On the Computational Efficiency of the Hybrid Approach in Numerical Simulation of Rockall Flexible Chain-Link Mesh

  • S. TahmasbiEmail author
  • A. Giacomini
  • C. Wendeler
  • O. Buzzi
Original Paper


Rigorous design of flexible rockfall protection systems requires an adequate understanding of the system performance. In recent decades, finite element simulations have complemented experimental testing for economical and practical reasons. However, complex modelling techniques are required to capture the dynamic response of such systems, which leads to considerable computational costs. This paper presents a new approach called “hybrid method” to improve the computational efficiency of FE models with minimum effects on the results accuracy. The method is based on the idea to model the exact architecture of the wire net in the vicinity of impact (zone undergoing plastic deformation and failure) and to model the mesh with less computationally expensive elements far from the impact (zones undergoing elastic deformation). To this aim, a three-dimensional model of chain-link mesh was developed using commercial finite element code ABAQUS. The real architecture of the wires is modelled and discretised using three-dimensional beam elements. Homogenised shell surfaces are used to model the chain-link away from the impact zone. The model was calibrated and validated against published experimental data. The results prove that the proposed hybrid method leads to considerable reduction in computational costs of the finite element analysis while producing accurate results.


Rockfall barrier Chain-link wire net Finite element analysis Hybrid method Shell elements 

List of Symbols


The smaller diagonal of the chain-link rhomboid


The larger diagonal of the chain-link rhomboid


The smaller angle of the chain-link rhomboid


The aperture size of the chain-link rhomboid


The diameter of the chain-link wires


Stress triaxiality


Hydrostatic pressure


Mises equivalent stress

\(\dot{\bar{\varepsilon }}^{\text{pl}}\)

Equivalent plastic strain rate

\(\dot{\varepsilon }^{\text{pl}}\)

Plastic strain rate


Damage factor


Exponent of the damage evolution law formulation


Equivalent plastic displacement


Equivalent plastic displacement at failure


Characteristic length of the element


Block impact velocity


Block initial velocity


Gravity acceleration


Vertical distance between the block and the mesh at the end of gravity step


Initial distance (before gravity step) between the block and the mesh


Initial sag of the mesh at the end of gravity step




Young’s modulus


Poisson ratio


Shear modulus






Area of the shell surface


Mass of the mesh replaced with shell surface


Thickness of the shell surface



  1. ABAQUS (2011) ABAQUS/CAE 6.11 User’s Manual, Online Documentation Help. In: Dassault SystèmesGoogle Scholar
  2. Anderheggen E, Volkwein A, Grassl H (2002) Numerical simulation of highly flexible rockfall protection systems. In: Fifth world congress on computational geomechanics, Vienna, AustriaGoogle Scholar
  3. Bertrand D, Nicot F, Gotteland P, Lambert S (2008) Discrete element method (DEM) numerical modeling of double-twisted hexagonal mesh. Can Geotech J 45(8):1104–1117CrossRefGoogle Scholar
  4. Breugnot A, Lambert S, Villard P, Gotteland P (2016) A discrete/continuous coupled approach for modeling impacts on cellular geostructures. Rock Mech Min Sci 49(5):1831–1848Google Scholar
  5. Buzzi O, Giacomini A, Spadari M, Fityus S (2011) Numerical modeling of a rock fall mesh perforation upon impact In: 13th international conference of IACMAG, Melbourn, AustraliaGoogle Scholar
  6. Buzzi O, Leonarduzzi E, Krummenacher B, Volkwein A, Giacomini A (2015) Performance of high strength rock fall meshes: effect of block size and mesh geometry. Rock Mech Rock Eng 48:1221–1231CrossRefGoogle 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 29:303–321CrossRefGoogle Scholar
  8. Duffy JD, Hoon W (1996a) Field Tests and Evaluation of Hi-Tech Low Energy Chain Link Rockfall Fence, Report No. CA/05-96-01. In: California Department of Transportation, San Luis Obispo, California, USAGoogle Scholar
  9. Duffy JD, Smith DD (1990) Field test and evaluation of rockfall restraining nets. Research Report CA/TL-90/05. In: California Department of TransportationGoogle Scholar
  10. EOTA (2008) ETAG 027: guideline for European technical approval of falling rock protection kits; 06, 2013Google Scholar
  11. Escallón JP, Boetticher V, Wendeler C, Chatzi E, Bartelt P (2015) Mechanics of chain-link wire nets with loose connections. Eng Struct 101:68–87CrossRefGoogle Scholar
  12. Gentilini C, Govoni L, de Miranda S, Gottardi G, Ubertini F (2012) Three-dimensional numerical modelling of falling rock protection barriers. Comput Geotech 44:58–72CrossRefGoogle Scholar
  13. Grassl H, Bartelt P, Volkwein A, Wartmann S (2003) (2003). Experimental and numerical modelling of highly flexible rockfall protection barriers. In: 12th Panamerican conference on soil mechanics and geotechnical engineering, Cambridge, Massachusetts, USA, pp 2589–2594Google Scholar
  14. Hearn G (1992) High-capacity flexpost rockfall fences. In: Colorado Department of Transportation, Denver, ColoradoGoogle Scholar
  15. Mentani A, Govoni L, Gottardi G, Lambert S, Bourrier F, Toe D (2016) A new approach to evaluate the effectiveness of rockfall barriers. Procedia Eng 158:398–403CrossRefGoogle Scholar
  16. Mentani A, Govoni L, Giacomini A, Gottardi G, Buzzi O (2018) An equivalent continuum approach to efficiently model the response of steel wire meshes to rockfall impacts. Rock Mech Rock Eng 2018:1–14Google Scholar
  17. Muhunthan B, Shu S, Sasiharan N, Hattamleh OA (2005) Analysis and design of wire mesh/cable net slope protection. In: Washington State Department of Transportation, WashingtonGoogle Scholar
  18. Nilakantan G, Keefe M, Bogetti TA, Adkinson R, Gillespie JW (2010) On the finite element analysis of woven fabric impact using multiscale modeling techniques. Int J Solids Struct 47(17):2300–2315CrossRefGoogle Scholar
  19. Peila D, Pelizza S, Sassudelli F (1998) Evaluation of behaviour of rockfall restraining nets by full scale tests. Rock Mech Rock Eng 1998:1–24CrossRefGoogle Scholar
  20. Persson BNJ (2000) Sliding friction: physical principles and applications, nanoscience and technology. Springer, BerlinCrossRefGoogle Scholar
  21. Thoeni K, Lambert C, Giacomini A, Sloan S (2011) Discrete modelling of a rockfall protective system. In: International conference on particle-based methods—fundamentals and applications, pp 24–32Google Scholar
  22. 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 EngGoogle Scholar
  23. Tran PV, Maegawa K, Fukada S (2012) Experiments and dynamic finite element analysis of a wire-rope rockfall protective fence. Rock Mech Rock Eng 46:1183–1198CrossRefGoogle Scholar
  24. Volkwein A (2005) Numerical simulation of flexible rockfall protection systems. In: Computing in civil engineering, Cancun, Mexico.

Copyright information

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

Authors and Affiliations

  1. 1.Priority Research Centre for Geotechnical Science in EngineeringUniversity of NewcastleCallaghanAustralia
  2. 2.Geobrugg AG-Geohazard SolutionsRomanshornSwitzerland

Personalised recommendations