E3S Web of Conferences 415, 02017 (2023)
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https://doi.org/10.1051/e3sconf/202341502017

Granular column collapse: the role
polydispersity on the velocity and runoutofparticle

size

Oscar Polanía 1,2*, Nicolás Estrada 2, Mathieu Renouf 1, Emilien Azéma 1,3, and Miguel Cabrera 4
1 LMGC, Université de Montpellier, CNRS, Montpellier, France
2 Departamento de Ingeniería Civil y Ambiental, Universidad de Los Andes, Bogotá D.C., Colombia
3

Institut Universitaire de France (IUF), Paris

4 Department of Geoscience & Engineering, TU Delft, Delft, The Netherlands

Abstract. Geophysical mass flows involve particles of different sizes, a property termed polydispersity.
The granular column collapse is a simplified experiment for studying transitional granular flows. Our
research focuses on the role that polydispersity has on the velocity and runout distance of dry and immersed
granular columns, undergoing a numerical and experimental study. Our results highlight that polydispersity
does not have a strong effect on the collapse of dry columns. On the contrary, the collapse sequence of
immerse granular columns strongly depend on the polydispersity level.

1 Motivation
Granular flows are found in geophysical processes likelandslides, debris flows or pyroclastic flows. Those
flows are subaerial, but occasionally they are submerged
in a viscous fluid environment. They could reach longrunout distances and develop a fast-spreading velocity
during flow, resulting in several damages. A
characteristic among them is the presence of particles ofdifferent sizes, a property termed polydispersity. The
flow of granular materials can be distinguished in three
regimes according to the motion of the grains with theStokes number St = (𝜌pΔ𝜌gd3)1/2 / (18μf √2) and thedensity ratio χ = (𝜌p / 𝜌f) ½, where d is the particle
diameter, g is Earth’s gravity, μf is the fluid dynamicviscosity, Δ𝜌 is the density difference between theparticles 𝜌p and fluid 𝜌f. The combination of these
dimensionless numbers leads to three flow regimes, thatare: the inertial regime, the free-fall regime, and theviscous regime [1]. Natural flows like debris flows andslides are commonly in the free-fall and inertial regime.
A benchmark study case for granular flows is thecollapse of a granular column [2, 3, 4]. In thisexperiment, a column built up with particles with an
initial length L0, an initial height H0, and an aspect ratio
A = H0/L0 is let to collapse by self-weight in a horizontal
plane, reaching a final runout Lf and a final height Hf(see Fig. 1.). During collapse, the column front has an
initial acceleration phase followed by a steadypropagation stage with constant velocity U, and then thecollapse comes to a halt. The final runout of granularcolumns is found to be longer in dry systems than inimmersed systems [5, 6], and for dry cases,
polydispersity does not influence the column mobility[7]. Moreover, it has been found that the normalized

runout L* = (Lf – L0) / L0 increases with A and collapses
on a power-law function with different exponent for
short and tall columns [5, 6].
The collapse velocity during the steady propagation
stage increases with A, but it is found that U normalized
by the theorical free-fall velocity UFF = (2g*H0)0.5 has acharacteristic value depending on the flow regime with
U/UFF = [0.55, 0.27, 0.196, 0.024] for free-fall, inertial,viscous inertial and viscous regime, respectively [5].
Previous studies have linked the column mobility withthe collapse kinematics at the particle scale [3],considering the peak energy of a particle, and at thecolumn scale [6], considering the collapse velocity U.
Although previous studies have done a great effort
to understand the flow of granular columns, theinfluence that polydispersity has is still unclear.
Understanding the role that polydispersity has on
granular flows is important because it is intrinsic inmany natural processes. Therefore, our research focuses
on exploring the influence that polydispersity has on thecollapse and runout of dry and immersed granularcolumns with two methodologies. We do 2D numericalsimulations capable of managing high polydispersity
levels, and we do experiments to study the threedimensional nature of the process. We focus onprocesses that are in the free-fall and inertial regime,
studying flows on the same regime as in natural flows.

2 Methodology
2.1 NumericalWe study the collapse of dry and immersed twodimensional granular columns using a coupled Finite* Corresponding author: oscar.polania@umontpellier.fr os.polaniao@uniandes.edu.co© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 02017 (2023)
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https://doi.org/10.1051/e3sconf/202341502017

The experimental setup is backlighted with a LEDpanel, and the column collapse sequence is recordedwith a high-speed camera at a frame rate of 500 Hz. The
same rate is used to register the pore pressure
measurements. We do digital-image analysis to track thefront position evolution and make a parallel analysis of
the collapse with the pore pressure evolution (see Fig.
2.).

Element Method (FEM) with a Discrete ElementMethod (DEM). The fluid motion in immersed
simulations is solved with a finite element spatial
discretization combined with an implicit temporal
discretization of the incompressible Navier-Stokes
equations [9]. The solid phase is simulated with theNon-Smooth Contact Dynamics approach, a class of
Non-Smooth DEM [10]. In Contact Dynamics, theparticles are assumed to be perfectly rigid, interact byvolume exclusion and Coulomb friction. This method
requires no elastic repulsive potential and no smoothingof the Coulomb friction law for the determination offorces. For this reason, this method appears to be
perfectly suited to the simulations of highly
polydisperse systems without the need of tuningstiffness
parameters as in the smooth DEM class.
We systematically vary H0 = [0.015 – 0.25] m,studying short and tall columns with A = [0.3 – 5.0]. We
also study different grain size distribution GSD, varying
the ratio between the biggest and smallest grain λ = dmax
/ dmin = [1 - 19]. All GSDs have 25 grain sizes linearly
distributed between dmin and dmax sharing a common
cumulative unitary mass 0.5 at d50 = 1.0 mm. Grains
have density 𝜌p = 1500 kg/m3, with a friction coefficientof 0.3, and restitution coefficient of 0. For immersed
simulations, the fluid has the physical properties ofwaterwith density 𝜌f = 1000 kg/m3 and viscosity μf =0.001 Pa s. Those properties allow us to study granular
flows in the free-fall regime for dry simulations, andgranular flows in the inertial regime for immersed
simulations, but near the transition towards

3 Results and ongoing work
We observed, numerically and experimentally, that dry
column collapses are not affected by the increment of
the polydispersity level, confirming previous results [7].
For dry columns, although polydispersity slightly
increases the column front velocity, the ratio U/UFF
remains around a characteristic value of free-fall regime.
H00.0 s
0.4 s

Hf
Hf

1.0 s

L0Lf

L0
Lf
Fluid velocity [m/s]Particles velocity [m/s]

0.00

the viscous regime.

0.05

0.10Fig. 1. Snapshots of an immersed granular column collapse
with aspect ratio A = H0 / L0 = 1.0 and monodisperse particles
with λ = 1. Collapse sequence from (left column) numericalsimulations and (right column) experiments. Note that thecolor bars correspond to the velocity magnitude of fluid andparticles obtained in the numerical simulations.

2.2 Experimental
We study the three-dimensional nature of the processwith granular column experiments in a rectangularchannel of 100 cm long, 70 cm height, and 15 cm width.
We study dry and immersed conditions and vary thepolydispersity level between λ = [1 - 20], with d50 = 1.15
mm. We use glass beads particles with 𝜌p = 2500 kg/m3.
The ambient fluid for immersed experiments is waterwith 𝜌f = 1000 kg/m3 and μf = 0.001 Pa s, studying flows
in the inertial regime.
Besides the novelty of the use of different GSDs,
our experimental setup is instrumented with a networkof basal and side pore pressure sensors, allowing toevaluate pore pressure during collapse and its variationin the channel. Moreover, the experimental setup
employs a novel release mechanism that diminishes theeffects generated for the relative displacement of thereleasing gate and the granular column. For thismechanism, we have covered the gate with a smooth
PTFE film of 0.5 mm thick. One end of the PTFE film
is fixed to a roller, and the other one has displacement
constraints. A motor rotates the roller that pulls thePTFE film from one side, and removes vertically thegate. This mechanism diminishes the effects generated
by the relative displacement of the gate and the granularcolumn because they are not in contact. In consequence,
the granular column is only in contact with the PTFE
film that wraps on the roller.

Fig. 2. Evolution of the front position of an experimental
granular column with A = 2.8. The dashed grey lines delimit
the collapse steady propagation stage interval. The side colorbar shows the magnitude of the pore pressure change relative
to the initial value for the sensors of the base.

2E3S Web of Conferences 415, 02017 (2023)
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https://doi.org/10.1051/e3sconf/202341502017

References

The entire collapse process of dry columns shows
independent of the polydispersity, having granular flows
with similar time-stages, front velocity, and runout. This
result, considered in a large-scale scenario as alandslide,suggest that the GSD does not control/affect the granularflow.
Contrary to dry granular flows, immersed columns
are affected by polydispersity. We have observed thatthe collapse sequence changes with the increase of thepolydispersity, delaying the column collapse. Then,
during the stage of nearly constant velocity, the increaseof the polydispersity makes that the collapse remains
longer in this stage and changes the column mobility. A
similar behavior could be expected in submarinelandslides where GSD plays an important role.
Moreover, the previous observations addressed us
to link the kinematics of the column collapse with its
mobility and based on a simple model of a sliding bloc,
we found that the column mobility scales with thekinetic energy, considered as the 𝐸𝐾𝑈 = UM/2, where M
is the column mass. This simplified model works forflows in the free-fall and inertial regime [11] (see Fig.
3.).
We are aware that the methodology employed in thenumerical simulations is a simplification of a complex
process; however, preliminary experimental results
validate the simplified model that links the final runout
and the column kinematics, evidencing its relevance ina three-dimensional process.
Our study provides evidence that the collapse of
immersed granular columns strongly depends on thepolydispersity level. On the contrary, polydispersity
does not have a strong effect on the collapse of drycolumns. Our results could be of great use inunderstanding ancient geophysical flows but also for
improving hazard evaluation methods that could benefit
from accounting extreme grain size variations.
Moreover, our ongoing experimental work counts withthe observations from the collapse sequence and theinternal pore pressure variations, providing a novel
insight on the collapse kinematics of immersed flows.

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10 110 210 1100( p/)(EKU)0.5101Fig. 3. Scaling of the column runout with the kinetic energy
during the stage of constant propagation. The exes (x) andcircle markers (o) are experiments. For these experiments, thedarker the marker the greater the polydispersity level. Blackpentagons are the data of the reference [11] obtained withnumerical simulations with the methodology described in
section 2.1.

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