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

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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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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


Discrete element method


Energy dissipator


Finite element method


Flexible barriers without and with energy dissipators


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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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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).

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