Effect of Impact Angle and Rotational Motion of Spherical Blocks on the Coefficients of Restitution for Rockfalls

  • Pavlos Asteriou
Original Paper


The coefficients of restitution are among the most important parameters in rockfall trajectory modelling. However, they are difficult to obtain, they depend on many parameters and they present a significant variation even for similar geotechnical and kinematic conditions. Many definitions for the coefficients of restitution exist, but there is no agreement on which describes better the response of a block to an impact. In this paper, an extensive experimental investigation is presented, consisting of 600 oblique impact tests and the various coefficient of restitution definitions are assessed, with an emphasis on the effects of impact angle and angular velocity. These tests follow on the research presented in Asteriou and Tsiambaos (Int J Rock Mech Min Sci 106:41–50, 2018), where free-fall tests were performed to address the effects of impact velocity, block mass and material type. It was found that all those parameters affect significantly the coefficients of restitution. Moreover, an empirical model was proposed to estimate the coefficient of restitution for central impacts. The applicability of this model is extended for oblique impacts based on the results of the tests presented in this paper.


Coefficients of restitution Impact angle Translational and rotational motion Rockfall modelling 



This post-doctoral research was carried out with a scholarship granted by the State Scholarships Foundation of Greece (IKY) under the act “Supporting Post-Doctoral Researchers” of the Operational Program “Human Resources Development, Education and Life Lifelong Learning” (Thematic Priority Axes 6, 8, 9) and is co-funded by the European Social Fund (ESF) and the Greek Government.


  1. Asteriou P, Tsiambaos G (2016) Empirical model for predicting rockfall trajectory direction. Rock Mech Eng 49(3):927–941CrossRefGoogle 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. Asteriou P, Saroglou H, Tsiambaos G (2013) Rockfalls: influence of rock hardness on the trajectory of falling rock blocks. Bulletin of the Geological Society of Greece, Greece, vol XLVIIGoogle Scholar
  5. Broili L (1977) Relations between scree slope morphometry and dynamics of accumulation processes. In: Meeting on Rockfall dynamics and protective works effectiveness, pp 11–23Google Scholar
  6. Buzzi O, Giacomini A, Spadari M (2012) Laboratory investigation on high values of restitution coefficients. Rock Mech Rock Eng 45(1):35–43CrossRefGoogle Scholar
  7. Cagnoli B, Manga M (2003) Pumice-pumice collisions and the effect of the impact angle. Geophys Res Lett 30(12):1636 CrossRefGoogle Scholar
  8. Chau K, Wong R, Wu J (2002) Coefficient of restitution and rotational motions of rockfall impacts. Int J Rock Mech Min Sci 39(1):69–77CrossRefGoogle Scholar
  9. Descoeudres F, Zimmermann T et al (1987) Three-dimensional dynamic calculation of rockfalls. In: 6th ISRM Congress, International Society for Rock MechanicsGoogle Scholar
  10. Dorren L (2015) Rockyfor3d (v5.2) revealed-transparent description of the complete 3d rockfall model. Technical. Report.
  11. Ferrari F, Giani G, Apuani T (2013) Why can rockfall normal restitution coefficient be higher than one. Rend Online Soc Geol Ital 24:122–124Google Scholar
  12. Giacomini A, Thoeni K, Lambert C, Booth S, Sloan S (2012) Experimental study on rockfall drapery systems for open pit highwalls. Int J Rock Mech Min Sci 56:171–181CrossRefGoogle Scholar
  13. Giani G (1992) Rock slope stability analysis. CRC Press, Boca RatonGoogle Scholar
  14. Goldsmith W (1960) Impact: the theory and physical behavior of colliding solids. Arnold, LondonGoogle Scholar
  15. Habib P (1977) Note sur le rebondissement des blocs rocheux. Rockfall dynamics and protective works effectiveness, ISMES Publication No. 90, pp 123–125Google Scholar
  16. Jones C, Higgins J, Andrew R (2000) Colorado Rockfall Simulation Program: Version 4.0 (for Windows)Google Scholar
  17. Labiouse V, Heidenreich B (2009) Half-scale experimental study of rockfall impacts on sandy slopes. Nat Hazards Earth Syst Sci 9(6):1981–1993CrossRefGoogle Scholar
  18. Paronuzzi P (2009) Field evidence and kinematical back-analysis of block rebounds: the Lavone Rockfall, northern Italy. Rock Mech Rock Eng 42(5):783–813CrossRefGoogle Scholar
  19. Pfeiffer T, Bowen T (1989) Computer simulation of rockfalls. Bull Assoc Eng Geol 26(1):135–146Google Scholar
  20. RocScience (2003) Advanced tutorial: determining input parameters for a RocFall analysis.
  21. Spadari M, Giacomini A, Buzzi O, Fityus S, Giani G (2012) In situ rockfall testing in new south wales, australia. Int J Rock Mech Min Sci 49:84–93CrossRefGoogle Scholar
  22. Ulusay R, Hudson J (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. International Society for Rock Mechanics, Commission on Testing MethodsGoogle Scholar
  23. Umbach D, Jones K (2003) A few methods for fitting circles to data. IEEE Trans Instrum Meas 52(6):1881–1885CrossRefGoogle Scholar
  24. Wu J (1985) Rockfall evaluation by computer simulation. No. 1031Google Scholar
  25. Wyllie D (2014) Calibration of rock fall modeling parameters. Int J Rock Mech Min Sci 67:170–180CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.National Technical University of AthensZografou, AthensGreece

Personalised recommendations