E3S Web of Conferences 415, 01027 (2023)
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https://doi.org/10.1051/e3sconf/202341501027

How are fine sediments described in sediment sheet flow?
Taro Uchida1*, Yuki Nishiguchi2, Satoshi Niwa3, Takeshi Kubo4, Yutaka Gonda5 , and Yoshifumi Satofuka6
1Faculty of Life and Environmental Sciences, University of Tsukuba, Tsukuba, Ibaraki, 3058572, Japan
2CTI Engineering, Co., Ltd., Tsukuba, Ibaraki, 3002358, Japan
3Japan Conservation Engineers, Co., Ltd., Urawa, Saitama, 3300074, Japan
4Kokusai Kogyo, Co., Ltd., Fuchu, Tokyo, 1830057, Japan5Faculty of Agriculture, Niigata University, Niigata, 9502181, Japan
6College of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, 5258577, JapanAbstract. Stony debris flow transits to sediment sheet flow when the river bed gradient becomes gentle.
The sediment sheet flow consists of a water flow layer and a sediment moving layer. Fine sediments areexpected to behave as a part of the fluid rather than a solid phase in the sediment moving layer. Further, it
can be thought that a part of fine sediment can be suspended in the water flow layer. However, it was notpossible to physically express whether the fine sediment behaves as a solid phase or a fluid phase in thenumerical simulation model. Here we physically modeled fine sediment behavior in sediment sheet flow.
We confirmed the applicability of the new model to describe the longitudinal deposited sediment gradientin flume experiments.

A variety of flow types have been observed in mountainstreams and laboratory experiments [1, 2]. Furthermore,
several classifications have been proposed in terms ofsediment concentration, flow velocity, grain size, and soon. In recent decades, several researchers have clarified
that the thickness of the sediment moving (mixture)layer is one of the key characteristics of flow inmountain streams [3, 4]. In gentle streams withrelatively coarse sediment, normal flow with bed load
was commonly observed (Fig. 1a) [3, 4].
Several flume experiments demonstrated that thethickness of the sediment moving layer increases as theriverbed gradient increases (Fig. 1) [3, 4]. If theriverbed’s critical value was exceeded, the sediments
were distributed uniformly throughout the entire flow
depth (Fig. 1c). This was referred to as “(stony) debrisflow” [3]. If the riverbed gradient was less than thecritical value, the sediment moving layer would occur
only in the lower part of the flow (Fig. 1b) [3, 4]. This
type of flow was referred to as “immature debris flow,”“sediment sheet flow,” and so on [3].
Stony debris flows composed consists of twophases: solid (e.g., rocks, stones, etc) and fluid. In stonydebris flow, relatively coarse sediments move in alaminar manner [3, 4, 5]. However, interstitial fluid
behaves as a turbulent flow. Flume experiments also
revealed that when the particle size of bed sedimentdecreases, turbulent suspension occurs [4, 6]. Thus, finesediments are expected to behave as a fluid phase rather
than a solid phase in stony debris flows. Suspended
sediment influenced pore water pressure [2, 4, 7]. This
process increased the bouyon force acting on coarse
sediment while decreasing energy dissipation caused bysediment collisions [5, 7]. Several numerical simulation
models have been created [8]. Several models haveincorporated this fine sediment processes [7, 9, 10]. In
recent studies, we successfully reproduced various

debris flow behaviors using these models [7, 10],demonstrating the importance of fine sediments indebris flow.
It is possible that even in sediment sheet flow, finesediment in the sediment moving layer behaves as aninterstitial fluid (type B in Fig. 2). Furthermore, if a large
amount of fine sediment is included in the sediment
sheet flow, a part of the fine sediment may be turbulently
suspended in the surface water flow layer (type A in Fig.
2). However, fine sediment behavior is not fully
understood in sediment sheet flow. Thus, in many cases,
types A and B sediment are not directly described inphysically-based models. Here we created new
numerical simulation models to physically describe finesediment behavior in sediment sheet flow and used themin flume experiments.
(a) Flow withbedloadGentle(b) Sediment sheet
flow/immaturedebris flow

Riverbed gradient

1 Introduction(c) Stony debris flow
SteepFig. 1. Schematic illustration of flow type transition due
to riverbed gradient change* Corresponding author: uchida.taro.fw@u.tsukuba.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/).

E3S Web of Conferences 415, 01027 (2023)
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Table 1. Experimental condition

Fig. 2. Schematic illustration of sediment sheet flow

2 Flume experiments
We examined the sediment transport capacity ofsediment sheet flow flume experiment data. The
experimental flume was a straight rectangular channel
10 cm wide and 7 m long (Fig. 3). The flume's gradient
was adjusted by 10 or 15 degrees. A 20-cm-high plate isinstalled at the downstream end of the flume. Then, wecreated a steady-state debris flow using a hopper and apump. The equilibrium longitudinal gradient, defined as
the gradient without bed erosion or deposition, wasmeasured using three ultrasonic sensors. So, we canassess the sediment transport capacity under a given
hydraulic condition.
We examined 56 experimental results in which thesediment concentration, water flow rate, flume gradient,and particle size distribution all varied (Table 1). The
volumetric sediment concentration was set between 6.2
and 29.8 %. The water flow rate ranged from 0.75 to 2.5
L/s. In the experiments, four types of sand with varying
particle size distributions and average diameters ranging
from 1.03 to 3.62 mm were supplied from the hopper.
The grain size distribution of used sand is shown in Fig.
4Fig. 4. Schematic illustration of flume experiments.

Case

Sediment

123
4
5678
9101112
13
14
15
16
17
18
1920
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56

Sediment I

Sediment III

Sediment III

Sediment IV

Gradient(deg.)

Water flow（ℓ /s）

Seiment conc.
（％）

15
15
15
10
1015
15
15
1010
15
15
15
15
15
1010101015
15
1015
1015
15
15
1015
15
10101015
15
101010101510101515
15
15
15
15
15
10
15
15
15
15
15
15

0.75
1
1.5
2
2.5
0.75
1
1.5
2
2.5
1
1.5
2
2.5
0.75
1
1.5
2
2.5
0.75
1
1.5
2
2.5
1
1.5
2
2.5
0.75
1
1.5
2
2.5
0.75
1
1.5
2
2.5
1
1.5
2
2.5
0.75
1
1.5
2
2.5
0.75
1
1.5
2
2.5
1
1.5
2
2.5

18.01
14.14
9.89
7.61
6.18
24.80
19.83
14.16
11.01
9.00
26.24
19.17
15.10
12.46
22.50
17.88
12.68
9.82
8.01
29.19
23.62
17.09
13.39
11.01
29.52
21.83
17.31
14.35
21.43
16.98
12.00
9.28
7.56
28.28
22.82
16.47
12.88
10.58
29.29
21.64
17.16
14.22
21.24
16.82
11.88
9.18
7.48
26.85
21.59
15.51
12.10
9.92
29.82
22.07
17.52
14.53

3 Numerical simulation
3.1 Numerical simulation model
In this study, we developed a new numerical simulation
model for describing three types of sediments insediment sheet flow (types A through C in Fig. 2). TheFig. 5. Grain size distribution of sand for flume experiments

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3.1.3 Suspended sediment in the water flow layer(type A sediment)

developed new numerical simulation model was built on
physical, mathematical, and computational foundationsof Kanako-LS [10]. Kanako-LS is a single-phase modelthat evaluates erosion and deposition rates as well as
riverbed shear stress based on Takahashi andcolleagues’ theories [1]. In the theories, the flow
conditions are classified into three types based on
sediment concentration: stony debris flow, immaturedebris flow, and turbulent water flow, and the dynamics
and effects of type C sediment are described in detail.
Three different theories were proposed to assess bed
shear stress for each flow condition. Then, Uchida et al(2013) added type B sediment to Takahashi’s theories
and created Kanako-LS [10]. Kanako-LS assumed thattype B sediments increase fluid bulk density but do notcontribute to energy dissipation due to sedimentcollisions [10, 11].
However, in Kanako-LS, the process of transitioning
from type C to type B sediment (phase-shift) was not
fully described physically. Additionally, type A
sediments were not represented. In this study, werevised Kanako-LS to describe sediment sheet flow
containing fine sediments.

Previous flume tests demonstrated that sediment in thewater flow layer was diffused in turbulent flow [13]. Ina steady state, the sediment concentration at the bottomof the water flow layer was the same as that of thesediment moving layer [13]. According to theseevidences, we modeled type A sediment as; (1) theprofile of sediment concentration was described by theLane-Kalinske equation, (2) the deposition rate of typeA sediment at the bottom of the water flow layer (Rs)
was calculated by multiplying the sedimentconcentration at the bottom of the water flow layer by
the setteling velocity obtained by Rubey's equation, and(3) the pickup rate of type C sediment at the interface
between the water flow layer and sediment moving layer(Rp) was obtained by multiplying the sedimentconcentration of sediment moving layer by the settling
velocity (blue broken arrow in Fig. 5).
Flow surface

Height in flow

described by Lane-Kalinske equation.

3.1.1 Coarse sediment in the sediment moving
layer (type C sediment)
Like Kanako-LS, Takahashi’s theories were adapted tomodel type C sediment and its effects, such as riverbed
shear stress. We calculated the equilibrium
concentration and erosion/deposition rate of type C
sediment using Takahashi’s theories [10, 11]. We also
assumed that the volumetric type C concentration(Cc=0.159) remained constant over time and space.
Thus, the thickness of the sediment moving layer (hs)was calculated by dividing the amount of type C by Cc(red solid arrows in Fig. 5).

calculated by multiplying CAb
by the setteling velocity

Type ARsType BhsRp

Type C

calculated by multiplying (CB+CC) by the setteling velocity
apply Takahashi’s theory
apply eq. (1)calculated by dividing theamount of Type C by CcCAb
CBCC
Sediment concentration

assume constantFig. 5. Schematic illustration of a proposed numericalsimulation method for describing sediment sheet flow
3.2 Calculation
We applied our new numerical simulation model to theprevious chapter's flume experiment. We calculated all
56 cases. We modeled the experimental flume andestablished the initial conditions for the experiments.
Then, water and sediments are inputted from the top, andcalculations are run until a steady-state condition isreached. We extracted the longitudinal gradient of theriverbed during the steady state.

3.1.2 Phase-shifted sediment in sediment moving
layer (type B sediment)
Previous flume experiments suggested that the phaseshift of fine sediment in stony debris flow can be
described as the ratio of the debris flow's shear velocity
or turbulent velocity to the sediment's settling velocity[6]. For example, Sakai et al. (2019) demonstrated thatthe ratio of fine sediment that behaves as a fluid
increased linearly with the ratio of shear velocity or
turbulent velocity to settling velocity [6]. According tothese studies, if the sediment met the following
condition, it would behave as an interstitial fluid in thesediment moving layer,𝑢 ∗> 𝛼𝜔(𝑑)(1)where 𝑢∗ is shear velocity, 𝛼 is coefficient, and w(d) issettling velocity of sediment with diameter d (black
dotted arrow in Fig. 5). However, if there is a lot of finesediment in the debris flow, the sediment satisfied by eq.
(1) should be very large. So, we set 0.45 as the upper
limit of fine sediment concentration in interstitial fluid.

4 Results and discussions
4.1 Summary of experimental results
The equilibrium longitudinal gradient increased assediment concentration increased. Furthermore, while
the sediment concentration remained constant, theequilibrium gradient changed. The equilibrium gradient
was steep in sediment I and gentle in sediment IV. Thisimplies that the equilibrium gradient decreased as thefine sediment ratio increased.
Figure 6 depicts the relationship based on
Takahashi’s theory for type C. The sediment I plot wasslightly larger than the theoretical line, but the data3

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followed the same trends as the theoretical relationship.
While the difference between the data of sediment II
through IV and the theoretical relationship was large, itsuggested that the type C sediment could not fully
describe the flume experiment results. This implies that
if the effects of fine sediments are ignored, theequilibrium gradients should be overestimated in thecase of sediments II through IV.

In this simulation, we searched best-fit by trial anderror. In suspended sediment theory, it has been
generally assumed that sediments whose friction
velocity exceeds their settling velocity will besuspended. While it has been reported that a part of theenergy was dissipated by collision and friction of type C
sediment in sediment sheet flow [1]. Thus, we believethat the =3 is reasonable.

4.2 Comparison between flume experiment andnumerical simulation

5 Conclusions

When we set =3, the calculated equilibrium
longitudinal gradients agreed well with the observed
equilibrium gradients (Fig. 7), even though the particle
size distribution differed greatly. This implies that once
we consider types A and B sediments and their effects,
the equilibrium longitudinal gradients could beevaluated. Flume experiments revealed that thesediment concentration was two to three times higher
than the theoretical values based on Takahashi’s theory
for type C sediments (dotted and broken lines in Fig. 6),
implying that the roles of types A and B, as well as theireffects on sediment transport capacity, maybe the sameto two holds of type C.

We demonstrated that the transport capacity of sediment
sheet flow cannot be described solely by sedimentmoving laminarly in the sediment moving layer. We
must consider the effects of fine sediment suspended ina fluid to evaluate the transport capacity of sediment
sheet flow. Here we proposed a simple method for aphysical description of fine sediment behaviors insediment sheet flow and developed a new numericalsimulation model. Then, we used a new model todescribe the equilibrium longitudinal gradient in flume
experiments. We successfully described the relationshipbetween sediment concentration, grain size distribution,and equilibrium longitudinal gradient, once we modeled
fine sediment suspended in both the interstitial fluid of
the sediment moving layer and the water flow layer.

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Fig. 6. Relationship between sediment concentration andequilibrium longitudinal gradient in flume experiments. The
dotted and broken lines show the relationship when thesediment concentration doubles and triples concerning thesediment concentration at a certain gradient derived from
Takahashi’s theory.

Fig. 7. Observed and calculated the longitudinal gradient ofdeposited sediment under steady condition

4