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A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments

Abstract

In this paper, we used a 3-D discrete-element model, Grains3D, which allows the simulation of unsteady granular flows of monodisperse soft spherical particles in a common situation (i.e., down a rectangular channel). A series of numerical dam-break experiments was performed to predict the behavior of granular columns that propagate down a rough horizontal surface from different initial conditions (varying the initial aspect ratio). Numerical results were compared to those obtained experimentally by Lajeunesse et al. (Phys Fluids 17:103302, 2005) from a similar configuration. Runout distance, temporal flow evolution, deposit morphology and internal flow structures of similar laboratory experiments were quantitatively reproduced as well as prediction of empirical and theoretical scaling laws. This paper highlights that such fully 3-D simulations of soft-spheres can remarkably capture dam-break collapses performed in a rectangular channel. Moreover, Grains3D can provide a complete physical description of such complex unsteady systems which will be the topic of future on-going studies.

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Abbreviations

δ ij :

Overlap distance between a particle i and j during the collision

Δt:

Computational time step

\({{\epsilon_n}}\) :

Coefficient of restitution

γ n :

Damping coefficient in the normal direction

γ t :

Dissipative friction coefficient in the tangential direction

μ c :

Interparticle Coulomb friction coefficient

μ w :

Particle-wall Coulomb friction coefficient

ω ij :

Relative angular velocity between a particle i and j

ρ i :

Density of a particle i

σ :

Poisson coefficient

τ c :

Characteristic free fall time of the granular column

θ c :

Internal friction angle

a:

Initial aspect ratio of the column in the reservoir

dp :

Particle diameter

E :

Young modulus

F i :

Sum of the forces applied to a particle i

F ij :

Colliding force between a particle i and j

F ij,dn :

Normal component of the dissipative force

F ij,el :

Hookean elastic restoring force

F ij,t :

Shear component of the dissipative force

h:

Flow thickness at the time t

hf :

Deposit thickness taken at x = Li

H:

Reservoir height

Hi :

Initial height of the column

kms :

Coefficient of rolling resistance

k n :

Stiffness coefficient

lf :

Length of the final deposit taken at x = 0

Li :

Initial length of the column

M i :

Mass of a particle i

\({\mathcal{M}_{rf}}\) :

Artificial rolling friction

m ij :

Reduced mass of two particles i and j in contact

N :

Total number of particles constituting the system

n C :

Unit normal vector at the contact point

R :

Particle radius

R ij :

Reduced particle radius

t C :

Unit tangential vector at the contact point

t :

Time from gate opening

U rn :

Relative velocity between a particle i and j in the normal direction

U rt :

Relative velocity between a particle i and j in the tangential direction

w:

Channel width

x:

Flow length at the time t

xf :

Flow length measured from x = Li

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Correspondence to L. Girolami.

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Girolami, L., Hergault, V., Vinay, G. et al. A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments. Granular Matter 14, 381–392 (2012). https://doi.org/10.1007/s10035-012-0342-3

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  • DOI: https://doi.org/10.1007/s10035-012-0342-3

Keywords

  • Discrete-element modeling
  • Dam-break flows
  • Quantitative reproduction