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A Discrete/continuous Coupled Approach for Modeling Impacts on Cellular Geostructures

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Abstract

This article presents a numerical model coupling the finite difference method and discrete element methods (FDM, DEM) for simulating the response of cellular geostructures to impacts. DEM is used in the vicinity of the impacted area while FDM is used far away. The continuity between the DEM and FDM domains is insured using the edge-to-edge method. The numerical parameters are calibrated based on compression and impact experiments conducted on elementary cells. Numerical simulations at the structure scale are compared with real-scale experimental data. The response of the structure is addressed varying the impact conditions. The projectile shape and the position of the impact point appear to be the most influential parameters.

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Abbreviations

α :

Discrete/continuous domains coupling coefficient

β :

Continuous/discrete domains coupling coefficient

\(C_{u/l}\) :

Ratio between unloading and loading stiffness of wire elements

\({\mathbf{d}}_{{\mathbf{j}}}\) :

Displacement of particle j

\({\mathbf{\textit{\"{d}}}}_{{\mathbf{j}}}\) :

Acceleration of particle j

DEM:

Discrete element method

D r :

Relative density

E :

Young’s modulus

E t :

Wire mesh tensile modulus

FDM:

Finite difference method

\({\mathbf{F}}_{{\mathbf{i}}}^{{{\mathbf{tot}}}}\) :

External forces on continuous element i

\({\mathbf{F}}_{{\mathbf{j}}}^{{{\mathbf{tot}}}}\) :

External forces applied on particle j

H:

Hamiltonian operator

\({\mathbf{K}}\) :

Kinematic matrix

\({\mathbf{k}}_{ik}\) :

Elementary kinematic matrix

K l :

Tensile stiffness of wire elements

k n :

Interparticles normal contact stiffness

K n :

Constitutive material normal stiffness

k s :

Interparticles tangential contact stiffness

K s :

Constitutive material tangential stiffness

K u :

Unloading stiffness of wire elements

\({\varvec{\uplambda}}\) :

Lagrange multiplier coefficients

\({\varvec{\Lambda}}\) :

Vector composed of the Lagrange multiplier coefficients

µ :

Microscopic interparticle friction parameter

\(m_{j}\) :

Mass of particle j

\(M_{i}\) :

Mass of continuous element i

\(R_{j}\) :

Radius of discrete particle j

\({\mathbf{\textit{\"{u}}}}_{{\mathbf{i}}}\) :

Acceleration of the continuous element i

\({\mathbf{u}}_{{\mathbf{i}}}\) :

Displacement of the continuous element i

v :

Poisson ratio

References

  • Amato G, O’Brien F, Simms CK, Ghosh B (2013) Multibody modelling of gabion beams for impact applications. Int J Crashworthin. doi:10.1080/13588265.2013.775739

    Google Scholar 

  • Anciaux G (2007) Simulation multi-échelle des solides par une approche couplée dynamique moléculaire/éléments finis. De la modélisation à la simulation haute performance, Ph.D dissertation, University of Bordeaux

  • Bardet JP (1998) Introduction to computational granular mechanics. In: Cambou B (ed) Behaviour of granular materials. Springer, Vienna, pp 99–169

    Chapter  Google Scholar 

  • Bertrand D, Nicot F, Gotteland P, Lambert S (2005) Modelling a geo-composite cell using discrete analysis. Comput Geotech. doi:10.1016/j.compgeo.2005.11.004

    Google Scholar 

  • Bertrand D, Nicot F, Gotteland P, Lambert S (2008) Discrete element method (DEM) numerical modeling of double-twisted hexagonal mesh. Can Geotech J. doi:10.1139/T08-036

    Google Scholar 

  • Bertrand D, Lambert S, Gotteland P, Nicot F (2010) Les merlons à structure cellulaire. In: Lambert S, Nicot F (eds) Géo-mécanique des instabilités rocheuses: du déclenchement à l’ouvrage. Lavoisier, Paris, pp 369–402

    Google Scholar 

  • Bourrier F, Lambert S, Heymann A, Gotteland P, Nicot F (2011) How multi-scale approaches can benefit cellular structure design. Can Geotech J. doi:10.1139/cgj-2013-0194

    Google Scholar 

  • Breugnot A, Gotteland P, Villard P, Garcin P (2010) Modelling of block impacts with a combined discrete-continuum approach. In: proceedings of the 3rd Euro Mediterranean Symposium on Advances in Geomaterials and Structures, Djerba, Tunisia, 10–12 May 2010, pp 289–295

  • Broughton J, Abraham F, Bernstein N, Kasiras E (1999) Concurrent coupling of length scales: methodology and application. Phys Rev B. doi:10.1103/PhysRevB.60.2391

    Google Scholar 

  • Cai M, Kaiser PK, Morioka H, Minami M, Maejima T, Tasaka Y, Kurose H (2007) FLAC/PFC coupled numerical simulation of AE in large-scale underground excavations. Int J Rock Mech Min. doi:10.1016/j.ijrmms.2006.09.013

    Google Scholar 

  • Chareyre B, Villard P (2005) Dynamic spar elements and discrete element methods in two dimensions for the modeling of soil-inclusion problems. J Eng Mech-ASCE. doi:10.1061/(ASCE)0733-9399(2005)131:7(689)

    Google Scholar 

  • Curtin WA, Miller RE (2003) Atomistic/continuum coupling in computational materials science. Model Simulation Mater Sci Eng. doi:10.1088/0965-0393/11/3/201

    Google Scholar 

  • Degago SA, Ebeltoft R, Nordal S (2008) Effect of rock fall geometries impacting soil cushion: a numerical procedure. In: proceedings of the 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG), Goa, India, 1–6 October 2008, pp 4517–4521

  • Dimnet E, Haza-Rozier E, Vinceslas G, Leon R, Hernandez G (2013) Experimental and numerical study of a shock-absorbing structure. Acta Mech. doi:10.1007/s00707-013-0900-8

    Google Scholar 

  • Frangin E, Marin P, Daudeville L (2007) Approche couplée éléments discrets/finis pour la simulation d’un impact sur ouvrage. Revue Européenne de Mécanique Numérique. doi:10.3166/remn.16.989-1009

    Google Scholar 

  • Frossard E (2001) L’approche énergétique en mécanique des milieux granulaires. Poudres et grains, NS-2:1-56

  • Gotteland P, Lambert S, Balachovski L (2005) Strenght characteristics of tyre chips-sand mixtures. Stud Geotech Mech 27:55–66

    Google Scholar 

  • Ho TS, Masuya H (2013) Finite element analysis of the dynamic behavior of sand-filled geocells subjected to impact load by rockfall. Int J of Erosion Control Eng 6(1):1–12

    Article  Google Scholar 

  • Itasca Consulting Group (2006) Fish in PFC3D, AC/DC (Adaptive Continuum/Discontinuum) logic

  • Lambert S, Bourrier F (2013) Design of rockfall protection embankments: a review. Eng Geol. doi:10.1016/j.enggeo.2012.12.012

  • Lambert S, Gotteland P, Nicot F (2009) Experimental study of the impact response of geocells as components of rockfall protection embankments. Nat Hazards Earth Syst. doi:10.5194/nhess-9-459-2009

    Google Scholar 

  • Lambert S, Nicot F, Gotteland P (2011) Uniaxial compressive behavior of scrapped-tire and sand-filled wire netted geocell with a geotextile envelope. Geotext geomembranes. doi:10.1016/j.geotexmem.2011.04.001

    Google Scholar 

  • Lambert S, Heymann A, Gotteland P, Nicot F (2014) Real-scale investigation of the kinematic response of a rockfall protection embankment. Nat Hazards Earth Syst. doi:10.5194/nhess-14-1269-2014

    Google Scholar 

  • Li M, Yu H, Wang J, Xia X, Chen J (2015) A multiscale coupling approach between discrete element method and finite difference method for dynamic analysis. Int J Num Method Eng. 102:1–21. doi:10.1002/nme.4771

    Article  Google Scholar 

  • Liu WK, Karpov EG, Park HS (2006) Nano mechanics and materials. Wiley, New York

    Book  Google Scholar 

  • Lorentz J, Plassiard JP, Muquet L (2010) An innovative design process for rockfall embankments: application in the protection of a building at Val d’Isère. In: proceedings of the 3rd Euro Mediterranean Symposium on Advances in Geomaterials and Structures, Djerba, Tunisia, 10–12 May 2010, pp 277–282

  • Miller RE, Tadmor EB (2003) The quasicontinuum method: overviews, applications and current direction. J Comput Aided Mater Des. doi:10.1023/A:1026098010127

    Google Scholar 

  • Munjiza A (2004) The Combined Finite-Discrete Element Method. Wiley, New York

    Book  Google Scholar 

  • Oñate E (2003) Multiscale computational analysis in mechanics using finite calculus: an introduction. Comput Method Appl M. doi:10.1016/S00457825(03)00340-2

    Google Scholar 

  • ÖNORM 24810 (2013) Technical protection against rockfall—Terms and definitions, effects of actions, design, monitoring and maintenance. Austrian standard. Vienna. p 65

  • Peila D, Oggeri C, Castiglia C (2007) Ground reinforced embankments for rockfall protection: design and evaluation of full scale tests. Landslides. doi:10.1007/s10346-007-0081-4

    Google Scholar 

  • Plassiard JP, Donzé FV (2009) Rockfall impact parameters on embankments: a discrete element method analysis. Structural Eng Int. doi:10.2749/101686609788957874

    Google Scholar 

  • Plassiard JP, Donzé FV (2010) Optimizing the design of rockfall embankments with a discrete element method. Eng Struct. doi:10.1016/j.engstruct.2010.08.025

    Google Scholar 

  • Ronco C, Oggeri C, Peila D (2009) Design of reinforced ground embankments used for rockfall protection. Hazards Earth Syst, Nat. doi:10.5194/nhess-9-1189-2009

    Google Scholar 

  • Salot C, Gotteland P, Villard P (2009) Influence of relative density on granular materials behavior: DEM simulations of triaxial tests. Granular Matter. doi:10.1007/s10035-009-0138-2

    Google Scholar 

  • Scherbatiuk K, Rattanawangcharoen N, Pope DJ, Fowler J (2008) Generation of a pressure-impulse for a temporary soil wall using an analytical rigid-body rotation model. Int J Impact Eng. doi:10.1016/j.ijimpeng.2007.04.006

    Google Scholar 

  • Soudé M, Chevalier B, Grédiac M, Talon A, Gourvès R (2013) Experimental and numerical investigation of the response of geocell-reinforced walls to horizontal localized impact. Geotext Geomembranes. doi:10.1016/j.geotexmem.2013.07.006

    Google Scholar 

  • Villard P, Chevalier B, Le Hello B, Combe G (2009) Coupling between finite and discrete element methods for the modelling of earth structures reinforced by geosynthetic. Comput Geotech. doi:10.1016/j.compgeo.2008.11.005

    Google Scholar 

  • Wang B, Cavers DS (2008) A simplified approach for rockfall ground penetration and impact stress calculations. Landslides. doi:10.1007/s10346-008-0123-6

  • Xiao SP, Belytschko T (2004) A bridging domain method for coupling continua with molecular dynamics. Comput Method Appl M. doi:10.1016/j.cma.2003.12.053

    Google Scholar 

  • Xiao S, Hou W (2007) Studies of nanotube-based aluminium composites using the bridge domain coupling method. Int J for Multiscale Com 5(6):447–459

    Article  Google Scholar 

Download references

Acknowledgments

This research was completed within the framework of the REMPARe project, funded by the French National Research Agency (ANR). The authors would like to thank EGIS and Irstea for their contribution to setting up the instrumentation and conducting the experiments.

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Author notes

  1. A. Breugnot

    Present address: EGIS Géotechnique, 3 rue du Docteur Schweitzer, 38180, Seyssins, France

  2. P. Gotteland

    Present address: FNTP, 3 rue de Berri, 75008, Paris, France

Authors and Affiliations

  1. 3SR, CNRS UMR 5521, 38000, Grenoble, France

    A. Breugnot, P. Villard & P. Gotteland

  2. Irstea, UR ETGR, 2 rue de la Papeterie, 38402, St-Martin d’Hères, France

    A. Breugnot & S. Lambert

  3. Univ. Grenoble Alpes, 38402, Grenoble, France

    S. Lambert, P. Villard & P. Gotteland

Authors
  1. A. Breugnot
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  2. S. Lambert
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  4. P. Gotteland
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Correspondence to S. Lambert.

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Breugnot, A., Lambert, S., Villard, P. et al. A Discrete/continuous Coupled Approach for Modeling Impacts on Cellular Geostructures. Rock Mech Rock Eng 49, 1831–1848 (2016). https://doi.org/10.1007/s00603-015-0886-8

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