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DEM Modeling of a Flexible Barrier Impacted by a Dry Granular Flow

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Abstract

Flexible barriers are widely used as protection structures against natural hazards in mountainous regions, in particular for containing granular materials such as debris flows, snow avalanches and rock slides. This article presents a discrete element method-based model developed in the aim of investigating the response of flexible barriers in such contexts. It allows for accounting for the peculiar mechanical and geometrical characteristics of both the granular flow and the barrier in a same framework, and with limited assumptions. The model, developed with YADE software, is described in detail, as well as its calibration. In particular, cables are modeled as continuous bodies. Besides, it naturally considers the sliding of rings along supporting cables. The model is then applied for a generic flexible barrier to demonstrate its capacities in accounting for the behavior of different components. A detailed analysis of the forces in the different components showed that energy dissipators (ED) had limited influence on total force applied to the barrier and retaining capacity, but greatly influenced the load transmission within the barrier and the force in anchors. A sensitivity analysis showed that the barrier’s response significantly changes according to the choice of ED activation force and incoming flow conditions.

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Abbreviations

A, B :

Segments representing cylinders

\({\mathbf {a}}\), \({\mathbf {b}}\) :

Direction vectors

\(A_{\mathrm{c}}\) :

Surface area of a cylindrical element

\(D_{\mathrm{c}}\) :

Minimum distance vector between two cylinders

\(D_{\mathrm{n}}\), \(D_{\mathrm{mc}}\), \(D_{\mathrm{lc}}\) :

Net, main cable and lateral cable diameters

\(D_{50}\) :

Particle’s diameter at 50% of the cumulative distribution

E :

Elastic modulus

\(F_{\mathrm{a}}\) :

Mean force of two anchors installed on the same main cable

\(F_{\text{ED-els}}\) :

Elastic limit of forces in energy dissipators

\({\mathbf {F}}_{\mathbf{int}}\) :

Interaction force

\({\mathbf {F}}_{\mathbf{n}}\), \({\mathbf {F}}_{\mathbf{t}}\) :

Normal and Tangential contact force

\(F_{\mathrm{tot}}\) :

Total force applied by the flow

Fr :

Froude number

g :

Gravity acceleration

\(G_{\mathrm{tw}}\) :

Shear modulus for the twisting moment

h :

Flow depth

\(I_{\mathrm{b}}\), \(I_{\mathrm{tw}}\) :

Bending and polar moments of inertia

\(k_{\mathrm{b}}\), \(k_{\mathrm{tw}}\) :

Bending and twisting stiffness parameter

\(L_{\mathrm{c}}\) :

Cylinder’s length

m, n :

Coefficients between 0 and 1

\(m_{\mathrm{dz}}\), \(m_{\mathrm{tot}}\) :

Dead zone mass and total initial mass

\({\mathbf {M}}_{\mathbf{b}}\), \({\mathbf {M}}_{\mathbf{tw}}\) :

Bending and twisting moments

\(R^{'}\) :

Radius of the spheres composing the clump

\(r_{\mathrm{s}}\), \(r_{\mathrm{c}}\) :

Sphere and cylinder radii

\(S_{\mathrm{vir}}\) :

Virtual sphere placed at a cylinder’s axis

\(u_{\mathrm{n}}\), \(u_{\mathrm{t}}\) :

Normal and Tangential displacements

\({\dot{{\mathbf{u}}_{\mathbf{t}}}}\) :

Relative tangential velocity

\(\overline{v}\) :

Depth-averaged velocity of the flow

\(W_{\mathrm{fb}}\), \(H_{\mathrm{fb}}\) :

Width and height of the flexible barrier

\(w_{\mathrm{ch}}\), \(l_{\mathrm{ch}}\), \(h_{\mathrm{ch}}\) :

Width, length and height of the channel

\(\alpha\) :

Inclination angle of the channel base

\(\gamma _{\mathrm{n}}\) :

Normal visco-elastic coefficient

\(\phi\) :

Microscopic friction angle

\(\varepsilon\) :

Restitution coefficient

\(\Delta t\) :

Time step

\({\varvec{\Omega }}{_{12}^{\mathrm{b}}}\), \({\varvec{\Omega }}{_{12}^{\mathrm{tw}}}\) :

Bending and twisting component of spheres’ relative rotation

\(\sigma _{\mathrm{n}}^{\mathrm{el}}\) :

Elastic tensile limit

\(\delta _{\mathrm{rc}}\) :

Friction angle between main cables and sliding rings

\(\delta _{\mathrm{ED}}\) :

Mean deformation of two energy dissipators of a main cable

\(\delta _{\text{ED-brk}}\) :

Maximum allowable deformation of energy dissipators

\(\theta _{F_{\mathrm{tot}}}\) :

Orientation of the total force applied by the flow

DEM:

Discrete element method

ED:

Energy dissipator

FEM:

Finite element method

SA, SB:

Flexible barriers without and with energy dissipators

References

  • Agostini R, Mazzalai P, Papetti A (1988) Le reti metalliche a maglia esagonale nella difesa dei versanti. Officine Maccaferri, Zola Predosa

    Google Scholar 

  • Albaba A (2015) Discrete element modeling of the impact of granular debris flows on rigid and flexible structures. Ph.D. thesis, Université Grenoble Alpes

  • Albaba A, Lambert S, Nicot F, Chareyre B (2015a) Modeling the impact of granular flow against an obstacle. In: Wu W (ed) Recent advances in modeling landslides and debris flows. Springer, pp 95–105

  • Albaba A, Lambert S, Nicot F, Chareyre B (2015b) Relation between microstructure and loading applied by a granular flow to a rigid wall using DEM modeling. Granul Matter 17(5):603–616

    Article  Google Scholar 

  • Bertolo P, Oggeri C, Peila D (2009) Full-scale testing of draped nets for rock fall protection. Can Geotech J 46(3):306–317

    Article  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 45(8):1104–1117

    Article  Google Scholar 

  • Bertrand D, Trad A, Limam A, Silvani C (2012) Full-scale dynamic analysis of an innovative rockfall fence under impact using the discrete element method: from the local scale to the structure scale. Rock Mech Rock Eng 45(5):885–900

    Google Scholar 

  • Boetticher A, Hübl J, Wendeler C, Volkwein A (2011) Modeling the impact of shallow landslides on flexible protection barriers. In: Marschallinger R, Zobl F (eds) Mathematical geosciences at the crossroads of theory and practice, Salzburg, Austria, pp 659–670

  • Bonati A, Galimberti V (2004) La valutazione sperimentale di sistemi di difesa attiva dalla caduta massi. In: Proceedings of the conference on Bonifica dei versanti rocciosi per la protezione del territorio, Trento, Italy, pp 11–15

  • Bourrier F, Kneib F, Chareyre B, Fourcaud T (2013) Discrete modeling of granular soils reinforcement by plant roots. Ecol Eng 61:646–657

    Article  Google Scholar 

  • Bourrier F, Lambert S, Baroth J (2015) A reliability-based approach for the design of rockfall protection fences. Rock Mech Rock Eng 48(1):247–259

    Article  Google Scholar 

  • Brighenti R, Segalini A, Ferrero AM (2013) Debris flow hazard mitigation: a simplified analytical model for the design of flexible barriers. Comput Geotech 54:1–15

    Article  Google Scholar 

  • Castanon-Jano L, Blanco-Fernandez E, Castro-Fresno D, Ballester-Muñoz F (2017) Energy dissipating devices in falling rock protection barriers. Rock Mech Rock Eng 50(3):603–619

    Article  Google Scholar 

  • Castro-Fresno D, del Coz Diaz J, López L, Nieto PG (2008) Evaluation of the resistant capacity of cable nets using the finite element method and experimental validation. Eng Geol 100(1):1–10

    Article  Google Scholar 

  • Cazzani A, Mongiovı L, Frenez T (2002) Dynamic finite element analysis of interceptive devices for falling rocks. Int J Rock Mech Min Sci 39(3):303–321

    Article  Google Scholar 

  • Coulibaly JB, Chanut M-A, Lambert S, Nicot F (2017) Non-linear discrete mechanical model of steel rings. J Eng Mech 143(9):04017087

    Article  Google Scholar 

  • Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

    Article  Google Scholar 

  • Domnik B, Pudasaini SP (2012) Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations. J Nonnewton Fluid Mech 173:72–86

    Article  Google Scholar 

  • Effeindzourou A, Chareyre B, Thoeni K, Giacomini A, Kneib F (2016) Modelling of deformable structures in the general framework of the discrete element method. Geotext Geomembr 44(2):143–156

    Article  Google Scholar 

  • Escallón J, Wendeler C, Chatzi E, Bartelt P (2014) Parameter identification of rockfall protection barrier components through an inverse formulation. Eng Struct 77:1–16

    Article  Google Scholar 

  • Faug T, Beguin R, Chanut B (2009) Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows. Phys Rev E 80(2):021305

    Article  Google Scholar 

  • Faug T, Caccamo P, Chanut B (2012) A scaling law for impact force of a granular avalanche flowing past a wall. Geophys Res Lett 39(23):021305

    Article  Google Scholar 

  • Gentilini C, Gottardi G, Govoni L, Mentani A, Ubertini F (2013) Design of falling rock protection barriers using numerical models. Eng Struct 50:96–106

    Article  Google Scholar 

  • Gentilini C, Govoni L, de Miranda S, Gottardi G, Ubertini F (2012) Three-dimensional numerical modelling of falling rock protection barriers. Comput Geotech 44:58–72

    Article  Google Scholar 

  • Gottardi G, Govoni L (2010) Full-scale modelling of falling rock protection barriers. Rock Mech Rock Eng 43(3):261–274

    Article  Google Scholar 

  • Grassl H (2002) Experimentelle und numerische Modellierung des dynamischen Trag-und Verformungsverhaltens von hochflexiblen Schutzsystemen gegen Steinschlag. Ph.D. thesis, Dissertation, Technische Wissenschaften ETH Zürich, Nr. 14817, 2002

  • Guasti G, Volkwein A, Wendeler C (2011) Design of flexible debris flow barriers. In: 5th international conference on Debris-flow hazard mitigation, mechanics, prediction and assessment, Padua, Italy, June, pp 14–17

  • Hearn G (1992) High-capacity flexpost rockfall fences. Final report. Technical report

  • Jiang Y-J, Towhata I (2013) Experimental study of dry granular flow and impact behavior against a rigid retaining wall. Rock Mech Rock Eng 46(4):713–729

    Article  Google Scholar 

  • Leonardi A, Wittel FK, Mendoza M, Vetter R, Herrmann HJ (2015) Particle-fluid-structure interaction for debris flow impact on flexible barriers. Comput Aided Civil Infrastruct Eng 31:323–333

    Article  Google Scholar 

  • Majoral R, Bertolo P, Giachetti G (2008) Las mallas en la estabilizacion de taludes, II curso sobre proteccion contra caida de rocas. Colegio de Ingegneros de Caminos, Canales y puertos, Madrid, p 26

    Google Scholar 

  • Mentani A, Giacomini A, Buzzi O, Govoni L, Gottardi G, Fityus S (2016) Numerical modelling of a low-energy rockfall barrier: new insight into the bullet effect. Rock Mech Rock Eng 49(4):1247–1262

    Article  Google Scholar 

  • Nicot F, Cambou B, Mazzoleni G (2001) From a constitutive modelling of metallic rings to the design of rockfall restraining nets. Int J Numer Anal Methods Geomech 25(1):49–70

    Article  Google Scholar 

  • Nicot F, Nouvel P, Cambou B, Rochet L, Mazzoléni G (1999) Etude du comportement mecanique des ouvrages souples de protection contre les eboulements rocheux. Revue française de génie civil 3(5):295–319

    Article  Google Scholar 

  • Peila D, Pelizza S, Sassudelli F (1998) Evaluation of behaviour of rockfall restraining nets by full scale tests. Rock Mech Rock Eng 31(1):1–24

    Article  Google Scholar 

  • Pudasaini S, Domnik B (2009) Energy considerations in accelerating rapid shear granular flows. Nonlinear Process Geophys 16(3):399–407

    Article  Google Scholar 

  • Savage SB (1979) Gravity flow of cohesionless granular materials in chutes and channels. J Fluid Mech 92(01):53–96

    Article  Google Scholar 

  • Schwager T, Pöschel T (2007) Coefficient of restitution and linear-dashpot model revisited. Granular Matter 9(6):465–469

    Article  Google Scholar 

  • Silbert LE, Ertaş D, Grest GS, Halsey TC, Levine D, Plimpton SJ (2001) Granular flow down an inclined plane: Bagnold scaling and rheology. Phys Rev E 64(5):051302

    Article  Google Scholar 

  • Šmilauer V et al (2015) Yade documentation, 2nd ed. The Yade Project. doi:10.5281/zenodo.34073

  • Spadari M, Giacomini A, Buzzi O, Hambleton J (2012) Prediction of the bullet effect for rockfall barriers: a scaling approach. Rock Mech Rock Eng 45(2):131–144

    Article  Google Scholar 

  • Thoeni K, Lambert C, Giacomini A, Sloan SW (2013) Discrete modelling of hexagonal wire meshes with a stochastically distorted contact model. Comput Geotech 49:158–169

    Article  Google Scholar 

  • Van Tran P, Maegawa K, Fukada S (2013) Prototype of a wire-rope rockfall protective fence developed with three-dimensional numerical modeling. Comput Geotech 54:84–93

    Article  Google Scholar 

  • Volkwein A (2005) Numerical simulation of flexible rockfall protection systems. In: Proceedings of computing in civil engineering

  • Volkwein A (2014) Flexible debris flow barriers—design and application. Technical report, WSL Ber. 18

  • Wendeler C, Volkwein A, Roth A, Herzog B, Hahlen N, Wenger M (2008) Hazard prevention using flexible multi-level debris flow barrier. In: Interpraevent, vol 1, pp 547–554

  • Wendeler CSI (2008) Murgangrückhalt in Wildbächen: Grundlagen zu Planung und Berechnung von flexiblen Barrieren. Ph.D. thesis, Eidgenössische Technische Hochschule Zürich

  • Zienkiewicz O C, Taylor R L (2005) The finite element method for solid and structural mechanics. Butterworth-Heinemann, Oxford

    Google Scholar 

Download references

Acknowledgements

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement Number 289911. We would also like to acknowledge the valuable suggestions concerning the flexible barrier model made by Prof. Guido Gottardi from the University of Bologna. We also thank Dr. Frank Bourier (Irstea-Grenoble) and Dr. Ignacio Olmedo (GTS) for their contribution to the zipline experiment. In addition, comments and suggestions regarding the flow model made by Dr. Thierry Faug from Irstea-Grenoble are highly appreciated.

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Authors and Affiliations

  1. School of Agricultural, Forest and Food Science HAFL, Bern University of Applied Sciences, Länggasse 85, 3052, Zollikofen, Switzerland

    Adel Albaba

  2. Irstea, UR ETGR, Université Grenoble Alpes, 2 rue de la papeterie, 38402, St-Martin d’Hères, France

    Stéphane Lambert, François Kneib & François Nicot

  3. 3SR, Université Grenoble Alpes, 38000, Grenoble, France

    Bruno Chareyre

  4. 3SR, CNRS, 38000, Grenoble, France

    Bruno Chareyre

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  1. Adel Albaba
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  2. Stéphane Lambert
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  3. François Kneib
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  4. Bruno Chareyre
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  5. François Nicot
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Correspondence to Adel Albaba.

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Albaba, A., Lambert, S., Kneib, F. et al. DEM Modeling of a Flexible Barrier Impacted by a Dry Granular Flow. Rock Mech Rock Eng 50, 3029–3048 (2017). https://doi.org/10.1007/s00603-017-1286-z

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