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

Effects of particle shapes and sizes on fundamental movement
Organizing
committees
processesof particles and sediment transport rates
in gravel streams
Hazumu Tadokoro
International Scientific Committee

TOKEN C.E.E Consultants Co., Ltd.
1-8-63, Temmabashi, Osaka Kita-ku, Osaka 530-0042, Japan
Balachandar, S. (Universityof7636
Florida,Tel. +81 (06)1152,USA)
Fax: +81 (06) 7636 1153,

Blondeaux, P. (University of Genova, Italy)
e-mail : tadokoro-h@tokencon.co.jp
Brocchini, M. (Università
Politecnica delle Marche, Italy)
Dong, P. (University of Dundee, U.K.)
Elghobashi, S. (University of California Irvine, USA)
Shoji Fukuoka
Guillou, S. (University
Caen,France) Initiative, Chuo University
Researchofand
Development
Hsu, T.J. (Universityof Delaware,USA) Tokyo 112-8551, Japan
1-13-27,
Kasuga, Bunkyo-ku,
Tel. University,+81 (03) 3817
1625, Fax: +81 (03) 3817 1625,
Izumi, N. (Hokkaido
Japan)
Jenkins, J. T. (Cornell University, USA)e-mail : sfuku@tamacc.chuo-u.ac.jp
Meiburg, E. (University of California, USA)
Nguyen, K.D. (Laboratory for Hydraulics Saint-Venant, France)
Pham Van Bang, D. (Laboratory Tomoofor Hydraulics
FukudaSaint-Venant, France)
Shimizu, Y. (Hokkaido
University,
Japan)
Research and Development Initiative, Chuo University
Simonin, O. (Institut
National
Polytechniquede Toulouse,
1-13-27,
Kasuga,Bunkyo-ku, Tokyo
112-8551,France)
Japan
Tel. +81
3817
1625, Fax: +81 (03) 3817 1625,
Soldati, A. (Universityof (03)
Udine,
Italy)
Toorman, E.A. (KU Leuven, Belgium)
e-mail : t-fukuda@tamacc.chuo-u.ac.jp
Uhlmann, M. (KIT Karlsruhe, Germany)
Wang, G.Q. (Tsing-Hua University, China)
Gravel-bed rivers are composed of particles with a large variety of sizes and shapes. Largeparticles would resist against flood flows, but are picked up and move intermittently. We estimate
Local movement
Organizingprocesses
Committee
fundamentalof particles with different sizes and shapes and the sedimenttransport rate based on fundamental movement processes by numerical movable-bed simulations. The
Fukuoka,shapes
S. (Chair)(Chuo University)
effect of particle
on movement
processes of large particles is greater than that of small
Gotoh,
H.
(KyotoUniversity)
particles. Therefore, the effect of different particle shapes on sediment transport rate appears
conspicuously
in large
particles.University)
Izumi,
N. (Hokkaido
Kajishima, T. (Osaka University)
Key Words:
gravel bedK.
river,
particleshape, particle size, fundamental movement process,Kashiyama,(Chuo
University)
sediment transport rate, numerical movable-bed channel.
Mizuyama, T. (National Graduate Institute for Policy Studies)
Nakagawa, H. (Kyoto University)
1. Introduction
Sakai, M. (The University of Tokyo)
Sato, S. (The University of Tokyo)
Gravel-bed rivers consist of a large variety of particle sizes and shapes．Large particles at the bed
Sekine,M.flows,(Wasedaresist against
flood
butUniversity)
are picked up and move intermittently. These particle motions are
Shimizu,Y.
(Hokkaido
University)
different from those in sandy rivers
where most of particles tend to move continuously. The sediment
Ushijima,
S. (Kyoto
University)transport rateof mixed
particles
is given by Eq.(1) based on fundamental processes such as pick-up
Uchida,(Chuo
University)
rate and step
lengthT.of(Secretary)
particle withdiameter
dij.
3
A d
(1)
q  f ( d ) 3 ij    p s
Bijij

A 2 d ij

2

ij

ij

Where Secretariat
i: particle size , j particle shape, ps： pick-up rate, Λ： step length, A3d3：particle volume,
Research and Development Initiative (RDI), Chuo University
2
A2d ：particle area projected from above, f(dij): area ratio of dij.
To estimate sediment transport rates in gravel-bed rivers, fundamental movement processes ofparticles with different sizes and shapes have to be investigated. Fukuoka et al. (2014) developed anumerical movable-bed channel which could simulate three-dimensional motions of flows and gravel93

通過重量100分率(%)

Cumulative percentage

flow
x=8m

x=10m

Fig.1 Numerical movable-bed channel.

Sphere

80
60
40
20
0
10

100

粒径(mm)
Grain
Size (mm)1000

Fig.2 Particle size distribution.

Table 1. Shape factor and length of gravel particles.
Shape No.
a: Longest
b: Intermediatec: Shortest
Shape Factor

4

Shape 1
2
3
Fig.3 Shape of gravels particles.

100

Sphere Shape 1 Shape 2 Shape 3 Shape 4
1
1.26
1.29
1.36
1.49
1
0.98
1.06
0.99
0.89
1
0.88
0.81
0.78
0.76
1
0.79
0.69
0.67
0.66

particles with different shapes and sizes (see Fig.1). In this paper, numerical movable-bed simulations
were conducted under three conditions of spheres, gravel particles and mixed particles, and sedimenttransport rates and fundamental processes were measured to estimate respective effects of the own
particle shape and surrounding particles on sediment transport.

2. Numerical computation method
Particle motions were simulated in the Lagrangian method as the rigid-body and fluid motions werein the Eulerian method. To take into account the effect of the solid phase on the liquid phase, fluid
motions were simulated by the governing equations of one-fluid model for solid-liquid flows. Particle
contacts were computed by distinct element method (DEM). Fluid dynamic forces on particles werecomputed directly by integrating the forces on a particle. Gravel particles with different shapes andsizes were made by the superposition of small spheres. The validation of the numerical computation
method was checked by distributions of velocities and concentrations of real gravel particles measured
in a large open channel flow(Fukuoka et al., 2014).

3. Simulation conditions
In the numerical simulations, we used five particle sizes(40, 50, 70, 90, 120 mm) (see Fig.2), andfour gravel particle shapes (see Fig.3). Particles of 40, 50 and 70 mm were categorized as small
particles, 90 and 120 mm as large particles. The diameter of gravels was defined by a diameter ofspheres having the same volume. This means that A3d3 of Eq (1) is the same value for every particle
sizes in this stady. It is common to use the shape factor (Eq.(2)) which consists of long, middle andshort axes of particles.
S .F . 

c

(2)

ab

Where a: long axis, b: middle axis, c: short axis. The shape factors are close to 1 as particle shapes arealike to the sphere shape. Shape No.1 is the closest to the sphere, and other gravel shape factors arealmost similar values (see Table1). Particles were packed in numerical movable-bed simulation
channels (length is 15 m, width 1 m, depth 1 m and bed slope 1/20). A water discharge of 0.5 m3/s was
supplied at the upstream end of the channel, and the zero pressure condition was set at the downstream
end. The equal amount of water and particle volumes discharging out from the channel were suppliedat the upstream end of the channel. Sediment transport rate and movement processes of particles were
measured in sections from x=2 m to x=12 m.

4. Transport rates of particles with different shapes and sizes
Figure 4 and 5 show average sediment transport rates measured in 2m and 60 seconds intervals withrespect to space and time. To compare sediment transport rates of every particle with that mixed
particles, transport rates of spherical particles and gravel particles were multiplied by 1/5, and by 4/5
respectively. Transport rates of large particles become greater than that of small particles. Moreover,94

sediment transport rate became large as particle shapes were close to the sphere. Sphere transport rates
in mixed particles were smaller than that of sphere particles only due to the increase in engagement
effects of surrounding particles. In other words, the particle movement was affected by not only own
particle shape, but also surrounding particle shapes.

5. Fundamental movement processes of particles
Fundamental movement processes (pick-up rate, step length and particle projected area) ofsediments with different sizes and shapes are estimated from results of the numerical movable-bed
simulation. Effects of particle sizes and shapes on fundamental movement processes and sedimenttransport rates were discussed below.
The A2d2 is defined as a projected area measured from above at the time just before particles are
picked up. Figure 6 shows dimensionless average areas of particle from above just before picking up a
particle. They were nondimensionalized by the projected area of the equivalent size sphere (πd2/ 4).
We assume that particles are picked up when the velocity of particles exceeds 0.05m/s. Figure 7 shows
the pick-up process of particles. The A2d2 becomes large as the particle shape deviates from a sphereshape, because particles tend to rest stably by directing flat plane toward the top and lowering a centerof gravity (see Fig.7(a)). The dimentionless A2d2 of large particles is larger than that of small particles.
It is reason why large particles were not affected much by surrounding particles compared with small
particles.
Pick-up rates of particles in every shapes and sizes were evaluated by the ratio of area which someparticles picked up in a unit time had occupied on the bed surface to the area which the same particles
occupied on the bed surface. Figure 8 shows averaged pick-up rate of particles in every sizes andshapes. Pick-up rates of small particles became smaller as particle shapes deviate from a sphere, but
those of large particles took almost constant values. Pick-up rates did not greatly vary in comparison
with A2d2. In short, pick-up rates were mainly affected by the placement of the surrounding particles.
Therefore, it is hard to recognize conspicuously the effect of particle shape on pick-up rate.
The step length was defined as the distance that particles move from pick-up to deposition. Step
lengths of large particles were unable to be measured within length of the numerical channel. Figure 9shows step lengths of small particles nondimensionalized by particle diameters. The step length
became larger as particle shapes differed much from a sphere shape. Rolling particles had large
projected area to the flow and hard to stop as particle shapes deviated from a sphere. However, No.3
and 4 particles do not show such a characteristic. Therefore, it is difficult to evaluate effects of particle
shapes on step lengths by only using the conventional shape factor (Eq.(2)). Figure 10 shows therelationship between the step length and the smallest projected area of particles during moving periods.
Dimensionless step lengths are small except spheres as particles are small and have smallest projection
areas. Then, rolling particles are easy to stop, because projected areas in the streamwise direction
SpheresGravel particles

Mixed particles

2.5E‐04

Sediment transportrate(m3/s)

Sediment transportrate(m3/s)

2.5E‐04
2.0E‐04
1.5E‐04
1.0E‐04
5.0E‐05
0.0E+00

Sphere1

Shape1
nshp=1

Shape2
nshp=2 Shape3
nshp=3

Shape4
nshp=4

Dimensionless area ofparticle from above(A2d2/(πd2/4))

Spheres

1.0E‐04
5.0E‐05
SphereShape1

Shape2

Shape3

Shape4

Fig.5 Sediment transport rate in mixed conditions.

Mixed particles

40mm

1.2

50mm

flow

flow

(a) Stop(b) Pick-up

70mm

1.1

90mm

1
0.9

混合

1.5E‐04

0.0E+00

Fig.4 Sediment transport rate in sphere and gravel.
1.3

2.0E‐04

120mm
SphereSphereShape1

Shape2

Shape3

Shape4

Fig.6 Average area of particle measured from above,
just before picking up particles.

95

Fig.7 An example of picked up particle.

D=40mm20

D=50mm

15

D=70mm

120mm
SphereSphereShape1

Shape2

Shape3

Shape4

Fig.8 Pick-up rate with respect to particle
shapes and sizes.

step length(Λ/d)

D=50mm2

25
20 Shape 4

D=70mm1

Sphere shape

3

15
10
0.70

0.80

0.90

1.00

Dimensionless smallest projected area
Fig.10 Comparison between step length andsmallest projected area.

step length(Λ/d)

25

90mm

D=40mm30

Dimensionless

50mm
70mm

0.01
0

30

Dimensionless

0.02

40mm

10

SphereSphereShape1

Shape2

Shape3

Shape4

Fig.9 Step length with respect to particle
shapes and sizes.
Sediment transport rate(m3/s)

Pick-up rate (1/s)

0.03

3.0E‐05: Sediment transport rate calculated by Eq.(1): Sediment transport rate measured directly

2.0E‐05
1.0E‐05
0.0E+00

SphereSphereShape1

Shape2

Shape3

Shape4

Fig.11 Comparison between Eq.(1) andsediment transport rate.

become small.
Sediment transport rates of Eq.(1) calculated using results of fundamental movement processes
were compared with those of numerical movable-bed simulations(see Fig.11). It was confirmed thatEq.(1) reproduced well sediment transport rates of each particle sizes and shapes measured directly inthe numerical channel.
Finally, we investigated further the relationship between sediment transport rate and fundamental
movement processes (step length, pick-up rate and A2d2). In both small and large particles, A2d2
become large as particle shapes varied from the sphere, but the pick-up rate did not greatly change incomparison with A2d2. In short, the number of picked up particles per unit time (ps/ A2d2) become
small as particle shapes differ from the sphere. The step length becomes large as particle shapes aredifferent from the sphere. The product ((Ps /A2d2)×Λ) of the number of picked up particles and step
length is affected by the number of picked up particles (ps/ A2d2) than step length (Λ) , because of theeffect of particle shapes. Therefore, sediment transport rates are small as particle shapes vary from thesphere. In regard to large particles, effects of the bottom roughness on particle motions were relatively
small compared to own particle shapes. Therefore, the difference in particle shapes on sedimenttransport rates appears markedly on large particles. Sediment transport rates of small spheres and large
spheres were maximum 1.3 times larger and 2 times larger than those of gravel particles, respectively(see Fig.5). Fundamental movement processes are different in every sizes and shapes. Therefore, toassess direct effects of particle shapes and sizes on fundamental movement processes are important for
estimations of transport rates of mixed sediments.

6. Conclusions
The applicability of sediment transport equation(1) was checked with the fundamental movement
processes measured in the numerical channel. Eq.(1) reproduced well sediment transport rates of eachparticle sizes and shapes measured directly in the numerical channel. However, they are different inevery sizes and shapes. From the present investigations, it was found that the assessments of direct
effects of particle shapes and sizes on fundamental movement processes are important for moreaccurate estimations of mixed sediments transport rates.
References[1]

Fukuoka, S., Fukuda, T. and Uchida, T. (2014). Effects of sizes and shapes of gravel particles on
sediment transports and bed variations in a numerical movable-bed channel., Advances in Water
Resources, Volume 72, p. 84-96.

96