E3S Web of Conferences 415, 01031 (2023)
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https://doi.org/10.1051/e3sconf/202341501031

Simulations of non-stationary flows of dry granular material
along an inclined chuteFrancesco Zarattini1* and Fabio Gabrieli1
1University of Padova, ICEA dept., Italy

Abstract. In this work, the signals generated by grain-to-base multiple impacts of three different granularmaterials flowing along an inclined chute and characterized by unsteady-state conditions are investigatedthrough the discrete element method (DEM). The effect of different grain-size and angularity of the grainsare taken into account. Various instants of the flows are studied, focusing in particular on the analysis of thesignal produced by the passage of the material on a portion of the base of the chute, and on the study of themotion of the particles close to the base. The numerical results allow us to have an insight into thecharacteristics of the flows and to explain the behavior of the granular material at the contact with the base.

1 Introduction
In this work, the discrete element method (DEM) [1] isused to model an unsteady dry granular flow in a chuteproduced by a coarse material (i.e. gravel) and toinvestigate the signal transmitted to a portion of its base.
DEM allows to study the kinematics of the whole mass
as well as the single impacts between particles pairs andparticles with the base. Differently from experimental
tests, simulations can provide detailed information
about the forces exchanged by the particles, theirinstantaneous velocities and the effect ofmicromechanical aspects on the overall behavior.
Several literature works consider granular flows in
steady-state regimes simulating small volumes withperiodic boundary conditions [2] while few works weredevoted to unsteady conditions even if the laboratory
tests are mainly conducted in these conditions [3]. Mostof the research works are conducted using simple
spheres but the effect of different shapes was proved toplay a relevant role in the emergency of different
velocity profiles and wall friction [4].
The goal of the present study is to deduce thecharacteristics of the dynamics of the flows from thesignal generated by different material flowing along arigid chute with a smooth base and fixed slope angle.
Results obtained with DEM simulations are comparedfocusing on the effect of different grain size and shape.
Particularly rounded and sharp edges grains areconsidered by mimicking their real shape with rigid
aggregates of spheres (i.e. clumps). The energy content
and temperature of the granular flow is tracked along
time in a monitoring volume close to the base of thechute as well as the corresponding basal forces.

*2 DEM
model
simulations

parametersandA soft-sphere discrete element numerical approach
was adopted, and in particular, the Hertz-Mindlin
contact law, which comes from an approximation of
Mindlin-Deresiewicz theory [5]. DEM simulations wererun using the open-source framework for discreteelements Yade [6]. Three types of granular materials are
considered as in [7], with different grain-size androughness. Particle shape is discretized in DEM
simulations through rigid aggregates of spheres, named
clumps [8]. We synthetically report the material
characteristics in Table 1.
Table 1. Material parameters.

Particleangularity
Meandiameter,
d50 [mm]
Uniformity
coefficient,Cu [-]

M1(coarsegravel)M2(mediumgravel)M3(mediumgravel)

RoundedRounded

Sharp

19.7

12.4

12.6

1.105

1.536

1.478

Numerical contact parameters accounted for thesimulations are reported in Table 2 and are the same forthe three materials considered M1, M2 and M3.

Corresponding author: francesco.zarattini@phd.unipd.it© 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, 01031 (2023)
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3.1 Time evolution of forces and energies

Table 2. Numerical simulation parameters.
Value
Contact friction angle, ϕ [°]30

Normal restitution coeff., en [-]0.9

Tangential restitution coeff., et [-]0.9

Elastic contact modulus, E [MPa]100

Poisson contact coeff., v [-]0.2

Once the deposited granular material is let free offlowing along the flume through the removal of theretaining wall, the recording of the signal begins at theentering of the particles in the monitoring volume, andit ends once all of them have transited on it. In Figure 2
the time evolutions of the longitudinal tangential force(Fξ) and normal force (Fη) at the monitoring plate arereported for all three materials employed.
From the mere time history of the forces, a higher
fluctuation of M1 with respect to the other two materials
can be observed. This behavior can be explained by thecoarser particles impacting on the plate. Besides, thesize of the material influences the signal in terms of themean forces that it exerts on the base: the coarser thematerial, the higher the forces it transmits to the base ofthe flume.
On the other hand, an effect due to the shape can be
identified from the duration of the event: from Figure 3
it can be observed that particles with the same sizes but
different shapes (materials M2 and M3) take different
time to travel through a section (in our case a monitoring
volume) of the chute: as expected, the flow is slower
when the granular material is characterized by sharperedges. The duration of the event, on the contrary,
doesn’t seem to be influenced by the dimension of theparticles, as materials M1 and M2, take the same time totransit on the monitoring volume. This can be viewed as
indirect proof of the negligible effect of the width of theflow in these conditions [10].

The geometry of the model is given by an upperretaining tank in which 22 kg of granular material are
initially deposited; a flume 26.5 cm wide, 155 cm longand inclined of 40° with respect to the horizontal; adeposit box for the collection of the particles (Figure 1).
The removal of the retaining gate that separates thedeposit tank from the flume allows the granular material
to flow along the chute. Data are collected only in a
portion of the flume base – called monitoring plate –near its terminal part (1.5 m far from the position of theretaining wall). In this way, the plate is far enough fromthe release section to allow flow particles to break theforce chains they develop in a static condition and torefer to a fully collisional regime.

Fig. 1. Snapshots taken at different instants of the simulation:(a) view of the initial deposit of the granular material and (b)of the granular flow along the chute.

3 Numerical results
Results discussed hereafter stem from two different
data-collecting methodologies: (i) data recorded on themonitoring plate (overall force components andinteractions with the base); (ii) data recorded on a thinvolume above the measuring plate containing theparticles close to the base (individual kinematicquantities of the particles). Results for three materials at
a fixed inclination of the chute are reported, thus
allowing us to focus on the size and shape influence on
the signal.
In the analyses presented, the following aspects areconsidered: (i) the time evolution of the forces exerted
on the measuring plate, (ii) the time evolution of theenergies and their weighted squared fluctuations(expressed as granular temperatures [9]) carried by thebodies near the measuring plate.

Fig. 2. Time evolution of the normal and tangential forces
exerted by the granular flow on the measuring plate for thethree materials.

Both total kinetic energy (EkTOT) and mass (mTOT)
evolutions with time are reported for the three materials,
as can be seen in Figure 3. From Figure 3a the Ek starts
to grow up to a maximum value but for none of the threeflows a stationary condition is reached. After that adecreasing trend can be observed with a lower steepness
than the previous one.

2

E3S Web of Conferences 415, 01031 (2023)
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component considered with respect to a mean value,obtained for all particles within the basal volume at agiven instant.
𝑇𝑡𝑟𝑎𝑛𝑠𝑙 = (𝑇𝑡𝑟𝑎𝑛𝑠𝑙 𝑥𝑥 + 𝑇𝑡𝑎𝑛𝑠𝑙 𝜉𝜉 + 𝑇𝑡𝑟𝑎𝑛𝑠𝑙 𝜂𝜂 )/3(1)𝑇𝑡𝑟𝑎𝑛𝑠𝑙𝑖𝑗 = ⟨𝑣𝑖 𝑣𝑗 ⟩ − ⟨𝑣𝑖 ⟩⟨𝑣𝑗 ⟩(2)

where 𝑖, 𝑗 = {𝑥, 𝜉, 𝜂}.
Figure 5a shows how the shape of the particles has
an influence over 𝑇𝑡𝑟𝑎𝑛𝑠𝑙 : for sharp edge particles M3
the time trend is significantly different to the ones ofmaterials M1 and M2. In Figure 5b the 𝑇𝑟𝑜𝑡 component
is reported. From the comparison of the signals, both
granulometry and angularity of the material seem to playa role over this quantity.

Fig. 3. Time evolution of (a) the total energy and (b) the massof the particles above the monitoring area.

The rounded edge particles have a total kinetic
energy higher than sharp edge particles, as can be seenin Figure 3a; whereas the energy peak instant is reachedmore or less simultaneously for all materials. The masstrends present their respective peaks with a delay incomparison to energy. This behavior had been observed
for the same materials in [7] with a shorter and wider
flume.
3.2 Granular temperature of the particles
close to the baseIn order to examine more deeply the energetic contentof the flow, particularly in its portion in the immediateproximity to the basal surface, granular temperature [9]components are investigated. Assuming a further
subdivision of the monitoring volume with the elevation
η, and considering the lowest one (hereinafter calledbasal volume), from the kinematic characteristics of theclumps embedded in such a volume, the components ofthe granular temperatures are obtained. In Figure 4 theparticles within the basal volume are depicted and,among them, those in contact with the base areindicated.

»Further conclusions can be drawn considering theratio between rotational and translational kinetic energy
components in the basal volume, as presented in Figure
6. We have a monotonic increasing trend for roundedparticles with higher fluctuations for the coarser grain
fractions; for sharp particles the trend is different, as it
decreases throughout time, with the exception at its tail:only at the final instants of the flow are the particles
sufficiently sparse to be able to rotate freely at the base.

xFlow direction´Fig. 5. Time evolution of (a) translational and (c) rotational
granular temperatures in the basal volume.

Grain-basecontacts

Fig. 4. Grain-base contacts visualization from bottom of thechuteFig. 6. Time evolution of the ratio between rotational andtranslational kinetic energy components for the three materials
in the basal volume.

The granular temperature components Ttrans (Eq. 1)
and Trot, express the square of the fluctuation velocity

3

E3S Web of Conferences 415, 01031 (2023)
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https://doi.org/10.1051/e3sconf/202341501031

4 Conclusions

vibration signals in dry granular flows, in VI
International Conference on Particle-based
Methods – Fundamentals and Applications
PARTICLES 2019, Barcelona, Spain, 305-312(2019)
9. T. Wang, Y. He, R. K Dong, Powder Technology,
271, 35-48 (2015)10. S. C Du Pont, P. Gondret, B. Perrin, & M. Rabaud,Europhysics letters, 61(4), 492 (2003)

In this work, a numerical study through DEM of nonstationary flows characterized by different granulometry
and grain angularity is presented. Investigating theforces transmitted to the base of a monitoring volume
and the kinetic properties of the particles in proximity toit, we were able to assess the effect of the shape and sizeof the granular materials on the type of signal generated.
DEM easily provides in-depth information about
kinematics of each particle and contact forces between
particle pairs and at particle-base contact. The energy
content of the particles of the flow in proximity to thebase can be gathered as well as the fluctuation of theforces and in their average values with time.
From the comparison of the signal generated by thethree reference materials, we can observe that theparticle shape affects the normal and tangential force
fluctuations at the base and its mean value. The granularmass is more elongated along the chute for sharper
particles and consequently the transit time results
longer. The energy content of the flow is lower
considering sharp edge particles as well as the granulartemperature in a volume close to the monitoring plate.
For what concern the particle size, the larger thegrains are, the higher the force fluctuations and meanvalues. On the other hand, the grain size seems to play aminor role in the energy of the flow and its granulartemperature.

Acknowledgments
The financial support from the Italian Ministry ofEducation, University and Research (MIUR) within theframework of the REDREEF Project - PRIN 2017 Call(prot. 2017YPMBWJ) and the Fondazione Cariverona
R&D project are gratefully acknowledged.

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