Two-pHase modElling for Sediment dynamIcS in geophysical flows
THESIS-2016
September 12-14, 2016, Tokyo – Japan

Euler-Lagrange simulations of debris flow experiments

Organizing committees

Tomoo Fukuda

Research and Development Initiative, Chuo University
1-13-27 Kasuga, Bunkyou-ku, Tokyo 112-8551, Japan
Tel. +81 (03) 3817 1611
International Scientific Committee
Email: t-fukuda@tamacc.chuo-u.ac.jp

Balachandar, S. (University of Florida, USA)
Blondeaux, P. (University of Genova, Italy)
Shojidelle
Fukuoka
Brocchini, M. (Università Politecnica
Marche, Italy)
ResearchandDevelopment
Dong, P. (University of Dundee, U.K.) Initiative, Chuo University
1-13-27 Kasuga, Bunkyou-ku, Tokyo 112-8551, Japan
Elghobashi, S. (University of Tel.
CaliforniaUSA)+81 (03)Irvine,
3817 1625
Guillou, S. (University of Caen, France)
Email: sfuku@tamacc.chuo-u.ac.jp
Hsu, T.J. (University of Delaware,
USA)
Izumi, N. (Hokkaido University, Japan)
Jenkins, J. T. (Cornell University, USA)The applicability of an Euler-Lagrange simulation for debris flows is discussed in the paper. The
Meiburg, E. (University of California, USA)simulation model was applied to debris flow laboratory experiments conducted by Egashira et.al [1].
Nguyen,(Laboratoryfor Hydraulics
Saint-Venant,Experimental
casesK.D.
of sedimentconcentrationof 0.196
and 0.444France)
were simulated with particles of
Pham
Van
Bang,
D.
(Laboratory
for
Hydraulics
France)spheres and gravels. The results demonstrated that theSaint-Venant,simulation model
was able to reproduce
Shimizu,Y.
(Hokkaido
University,
Japan)
discharge rates of water and particles and vertical distributions of particle velocities. Moreover theO. (Institut
Polytechnique
Toulouse,
France)concentrated debris flows
simulation Simonin,
showed that
effects Nationalof particle
shapes arosedegreatly
in highly
because particle
shear
stresses became
dominant.
Soldati,A. (Universityof Udine,
Italy)
Toorman, E.A. (KU Leuven, Belgium)
Euler-Lagrange
simulation,
particleshape, debris flow, particle velocity, concentration
Key Words:
Uhlmann,
M. (KIT
Karlsruhe,
Germany),internal
frictionangle University, China)
Wang,
G.Q.
(Tsing-Hua

1. Introduction
Local Organizing Committee
Three-dimensional numerical simulations based on the Euler-Lagrange approach have been
S. (Chair)(ChuodevelopedFukuoka,
and become
powerful
tool University)
for investigations of fluid-particle interaction mechanism in twophase flows.
However,simulations
for highly concentrated sediment transport have not been validated
Gotoh,
H. (Kyoto
University)yet. We havedeveloped
a numericalsimulation model based on the Euler-Lagrange approach to
Izumi,
N. (Hokkaido
University)
investigateKajishima,
fluid–particle
interactions(Fukuoka et al. [2]). The present study applies our numericalT. (Osaka
University)model to thelaboratoryK.
experiments
on debris flows conducted by Egashira et al. [1]. Simulated motions
Kashiyama,(Chuo University)of particles and water in highly concentrated debris flows are validated by comparing with theMizuyama, T. (National Graduate Institute for Policy Studies)
experimental data. Moreover, shapes of particles play an important role in gravel transport in flows [2].
Nakagawa,
H. (Kyotomotions
University)
Differences
between simulatedof sphere and gravel particles are discussed in relation with theM. (TheUniversity of Tokyo)
variations Sakai,of sedimentconcentrations.
Sato, S. (The University of Tokyo)
M. (Waseda University)
2. DebrisSekine,
flow experiment
Shimizu, Y. (Hokkaido University)(Kyoto University)
EgashiraUshijima,
et al.[1] S.
conducted
the experiments of debris flow over rigid bed in a rectangular open
channel (12m long,T.0.1
m wide andbed slopeof 19 deg.) as follows; uniform debris flows with different
Uchida,(Secretary)(Chuo
University)
sediment concentrations cf (0.141 - 0.444) were created in the channel. The water was supplied at aconstant rate from upstream and the gravel (d50 = 2.18 mm) was fed at 6 m section from the end. The
water andthe sediment discharge were measured by sampling water-sediment mixture at the
Secretariat
downstream
end. Vertical
distributionsof particle
velocities
were photographed by video cameras from
Researchand Development
Initiative(RDI),
Chuo University
the side of the channel and measured by the image analysis. Vertical distributions of gravel
concentrations were also measured by using a sampler which had several inlets at different levels.

17

Gravel used for the experiments
ϕμ : Internal friction angle
38.7˚
c*: Stationary deposited concentration
0.512

Sphere29.7 ˚
0.60

Gravel38.9 ˚
0.62

Fig. 1. Particle conditions of the experiment and the simulation.
Table 1. Parameters used in the simulation.

∆x,∆y,∆z : Fluid computational grid sizeρw : Water density
ρs : Particle density

μw: Kinematic viscosity
CS : Smagorinsky constantϕs : Friction angle of particle surface
d : Diameter

0.545 mm3
1,000 kg/m
3
2,620 kg/m

−4

8.9×10
Pa·s
0.173
26.6
˚
2.18 mm

3. Simulation method
The numerical method is able to simulate detailed flows around particles by using smaller
computational grid than particles, see [2]. In the simulation of flow motion, particles are dealt as a liquidwith a different density. All domains of water and particles are computed by the governing equations of
one fluid model for incompressible solid-liquid multiphase flow based on the computation method(Ushijima et al. [3]). Smagorinsky model is employed for a turbulence model.
ui
(1)
0
Du i

Dt

 xi
1 p

2    t S ij 
gi 

 xi
x j


t

C s  

2 S ij S ij

(2)
(3)

where ui is i-th component of weight average velocity including particles, ρ is volume average density,
p is sum of pressure and isotropic component of SGS stresses, Sij is strain rate tensor, ν is kinematic
viscosity, Cs is Smagorinsky constant and ∆ is computational grid size. Fluid forces on particles arecomputed by integration of forces on particle-domain in the multiphase flow.
The Discrete Element Method is used for particle motions. Combined tetrahedron models (CTM) andsuperposed sphere models (SSM) are often used for nonspherical particles. CTM is also suitable forreproducing shapes of particles [4], but it needs many elements to reproduce particles like gravels. This
study has implemented simulations of motions of a number of gravel particles (about two hundred
thousand) by employing SSM that can reproduce gravel shapes with a few small spheres.

4. Simulation conditions
The simulation model was applied to two cases of the debris flow experiments (Case1: sediment
discharge concentrations cf = 0.196, depth 0.0139 m, Case2: cf =0.444, depth 0.0259 m) by using spheres
and gravel particles, see Fig.1. The length of numerical channel was 1 m. The width was 0.1 m and bed
slope was 19 degrees as with the experiment. Uniform flows were simulated by applying periodic
conditions in the streamwise direction. Numerical results of channel length 1.0 m were not different
from those with 6.0 m channel length for the case of cf = 0.196. Parameter used in the simulation are
shown in Table 1.

5. Validation of the numerical simulations with the debris flow experiments
Simulation results were compared with the data measured in the experiment. Fig.2 shows simulation
results of motions of gravel and sphere particles and water. Gravel particles had long axis directed thestreamwise direction in the manner of the imbrication structure. Gravel motions were strongly affectedby their shapes. Vertical distributions of particle velocities and concentrations were compared in Fig.3.
In the case of sediment discharge concentration 0.196, simulated vertical velocity distributions of sphere
were a little smaller than measured ones and those of gravel particles were a little greater thanexperimental ones. However, both particle velocity distributions were close to the experimental ones.
Vertical distributions of particle volume concentrations of spheres and gravel particles roughly
reproduced the experimental ones. The stationary deposited concentration c* measured in the experiment
was 0.512 and rather small compared to 0.60 and 0.62 used in the simulations. This means thatexperimental gravel particles were thought to have jagged shapes. The particle model requires many

18

z,x3
y,x2
x,x1

Gravel (cf = 0.196)

Sphere (cf = 0.196)

Concentration
Concentration
0.015

0

0.1

0.2

0.3

0.4

Gravel (cf = 0.444)

Sphere (cf = 0.444)

Fig. 2. Simulated particles and water surfaces.
0.5

0Concentration
0.1

0.2

0.3

0.4

0.5

0.0

0.030

0.2

0.4

Concentration

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Particle velocity (Cal.)

0.025

Water velocity (Cal.)

0.020

z(m)

z(m)

0.010

0.005

0.000

0.0

0.5

1.0

1.5

2.0

Velocity ( m/s )2.5 0.0

Sphere (cf = 0.196)

0.5

1.0

1.5

Velocity ( m/s )

2.0

2.5

Particle velocity (Exp.)

Particle Concentration (Cal.)

0.015

Particle Concentration (Exp.)

0.010

Particle Concentration(Cal.)

0.005

Water surface (Cal.)

0.000

0.0

Gravel (cf = 0.196)

0.5

1.0

1.5

Velocity ( m/s )

2.0

0.0

Sphere (cf = 0.444)

0.5

1.0

1.5

Velocity ( m/s )2.0

Gravel (cf = 0.444)

Discharge rate
( m3/s )Fig. 3. Vertical distributions of particle and water velocities and concentrations.
0.0015解Water discharge (Cal.)

0.0010

Sediment discharge (Cal.)解

0.00050.0000SphereGravel(cf = 0.444)

SphereGravel(cf = 0.196)

Water discharge (Exp.)
Sediment discharge (Exp.)

Fig. 4. Discharge rates of water and sediment.
small spheres to imitate gravel particles of jagged shapes. This brings difficulties in simulations due tohigh computation load. Therefore, simulations of gravel particles could not imitate properly thestationary deposited concentration of experimental particles. This seems to the cause of difference inconcentrations distributions between the experiment and the simulation.
In the experiment case of cf = 0.444, vertical distributions of particle volume concentrations could
not be measured because of the sediment sampler clogging. Only vertical particle velocities werecompared between simulated and experimental ones. Simulated gravel velocities were smaller thanexperimental ones, on the other hand, simulated sphere velocities were greater than experimental ones.
Fig.4 shows discharge rates of water and particles. Experimental values of water and sediment discharge
rates and particle velocities were nearly intermediate between simulated values of spheres and gravels
for both cases of cf = 0.196 and 0.444. It can be concluded that the present Euler-Lagrange simulation
is able to reproduce the distributions of particle velocities and discharge rates of water and particles invarious concentrations by selecting suitable particle shapes.

6. Stresses of water and particles in two phase flows
It is important to clarify the difference in stresses between sphere-water flows and gravel-water flows.
Here, stresses of water, spheres and gravels were predicted from the Euler-Lagrange simulation results.
Stresses of water and particles in uniform flows are able to be estimated by Eqs. (4) and (5)x(4)
    g 3  f 3 dx 3
 33 s3

x3

 31  

x 3s

x3

  g  f dx




1

1



3

(5)

where the superscript β denotes the values of water “w” and particles “p” respectively. σ is the stressand α is a volume fraction of water or particles. f is fluid force represented by the relationship of fi p = − fi w.
Superscript s denotes the value of the water surface. The coordinate systems are presented in Fig. 2.
The predicted vertical distributions of stresses and apparent particle friction angles, θ f =arctan(σ31/(−σ33)) are indicated in Fig.5. Apparent particle friction angles θf p of cf = 0.1 96 were greaterthan those of 0.444. The turbulence could bring greater apparent friction angles for cf = 0.196. Apparent
particle friction anglesθf p of cf = 0.444 were about 30˚ for spheres and about 40˚ for gravels. Those angles

190.005
0.000

0

50

100 150( Pa )

0.010
0.005
0.000

200

−σ33 (cf = 0.196)

z(m)

0.025
0.020
0.015
0.010

0.025
0.020
0.015
0.010

0.005

0.005

0.000

0.000

0

100 200 300 400 500( Pa )−σ33 (c = 0.444)
f

20

40
( Pa )

60

σ31 (cf = 0.196)z(m)−σ33p (S)−σ33w (S)−σ33m (S)−σ33p (G)−σ33w (G)−σ33m (G)

0

0.005
0.000

80
σ31p (S)σ31w (S)σ31m (S)σ31p (G)σ31w (G)σ31m (G)θf p (S)θf w (S)θf m (S)θf p (G)θf w (G)θf m (G)

0.010

z(m)

0.010

0.015

σ31p (S)σ31w (S)σ31m (S)σ31p (G)σ31w (G)σ31m (G)0.015

Particle (Sphere Case)

0

0.025
θf p (S)θf w (S)θf m (S)θf p (G)θf w (G)θf m (G)

0.015
0.010

σ31 (cf = 0.444)

0.000

Water (Sphere Case)
Mixture (Sphere Case)
Particle (Gravel Case)
Water (Gravel Case)

0.020

0.005

0 20 40 60 80 100120140160( Pa )

10 20 30 40 50 60°(deg.)

θf =arctan( σ31/(−σ33)) (cf = 0.196)z(m)−σ33p (S)−σ33w (S)−σ33m (S)−σ33p (G)−σ33w (G)−σ33m (G)

z(m)

z(m)

0.015

0

Mixture (Gravel Case)

10 20 30 40 50 60(deg.)

θf =arctan( σ31/(−σ33)) (cf = 0.444)

Fig. 5. Vertical distributions of stresses and apparent friction angles.

nearly coincided with the simulated internal particle friction angles ϕμ measured by the direct shear test
simulations (see Fig.1). 2D DEM simulations of the biaxial compression test [5] proved that circularcylinders had difficulty restraining particle rotations by just only increasing friction angles of particlesurfaces ϕs and reproducing internal friction angles ϕμ greater than about 30˚. In other words, althoughapparent friction anglesθf p is equivalent to the internal friction angles ϕμ in highly concentrated debris
flows, spheres could not produce large internal friction angles 40˚ as gravels. It was concluded that the useof spheres was hard to reproduce debris flows of gravels. In high concentration cf = 0.444, particle shear
stressσ31 p was dominant, while water shear stressσ31w was dominant in the debris flow of cf = 0.196.
Therefore, main resistances of highly concentrated debris flows were caused by particles and strongly
affected by apparent friction angles of particles. Then, in highly concentrated flows of cf = 0.444,
considerably smaller sediment discharge rate of gravels than that of spheres (see Fig.4) was brought by thedifference of friction angles of spheres and gravels.

7. Conclusions
The results of debris flow experiments of sediment discharge concentration of cf = 0.196 and 0.444
were examined using materials of spheres and gravels by the Euler-Lagrange approach. The
comparisons of the results of simulation and experiments brought that the present Euler-Lagrange
simulation was able to reproduce vertical distributions of particle velocities and discharge rates of waterand particles of various concentrations only if suitable particle shapes were selected for the debris flow
simulations. The difference of friction angles between spheres and gravel caused considerable effects
on the reproducibility of highly concentrated debris flows such as cf = 0.444 where particle shear stress
was dominant.
References
[1]
[2]
[3]
[4]
[5]

Egashira S., Itoh T. and Takeuchi H.: Transition mechanism of debris flows over rigid bed to over erodible
bed, Physics and chemistry of the Earth (B), Vol. 26, No. 2, pp.169-174, 2001.
Fukuoka, S., Fukuda, T. and Uchida, T.: Effects of sizes and shapes of gravel particles on sedimenttransports and bed variations in a numerical movable-bed channel, Advances in Water Resources, Vol.72,
pp.84-96, 2014.10.
Ushijima S, Fukutani A and Makino O. Prediction method for movements with collisions of arbitraryshaped objects in 3D free-surface flows. JSCE J B, Vol.64 (2), pp.128-38, 2008.
Latham,J.P., Munjiza,A., Mindel,J., Xiang,J., Guises,R. Garcia,X., Pain,C. Gorman,G and Piggott,M.:
Modelling of massive particulates for break water engineering using coupled FEMDEM and CFD,
Particuology, Vol.6, pp.573-583, 2008.
Maeda, K. and Hirabayashi, H.: Influence of grain properties on macro mechanical behaviors of granular
media by DEM, Journal of Applied Mechanics, Vol. 9, pp. 623-630, 2006.

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