Advertisement

Rock Mechanics and Rock Engineering

, Volume 45, Issue 2, pp 131–144 | Cite as

Prediction of the Bullet Effect for Rockfall Barriers: a Scaling Approach

  • M. Spadari
  • A. Giacomini
  • O. BuzziEmail author
  • J. P. Hambleton
Original Paper

Abstract

The so-called “bullet effect” refers to the perforation of a rockfall protection mesh by impact of a small block, which has a kinetic energy lower than the design value, where the design value is determined through tests with relatively large blocks. Despite playing a key role in the overall performance of a flexible rockfall barrier, this phenomenon is still poorly understood at present. An innovative approach for quantitatively characterizing this effect based on dimensional analysis is proposed in this paper. The analysis rests on a hypothesis that the relevant variables in the impact problem can be combined into three strongly correlated dimensionless parameters. The relationship between these dimensionless parameters (i.e., the scaling relationship) is subsequently investigated and validated by means of data generated with a finite element model. The validation process shows that the dimensionless parameters are apt and that the proposed scaling relationship characterizes the bullet effect with a reasonable level of accuracy. An example from the literature involving numerical simulation of a full rock barrier is considered, and satisfactory agreement between the calculated performance of the barrier and that predicted by the established scaling relationship is observed.

Keywords

Rockfall barrier Kinetic energy Bullet effect Stress concentration Dimensional analysis 

References

  1. Anderheggen E, Volkwein A, Grassl H (2002) Numerical simulation of highly flexible rockfall protection systems. In: Proceedings of Fifth World Congress on Computational Mechanics. Vienna, AustriaGoogle Scholar
  2. Arndt B, Ortiz T, Turner AK (2009) Colorado’s full-scale field testing of rockfall attenuator systems. Transp Res E-Circular, E-C141. Transportation Research Board, ColoradoGoogle Scholar
  3. Bertolo P, Oggeri C, Peila D (2009) Full-scale testing of draped nets for rock fall protection. Can Geotech J 46(3):306–317. doi: 10.1139/T08-126 CrossRefGoogle Scholar
  4. Buckingham E (1914) On physically similar systems: illustrations of the use of dimensional analysis. Phys Rev 4:345–376CrossRefGoogle Scholar
  5. Buzzi O, Giacomini A, Spadari M, Fityus S (2011) Numerical modeling of a rock fall mesh perforation upon impact. In: Proceedings of the 13th International Conference of the IACMAG 2011. Sydney, Australia, pp 1141–1146Google Scholar
  6. Cantarelli G, Giani GP, Gottardi G, Govoni L (2008) Modelling rockfall protection fences. In: The first world landslide forum—Proceedings. ICL, Tokyo, pp 103–108Google Scholar
  7. Cazzani A, Mongiovì L, Frenez T (2002) Dynamic finite element analysis of interceptive devices for falling rocks. Int J Rock Mech Min Sci 39(3):303–321. doi: 10.1016/s1365-1609(02)00037-0 CrossRefGoogle Scholar
  8. De Col R, Cocco (1996) Motivazioni tecniche ed economiche per la standardizzazione di prove sulle opere paramassi nella Provincia Autonoma di Trento. In: Giornata di studio su “La protezione contro la caduta di massi dai versanti rocciosi”. GEAM, Torino, pp 65–72Google Scholar
  9. Descoeudres F, Montani Stoffel S, Böll A, Gerber W, Labiouse V (1999) Rockfalls. In: Coping study on disaster resilient infrastructure. IDNDR, Zurich, pp 37–47Google Scholar
  10. Duffy JD, Smith DD (1990) Field tests and evaluation of rockfall restraining nets. No. CA/TL-90/05, Final Report. California Dept. of Transportation, San Luis ObispoGoogle Scholar
  11. EOTA (2008) Guideline for European technical approval of falling rock protection kits (ETAG 027). BrusselsGoogle Scholar
  12. Gerber W (2001) Guideline for the approval of rockfall protection kits. Swiss Agency for the Environment, Forests and Landscape (SAEFL), Swiss Federal Research Institute, BerneGoogle Scholar
  13. Giani GP (1992) Rock slope stability analysis. Balkema, RotterdamGoogle Scholar
  14. Grassl H, Volkwein A, Anderheggen E, Ammann WJ (2002) Steel-net rockfall protection—experimental and numerical simulation. In: Seventh International Conference on Structures Under Shock and Impact. Montreal, Canada, pp 143–153Google Scholar
  15. Hearn G, Barrett RK, Henson HH (1995) Testing and modeling of two rockfall barriers. In: Transportation research record, vol. 1504. National Research Council, Washington, pp 1–11Google Scholar
  16. Johnson W (1972) Impact strength of materials. Edward Arnold, LondonGoogle Scholar
  17. Langhaar HL (1951) Dimensional analysis and theory of models. Wiley, New YorkGoogle Scholar
  18. Li QM, Jones N (2000) On dimensionless numbers for dynamic plastic response of structural members. Arch Appl Mech 70(4):245–254CrossRefGoogle Scholar
  19. Peila D, Oggeri C (2005) Barriere paramassi a rete - Tecnologia e criteri pregettuali. GEAM, TorinoGoogle Scholar
  20. Peila D, Pelizza S, Sassudelli F (1998) Evaluation of behaviour of rockfall restraining nets by full scale tests. Rock Mech Rock Eng 31(1):1–24CrossRefGoogle Scholar
  21. Volkwein A (2005) Numerical Simulation of flexible rockfall protection systems. In: Proceedings of Computing in Civil Engineering. ASCE, CancunGoogle Scholar
  22. Volkwein A, Melis L, Haller B, Pfeifer R (2005) Protection from landslides and high speed rockfall events—reconstruction of Chapman’s Peak Drive. In: IABSE Symposium Lisbon 2005. Structures and extrem events. IABSE Reports vol. 90, incl. CD: 8 pGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • M. Spadari
    • 1
  • A. Giacomini
    • 1
  • O. Buzzi
    • 1
    Email author
  • J. P. Hambleton
    • 1
  1. 1.Centre for Geotechnical and Materials ModellingThe University of NewcastleCallaghanAustralia

Personalised recommendations