities on a falling rock motion. Geomech Geoeng 14:52–58CrossRefGoogle Scholar
  20. Lambert S, Bourrier F, Toe D (2013) Improving three-dimensional rockfall trajectory simulation codes for assessing the efficiency of protective embankments. Int J Rock Mech Min Sci 60:26–36CrossRefGoogle Scholar
  21. Leine RI, Schweizer A, Christen M, Glover J, Bartelt P, Gerber W (2014) Simulation of rockfall trajectories with consideration of rock shape. Multibody Syst Dyn 32:241–271CrossRefGoogle Scholar
  22. Li LP, Lan HX (2015) Probabilistic modeling of rockfall trajectories: a review. Bull Eng Geol Environ 74:1163–1176CrossRefGoogle Scholar
  23. Li XF, Li HB, Zhang QB, Jiang JL, Zhao J (2018) Dynamic fragmentation of rock material: characteristic size, fragment distribution and pulverization law. Eng Fract Mech 199:739–759CrossRefGoogle Scholar
  24. Lu G, Third JR, Müller CR (2015) Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem Eng Sci 127:425–465CrossRefGoogle Scholar
  25. Lu G, Caviezel A, Christen M, Bühler Y, Bartelt P (2018) Modelling rockfall dynamics using (convex) non-smooth mechanics. In: Cardoso AS, Borges JL, Costa PA, Gomes AT, Marques JC, Vieira CS (eds) Proc., 9th European Conference on Numerical Methods in Geotechnical Engineering, Faculty of Engineering, University of Porto, Taylor & Francis, Porto, Portugal, pp 575–583Google Scholar
  26. Macciotta R, Martin CD, Cruden DM (2015) Probabilistic estimation of rockfall height and kinetic energy based on a three-dimensional trajectory model and Monte Carlo simulation. Landslides 12:757–772CrossRefGoogle Scholar
  27. Studer C, Leine RI, Glocker C (2008) Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics. Int J Numer Methods Eng 76:1747–1781CrossRefGoogle Scholar
  28. Thoeni K, Giacomini A, Lambert C, Sloan SW, Carter JP (2014) A 3d discrete element modelling approach for rockfall analysis with drapery systems. Int J Rock Mech Min Sci 68:107–119CrossRefGoogle Scholar
  29. 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 51:1097–1109CrossRefGoogle Scholar
  30. Volkwein A, Schellenberg K, Labiouse V, Agliardi F, Berger F, Bourrier F, LKA D, Gerber W, Jaboyedoff M (2011) Rockfall characterisation and structural protection − a review. Nat Hazards Earth Syst Sci 11:2617–2651CrossRefGoogle Scholar
  31. Volkwein A, Brügger L, Gees F, Gerber W, Krummenacher B, Kummer P, Lardon J, Sutter T (2018) Repetitive rockfall trajectory testing. Geosciences 8:88CrossRefGoogle Scholar
  32. Wang YH, Jiang W, Cheng SG, Song PC, Mao C (2018) Effects of the impact angle on the coefficient of restitution in rockfall analysis based on a medium-scale laboratory test. Nat Hazards Earth Syst Sci 18:3045–3061CrossRefGoogle Scholar
  33. Zhang YL, Liu ZB, Shi C, Shao JF (2018) Three-dimensional reconstruction of block shape irregularity and its effects on block impacts using an energy-based approach. Rock Mech Rock Eng 51:1173–1191CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.WSL Institute for Snow and Avalanche Research SLFDavos DorfSwitzerland
  2. 2.Swiss Federal Institute for Forest, Snow and Landscape Research WSLBirmensdorfSwitzerland

Personalised recommendations