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https://doi.org/10.1051/e3sconf/202341501029

Effect of Including Sand Component in a Debris Flow onConcentration of Coarser Particles at the Flow Front
Takashi Wada1*, Hiroto Mushiake1, and Hiroshi Miwa1
1 Tottori University, Department of Social Systems and Civil Engineering, 4-101 Koyama-cho Minami, Tottori, Japan

Abstract. We conducted flume experiments for a debris flow consisting of coarser particles, finer particles
and sand, focusing on the concentration of coarser particles at the flow front. Our experimental results
revealed that the concentration of coarser particles at the flow front using sediment mixture with sand wasless than that without sand. This may be because including of sand component in the material contributed
to be a smaller averaged interstice between particles in the flow layer and a smaller averaged particle size.
These may lead to reduce the falling volume of sand or finer particles and dispersion pressure for the rise ofcoarser particles, respectively, resulting in the inhibition of inverse grading formation. Our experimental
results also suggested that the changing trend in the proportion of finer particles depended on the relationshipbetween their particle size and the average particle size of the flow. These are consistent with our previous
experimental results using material without sand. This consistency suggested that for the concentration ofcoarser particles at the flow front, the behavior of the sand component can be considered in the same manneras other coarser-sized components.

1 Introduction
A debris flow is composed of sediment particles ofvarious sizes. During its flowing down, particle size
segregation occurs in the flow layer by interacting ofthese particles, resulting in a concentration of coarser
particles at the flow front. This tendency is particularly
pronounced for a debris flow that includes many
boulders, as reported in many studies [1-3]. Therefore,
many flume experiments and theoretical considerations
have been conducted by many researchers to elucidate
their mechanisms [3-6]. We too investigated theirmechanisms for debris flows composed of several
particle sizes by measuring the proportion of their
particles at the flow front using many flume experiments[7-9]. These experimental results suggested that the"falling of finer particles through the interstices between
particles toward the lower flow layer" proposed by
Middleton [4] is the primary mechanism of an inverse
grading. This led to relatively faster transport of coarser
particles and their concentration at debris flow’s front
under various particle size compositions. In addition, wedeveloped a one-dimensional (1-D) numerical model todescribe this mechanism in a debris flow layer and to beable to estimate the sediment sorting at the flow front [9].
The finer component, whose diameter isapproximately 0.01 times a debris flow depth, is often
included in debris flow material. Therefore, it isnecessary to investigate how these components affectthe particle size segregation. In a flume experiment scale
where a debris flow depth is approximately 0.01 times
than that in a real scale, these components correspond to
the sand component with a diameter of 0.1 mm order.

Takahashi et al. [10] developed the numerical model
illustrating the particle size segregation of a debris flow.
In their model, they considered that the behavior of thesand components with a diameter of 0.1 mm order is thesame as that of other coarser-sized components. Theirexperiments for their model validation were conductedwith only one particle size composition of the debris
flow material. Therefore, it is necessary to verify
whether the behavior of sand component can beconsidered similar to other coarser-sized components
for particle size segregation of a debris flow with various
compositions of the material.
In this study, we conducted flume experiments on a
debris flow composed of three-sized particles, including
the sand component, under various compositions of thematerial. We compared these results with those of ourprevious experiment under the same conditions without
the sand component [8, 9], to investigate the effect of
the sand component in a debris flow on theconcentration of coarser particles at the flow front.

2 Setup andExperiment

Conditions

of

Flume

Figure 1 shows the experimental setup consisting of two
tilted straight flumes, a movable sampler with fourboxes, and a digital video camera for measuring
sampling time. The movable bed lengths of flumes A
and B were 90 cm and 300 cm, respectively, and thewidths of flumes A and B were 7 cm and 10 cm,
respectively. The intent for using these two types flumes
was to investigate the effect of including sand* Corresponding author: wada-t@tottori-u.ac.jp© 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/).

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Table 1. Experimental cases and conditions.

Flume B

Supply water;
67 cm2/s(a unit width)

Flume A

Sediment mixtures(Thickness; 5 cm)

Case

Digital video
cameraq =15°
Digital video
cameraDiameter constituting material (mm)
dC
dF
dsand
dm0

Case 1 A
A
10.7
7.1
0.6
6.38
Case 1 B
B
Case 2 A
A
10.7
3.0
0.6
3.75
Case 2 B
B
Case 3 A
A
10.7
1.4
0.6
2.73
Case 3 B
B
Case 4 A
A
7.1
3.0
0.6
3.18
Case 4 B
B
Case 5 A
A
7.1
1.4
0.6
2.15
Case 5 B
B
Case 6 A
A
3.0
1.4
0.6
1.50
Case 6 B
B
dC, dF, dsand and dm0 are the diameters of coarser particles, finerparticles, sand, and the initial mean diameter of materials,
respectively. The proportions of coarser particles, finerparticles, and sand in materials were 1:4:1.25 for all cases.

B=10 cm

B=7 cmFlumeq =15°

Fig. 1. Experimental setup.

component on the concentration of coarser particles atdebris flow’s front, under the different stages of theconcentration due to an increase in the flow distances.
The supplied flow rate per unit width was 0.67 cm²/s,
initial sediment thickness was 5 cm, and flume gradientswas set to 15°. These quantities were common to both
flumes.
The sediment materials were composed of sand witha diameter of 0.6 mm, and two particles (referred to ascoarser and finer particles, respectively) were chosenfrom four particles with diameters in the range of 1.4–
10.7 mm. The proportions of coarser particles, finerparticles, and sand in the materials was 1:4:1.25. The
averaged mass density of these materials () was 2.695
g/cm3, averaged internal friction angle of these materials() was 31.6°, and their concentration in the static
sediment bed (C*) was 0.557. The folloing discussion
defines PC, PF, and Psand as the proportions of the threeparticles to the total material volume, respectively.
The experiments combined various conditions basedon the coarser and finer particle sizes of the material andflow length (i.e., the experimental flume). Table 1 lists
the experimental cases and their corresponding
conditions.
The experimental procedure is described as follows.
After the materials were placed on the flume bed, water
was supplied at the default flow rate at the upstream endof the flume. The supplied water eroded the materials as
flowing down the flume, and a debris flow was
generated. When the debris flow arrived at thedownstream end of the flume, the flow front was
separated into four parts by the sampler, which moved
at a constant speed in the transverse direction withrespect to the flow direction. The time interval duringflowing the flow material into each box was measured
using a digital video camera. Each sample’s total flow
volume, all particle volume, and each sized particle
volume were measured to investigate the temporalchanges in the sediment flux concentration and eachparticle’s proportion. The above processes andmeasurements were repeated thrice for each material
composition and each flume. The above setting andprocedure are the same as the authors’ previous
experiment using debris flow material composed of thetwo particles without sand component [8, 9]. In thefollowing discussion, we compared these experimental
results with our previous ones to investigate the effectof sand component in a debris flow on the proportion ofcoarser and finer particles at the flow front.

PF

PC

(a) 1
0.8
0.6
0.4
0.2
0
1 3
0.8
0.6
0.4
0.2
0
3

Case 2B - Run 1
Case 2B - Run 2
Case 2B - Run 3

Initial Proportion: 0.16
4

5

6
7
8
9 10 11 12 13Time from Start of Water Supply (s)1415

Initial Proportion: 0.64
Finer particle: dF = 3.0 mm
4

5 6 7 8 9 10 11 12 13 14 15Time from Start of Water Supply (s)Excluding sand of Case 2B - Run 1*
Coarser particle:
Excluding sand of Case 2B - Run 2*
0.8
dC = 10.7 mm
Excluding sand of Case 2B - Run 3*
0.6*Wada et al. [9]0.4
Initial Proportion: 0.20
0.2
0
1 3 4 5 6 7 8 9 10 11 12 13 14 15Time from Start of Water Supply (s)0.8
0.6 Initial Proportion: 0.80
0.4
Finer particle:
0.2
dF = 3.0 mm
03 4 5 6 7 8 9 10 11 12 13 14 15Time from Start of Water Supply (s)

PF

PC

(b) 1

Coarser particle: dC = 10.7 mm

Fig. 2. Temporal changes in PC and PF at the front of thedebris flows that were obtained at the downstream end of the
flumes; (a) Case 2 B, (b) excluding sand from Case 2 B [9].

3 Experimental Results and Discussion
Figure 2 shows the temporal changes in PC and PF at thedebris flow front in Case 2 B. The figure also shows the
PC and PF for our previous experiment in which sand in
the materials for Case 2 was excluded [8, 9]. The
concentration of coarser particles at the flow front using
the material with sand was less than that without sand.
The possible reason for this is that the including of sandcontributes to a smaller averaged interstice between
particles in the debris flow layer. This made difficult forparticles to fall through the interstice toward the lower
flow layer, resulting in the inhibition of inverse grading
formation. In addition, the decrease in the averaged2

PSandPFhttps://doi.org/10.1051/e3sconf/202341501029

12
10
8
6
4
2
0

1
Coarser particle: dC = 10.7 mm
Case 1B - Run 1-3
0.8
Case 2B - Run 1-3
0.6
0.4
Initial Propotion: 0.16
0.2
0
1 3 Finer
4 particle:
5
6 dF =7 7.1 8mm (Case
9 101), 3.0
11 mm
12 (Case
13 2)14 15Time from Start of Water Supply (s)0.8Initial Proportion:
0.6
0.64
0.4
0.2
0
1 3 4 5 6 7 8 9 10 11 12 13 14 15
Sand: dSandTime= 0.6frommm Start of Water Supply (s)
0.8
0.6
0.4
Initial Proportion: 0.20
0.2
03 4 5 6 7 8 9 10 11 12 13 14 15

Volume Mean Diameter
(mm)

PC

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10.7 mm (Cases 1, 2)
7.1 mm (Case 1)
3.0 mm (Case 2)

Case 1B - Run 1-3
Case 2B - Run 1-3

0.6 mm (Cases 1, 2)

34

5 6 7 8 9 10 11 12 13 14 15Time from Start of Water Supply (s)Fig. 4. Temporal changes in mean diameter at the front of thedebris flows that were obtained at the flume’s downstream
end for Cases 1 B and 2 B. The red lines in the figure
represent the diameters of component particles of debris flow
materials.
1

Flume A (flow distance; 90cm)

0.8
Initial proportion
without sand; 0.20

0.6

PC

Time from Start of Water Supply (s)0.4

Fig. 3. Temporal changes in PC, PF and PSand at the front of
the debris flows that were obtained at the flume’s
downstream end for Cases 1 B and 2 B.

0.2

Initial proportion with sand; 0.16

02 3 4 5 6 7 8 9 10 11
1 0 1FlumeB (flow distance;d (mm)300cm)
m0

0.8

particle size of a debris flow caused by including sandcomponent also may contribute to reduce the dispersion
pressure owing to particle collisions for the rise ofcoarser particles in the flow layer.
The arrival time to the downstream end of the flumeusing the material with sand was shorter than thatwithout sand. The reason for this is that the decrease in
the averaged particle size by including sand reduced theflow energy dissipation owing to the friction andcollision of these particles in the flow layer. This
increasing in the debris flow velocity also may
contribute to the reduction in the falling of sand or finerparticles in the flow layer. This is because the migration
velocities of particles in the flow direction become more
apparent than those in the downward direction.
Figure 3 shows the temporal changes in PC, PF, andPSand at the debris flow front in Cases 1 B and 2 B. In
these cases, only the finer particle sizes of the materials
were different. In Case 1, PSand was almost zero, PC
increased, and PF decreased from the initial proportionof the material. These results suggested that the finersized particles had a more significant decrease in theflow front, and that when the finest particles were
sufficiently reduced, the proportion of slightly coarser
particles than the finest particles were reduced. In Case2, at the most flow front, PC increased, and PF and PSanddecreased from the initial proportion. These tendencies
are similar to that in Case 1. However, immediately after
the most front, PF became more than the initial
proportion. These results suggest that the change in the
proportion of intermediate-sized particles (in this paper,
we refer to the finer particles) depends on the particle
size composition of the debris flow. Specifically, in thecase where the intermediate-sized particle issignificantly coarser than the average particle size of thedebris flow material, it increases from its initial
proportion like the coarser particle. Otherwise, in thecase where the intermediate-sized particle is nearly
equal to or finer than the average particle size, it
decreases from its initial proportion like the finerparticle. The above inference is

PC

0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10 11Case 1A
Case 2A
Case 3A
Case 4A
Case 5A
Case 6A
Case 1A without sand*Case 2A without sand*Case 3A without sand*Case 4A without sand*Case 5A without sand*Case 6A without sand*Case 1B
Case 2B
Case 3B
Case 4B
Case 5B
Case 6B
Case 1B without sand*Case 2B without sand*Case 3B without sand*Case 4B without sand*Case 5B without sand*Case 6B without sand**Wada et al. [9]dm0 (mm)Fig. 5. Relationship between PC at debris flow front and dm0
for all cases with and without sand. Note that data in the
figures shows that PC in the materials flowed into the firstbox at the flume’s downstream end for three runs in eachcase.
1

Flume A (flow distance; 90cm)

0.8

Initial proportion
with sand; 0.16

PC

0.6

Initial proportion
without sand; 0.20

0.4
0.2
0
0.5 B 1(flow1.52
2.5
3
1 0 Flume
distance;dm0 (mm)300cm)
0.8

3.5 Case 1B

PC

0.6
0.4
0.2
0

0

0.5

1

1.5

2

2.5

3

Case 1A
Case 2A
Case 3A
Case 4A
Case 5A
Case 6A
Case 1A without sand*Case 2A without sand*Case 3A without sand*Case 4A without sand*Case 5A without sand*Case 6A without sand*

3.5

Case 2B
Case 3B
Case 4B
Case 5B
Case 6B
Case 1B without sand*Case 2B without sand*Case 3B without sand*Case 4B without sand*Case 5B without sand*Case 6B without sand**Wada et al. [9]Dimensionless shear stress, τ*Fig. 6. Relationship between PC at debris flow front anddimensionless shear stress, *, for all cases with and withoutsand. Note that data in the figures shows that PC in thematerials flowed into the first box at the flume’s downstream
end for three runs in each case.

also based on the temporal changes in the relationshipbetween the mean diameter and the diameter of each
sized particle in debris flow materials, as shown in
Figure 4. This inference corresponds with the inference
obtained by the authors' previous experimental results
using a material consisted of five or six particles with a3

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diameter of more than 1.4 mm [7]. Therefore, thebehavior of the sand component can be consideredsimilar to other coarser-sized components in themechanism of particle size segregation for various
material compositions.
Figures 5 and 6 show the relationship between the
PC of the materials flowing into the first box and theinitial mean diameter of the material, dm0, anddimensionless shear stress, *, for all cases and previous
cases without the sand [8, 9]. * was calculated by using
the following equation:
* = (ghI)0.5 /{(/ -1)gdm0(1)
where g is the gravitational acceleration, h is thecalculated debris flow depth using the cross-sectional
averaged flow velocity equation proposed by Takahashi[5] and the equation of continuity for a debris flow, I is
the flume gradient,  is the mass density of the materials,
and ρ is the mass density of the interstitial fluid. These
upper and lower figures suggest that, in both cases withdebris flow materials with or without sand, theconcentration of coarser particles at the flow front
becomes more significantly as the flow distanceincreases. These also suggest that with or without sand,the relationship between dm0 and PC is a directly
proportional, and the relationship between * and PC isan inversely proportional. These suggestions imply thatfor a debris flow including the sand component with adiameter of 0.1 mm order, the concentration of coarser
particles at the flow front can be investigated based on
the debris flow hydraulic quantities in the same manneras a debris flow without the sand component. Thus, forthe concentration of coarser particles at the flow front,
the behavior of the sand component can be consideredin the same manner as other coarser-sized components.

component [7]. Furthermore, in both cases with debris
flow materials with or without a sand component, thecommon relationship was observed between theconcentration of coarser particles at the flow front andthe debris flow hydraulic quantities. These results imply
that the concentration of coarser particles at the flow
front can be investigated, considering the behavior of
the sand component in the same manner as othercoarser-sized components.
However, it has not been sufficiently investigatedwhich mechanism is dominant for the coarser particle’s
concentration at the flow front, the "falling of finerparticles toward the lower flow layer," or the "rising ofcoarser particles by dispersion pressure derived fromparticle collisions." In our future works, we will
investigate whether our numerical model only
considered "falling of finer particles" in the flow layer
can estimate our experimental results. If it will bedifficult for our model to estimate, we will reveal thecontribution of "rising of coarser particles by dispersion
pressure" for particle size segregation of a debris flow
with experimental and numerical approaches.

References
1.

R. P. Sharp, L. H. Nobles, Bull. Geol. Soc. Am.,64, 547–560 (1953)
2. S. Okuda, H. Suwa, K. Okunishi, M. Nakano, K.
Yokoyama, Disaster Prev. Res. Inst. Annu. Kyoto
Univ., 20(B-1), 237–263 (1977) (in Japanese withEnglish abstract)
3. J. M. N. T. Gray, B. P. Kokelaar, J. Fluid Mech.
652, 105–137 (2010)
4. G. V. Middleton, Geol. Assoc. Canada, Spec.
Paper (7), 253–272 (1970)
5. T. Takahashi, Hydraul. Div. Proc. Am. Soc. Civ.
Eng., 106(HY3), 381–396 (1980)
6. R. M. Iverson, M. Logan, R. G. LaHusen, M.
Berti, J. Geophys. Res. 115, F03005 (2010)
7. T. Wada, T. Furuya, K. Nakatani, T. Mizuyama,
Y. Satofuka, Int. J. Eros. Control Eng. 8, 20–30(2015)
8. T. Wada, J. Maeda, H. Miwa, Effects of ParticleSize Distribution and Stream Gradient on
Sediment Sorting of a Debris Flow, in Proceedingsof the 22nd IAHR-APD Congress, 15-16
September 2020, Sapporo, Japan (2020)
9. T. Wada, J. Maeda, H. Miwa, J. Jpn. Soc. Civ.
Eng. Ser B1, 76(2), I_1105–I_1110 (2020) (inJapanese with English abstract)
10. T. Takahashi, H. Nakagawa, T. Harada, Y.
Yamashiki, J. Hydraul. Eng., 118, 1490–1570(1992)

4 Conclusion and Future Works
We conducted flume experiments on a debris flow
consisting of coarser particles, finer particles, and sandunder various debris flow compositions. And using our
experimental results, we investigated the effects ofincluding sand components in a debris flow on themechanisms of particle size segregation at the flow front.
In the experimental results, the concentration ofcoarser particles at the flow front using the debris flow
material with sand was less than that without sand. Thisis because including of sand component in debris flow
material contributed to decrease in an averaged
interstice between particles in the flow’s interior, which
made it difficult for sand or finer particles to fall throughthe interstices between particles toward the lower flow
layer. In addition, decreasing of the averaged particle
size could lead to a reduction in the dispersion pressure
for the rise of coarser particles in the flow layer,
resulting in the inhibition of the inverse grading
formation.
Our experimental results also suggested that thechanging trend in the proportion of the intermediatesized particles depended on the relationship between
their particle size and the average particle size of adebris flow. This is consistent with previous
experimental results using material without a sand4