E3S Web of Conferences 415, 02009 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341502009

Pilot study to explain runout distances of debris flow andimmature debris flow considering depositing rate
Hiroaki Izumiyama1*, Takao Yamakoshi1, Yuya Takahashi2, Yuki Nishiguchi2, and Ryosuke Okuyama2
1National Institute for Land and Infrastructure Management, SABO Department, Tsukuba, Japan
2CTI Engineering Co., LTD., Tsukuba, Japan

Abstract. In Japan, many debris flows and sediment-laden floods cause serious damage to human life andproperty. Effective measures require high-accuracy reproduction and prediction of runout distance (bedvariation reach) via numerical simulations. One possible method to increase the accuracy of numericalsimulation results involves reviewing the methods used to evaluate depositing rate for flows that containmany different sizes of sediments. This study performed experiments using an artificial channel and highspeed cameras to identify parameters that govern depositing rate. The channel implemented exhibited achange in slope point; thus, the slope of the upper reach differed from the slope of the lower reach. Theexperiments showed that the equation representing depositing rate is closely related to flow velocity.
Additionally, the equation of depositing rate can be determined if other parameters are consistentlyconsidered.

1 Introduction
In recent years, direct damage caused by debris flows
and sediment-laden floods has become increasinglyapparent, as exemplified by the torrential rain-related
disaster in Hiroshima Prefecture in July 2018 and thedisaster in northern Kyushu in July 2017.
The runout distance of debris flows and/or immaturedebris flows can be roughly estimated from the flow
volume [1,2] or evaluated by numerical calculations thatinvolve shallow water flow equations [3]; however, it isoften underestimated [1]. In this study, we define debris
flows as flows with hs/h = 1 and immature debris flows
as flows with hs/h < 1, where hs is the depth of thesediment movement layer and h is the flow depth. The
runout distance is defined by the downstream terminusof the deposited sediment after a debris flow orimmature debris flow. Although the scientificcommunity has not been in complete agreement
regarding constitutive equations for debris flows and/orimmature debris flows, it would be difficult to improve
such equations because their overall validity has been
confirmed by theoretical considerations and hydraulicexperiments [3,4,5,6]. However, models of entrainmentand deposition processes of debris flows and/orimmature debris flows are derived with the assumptionthat the flow contains a unit size of sediment. Thus, there
is potential for improvement in reproducing actual flowsthat contain many sizes of sediment [3, 7-12].
Therefore, we assumed that the entrainment anddepositing rate equation could be reviewed and revised
if needed. Takahashi [3], Egashira et al. [7], andMiyamoto et al. [12] estimated entrainment anddepositing rates with the assumption that the rate is

proportional to flow velocity. Conversely, Iverson &Ouyang [10] proposed a model proportional to bed shear
stress and inversely proportional to flow velocity.
Although the proportionality of the entrainment anddepositing rate equation to flow velocity can also beinferred from the Iverson & Ouyang model [10], theselection of a constitutive equation reveals acontradiction. If entrainment and depositing rates areassumed to be inversely proportional to flow velocity,
the amount of deposition is lower when the flow velocity
is higher and greater momentum can be retained
downstream. Therefore, the validity of these equations
must be confirmed by comparison with actualpropensity.
In this study, we conducted experiments to confirm
the depositing trend at a change in slope point. We
measured the sediment depositing rate at the change inslope point from camera images of debris flow andimmature debris flow that were descending to thegentler downstream slope section. The velocities of thedebris and immature debris flows were also measured.

2 Methods
2.1 Experimental setup
The experimental flume consisted of a straightchannel (length, 10 m; width, 50 cm; and height, 50 cm)
owned by the National Institute for Land andInfrastructure Management (Figure 1).
This channel can include a change in slope at twopoints along the longitudinal direction. In this

* Corresponding author: izumiyama-h92ta@mlit.go.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, 02009 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341502009

Table 1 Experimental conditions

experiment, the channel width was fixed at 10 cm torestrict lateral variations in flow.
The slope of the channel was varied at the upperchange point. The channel gradient was set at 15° in theupper reach and 5° in the lower reach; these settings
ensured that the debris flow could descend in the upper
section and be transformed into immature debris flow inthe lower section. Additionally, the channel gradient
was set at 5° in the upper reach and 1° in the lower reach;these settings ensured that immature debris flow could
descend in the upper reach and be transformed tobedload in the lower reach.

Slope change points

Fig. 1 Experimental flume

Case

Q*

Channel gradient

d*

dm *

No.

[L/s]

[degrees]

[mm]

[mm]

u *

d *

C1

3.5

15

5

7

7

C2

3.5

15

5

3.1, 12

7C3

3.5

155

3.1, 17

7C4

3.5

5

1

77C5

3.5

5

1

3.1, 127C6

3.5

5

1

3.1, 17

7C7

3.5

15

5

7

7C8

3.5

15

5

3.1, 12

7

C9

3.5

15

5

7

7C10

3.5

15

5

3.1

3.1

C11

3.5

5

1

3.1, 17

7

C12

3.5

5

1

3.1, 12

7

C13

3.5

5

1

1.3, 17

7

C14

3.5

5

1

1.3, 17

3.1

C15

3.5

5

1

7

7

C16

3.5

5

1

3.1

3.1

* Q is discharge of water supply, u is upstream channelgradient, d is downstream channel gradient, d is grain
diameter, dm is averaged grain diameter.
2.2 Measurements
The measurement variables were water level, flow
velocity, depositing height, and thickness of particle
mixture layer. Measurements were obtained byrecording flow conditions in the channel using threehigh-speed cameras that were installed on the sides of
the channel, then analyzing the resulting video images(Figure 2). The high-speed cameras were installed at theslope change point and at approximately 1 m upstream
and downstream of the slope change point (depending
on experimental conditions). The flow velocity profile
was obtained by tracking particles with a density of
approximately 1 g/cm3 (neutrally buoyant particles) thatwere descending with the debris/immature debris flowat several heights. The depth-averaged flow velocity U
and flow depth h were estimated from the profile atintervals of 0.5–1 s, then averaged over intervals of 0.5–
9 s (estimated errors were ± 0.5 cm/s and ± 1.1 cm,respectively). The depositing height was obtained bytracking the static layer surface. The depositing rate E
was obtained from the linear regression line calculated
from the relationship between the depositing height andtime. Specifically, E was time averaged value (estimatederror was ± 0.1 cm).

Fig. 2 Example of high-speed camera image

The experimental material was used in twoconditions:
mixed(polydisperse)
sandandhomogeneous (monodisperse) sand. The mixing ratiosof the materials were adjusted to ensure that the averagegrain sizes of the mixed sand were 7 mm and 3.1 mm,respectively. The diameters of the sands used were 1.3mm, 3.1 mm, 7 mm, 12 mm, and 17 mm. The
experimental material was sieved in accordance withJapanese Industrial Standards (JIS A 1204: 2009 test
method for particle size distribution of soils).
The experimental material was distributed over thebed with a thickness of 0.05 m. Subsequently, to erode
bed material in the upper reach section, water was
supplied from the upstream end at a constant flow rateof 3.5 L/s. The experimental conditions are shown in
Table 1.

2

E3S Web of Conferences 415, 02009 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341502009

The high-speed cameras used were model
MC031CG-SY-UB cameras (Ximea, Germany)equipped with a JHF25M lens (Space Inc., Tokyo,Japan). The camera frame rate was set at 200 fps, andthe image sizes were 1032 × 772 pixels.

h were obtained from values averaged over 0.5–9 s, thus
eliminating deviations in U. Overall, there was apositive correlation between the right-hand side ofEquation (4) and the depositing rate. There was also noclear difference between the relationship formonodisperse material and the relationship forpolydisperse material. Therefore, the entrainment ratio
can be expressed using an equation such as Equation (1),even if the debris flow or immature debris flow consistsof polydisperse particles.

2.3 Expression of entrainment rate
In Japan, entrainment rate E is considered
proportional to the depth-averaged flow velocity U (i.e.,𝐸 ∝ 𝑈), as indicated by Takahashi [3] and Egashira etal. [7]. We investigated the experimental data using
Equation (1):

E at slope change point
cm/s

𝐸 = 𝑈 tan 𝜃 ,2.5−𝜏𝜌1 𝑢1𝑏(2)𝑈.

00204060

2.5

Debris flow
Immature debris flow

2b1.5
10.5

Monodisperse005
10gh sin  / U15Fig. 3 Relationship between depositing rate E
and related factors

E at slope change point
cm/s𝑔ℎsin𝜃

Monodisperse

U tan where 𝜏1𝑏𝑜𝑡 is the shear stress exerted by flow on thebed, 𝜏2𝑡𝑜𝑝 is the shear stress exerted by the bed on flow,𝜌̅1 is the mass density of debris flow or immature debris
flow, and 𝑢1 (𝑧𝑏 ) is the velocity of debris flow orimmature debris flow at the bed surface. Consideringthat 𝑢1 (𝑧𝑏 ) is proportional to the depth-averaged
velocity U, the entrainment rate can be expressed asEquation (3):𝜏𝐸 ∝ 1𝑏𝑜𝑡.
(3)
𝑈This study used 𝜌̅1 𝑔ℎsin 𝜃 as 𝜏1𝑏𝑜𝑡 , where g is theacceleration of gravity and h is the flow depth of debris
or immature debris flow. Because we did not measure
volumetric sediment concentration, we were unable toestimate 𝜌̅1 . Therefore, we omitted the term 𝜌̅1 andexamined the experimental results using the relationshipin Equation (4):𝐸∝

10.5

E at slope change point
cm/s

𝜏

2a1.5

(1)

where is the riverbed gradient.
According to Iverson & Ouyang [10], the entrainment
rate E can be expressed by Equation (2) (in this study,
the term representing the effect of dilatancy wasignored):
2𝑡𝑜𝑝
𝐸 = 1𝑏𝑜𝑡,(𝑧 )̅Debris flow
Immature debris flow

(4)

Upon selection of a model in which 𝜏1𝑏𝑜𝑡 is
proportional to the square of U, Equation (3) assumes
the form of an equation proportional to the flow velocity.

2.5

Debris flow2

Immature debris flow

1.5
1Monodisperse

0.5
00200
Runout distance cm

400Fig. 4 Relationship between depositing rate Eand runout distance3 Results and Discussion

However, this result should be investigated in othercoherent experimental conditions. The constitutive lawof debris flow depends on the relative flow depth h/d(where d is the diameter of smaller sediment contained
in debris flow or immature debris flow) and the
movement of particles. In cases 13 and 14 with h/d (≅25), small particles (1.3 mm) may constitute mudflow.
Additionally, in other cases of polydisperse material,
smaller particles can change their vertical positions
because of spaces between large particles.
The relationships between the depositing rate and therunout distances of debris flow and immature debris
flow are shown in Figure 4. The runout distance

The relationship between the depositing rate obtained
experimentally at the slope change point and Equation(1) is shown in Figure 3a. U averaged over intervals of
0.5–9 s was used for calculation of Equation (1) toeliminate deviations in U. Overall, E was positively
correlated with U tan, and there was no clear difference
between the relationship for monodisperse material andthe relationship for polydisperse material.
The relationship between the depositing rate at theslope change point and the right-hand side of Equation(4) is shown in Figure 3b. U and h in Equation (4) are
obtained from measured values at the upper reach. U and3

E3S Web of Conferences 415, 02009 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341502009

constitutes the position of the flow front at 3 s after theinitiation of water supply. Although a clear trend cannot
be discerned because of the small number ofexperimental cases, there appear to be negative
correlations with debris flow and immature debris flow.

4 Conclusions
This study conducted experiments regarding thedepositing processes of debris flows and immaturedebris flows using channels with different gradients
upstream and downstream. Subsequently, it analyzed
the depositing rate at the slope change point and theassociated factors. The results showed that thedepositing rate could be expressed using previously
established formulae. To clarify the relationships amongdepositing rate, flow velocity, and runout distance,
future experiments will be conducted under more
coherent conditions of debris flows and immature debris
flows.

References
1.

A. Lucas, A. Mangeney, J.P. Ampuero, NatureCommunications, 5, 3417 (2014)
2. D. Rickenmann, Natural Hazards, 19 (1999)
3. T. Takahashi, Debris Flow, CRC Press (2014)
4. S. Egashira, K. Miyamoto, T. Itoh, Proceedings ofDFHM1 (1997)
5. J. Takahama, Y. Fujita, K. Hachiya, M. Sakamoto,
Annual Journal of Hydraulic Engineering, JSCE
(2002)
6. J. Takahama, Y. Fujita, Y. Kondo, K. Hachiya,
Annual Journal of Hydraulic Engineering, JSCE
(2002)
7. S. Egashira, N. Honda, T. Itoh, Physics andChemistry of the Earth, Part C, 26 (2001)
8. M. Pirulli, M. Pastor, Géotechnique, 62, 11 (2012)
9. F. Frank, B.W. McArdell, C. Huggel, A. Vieli,
Natural Hazards and Earth System Sciences, 15(2015)
10. R. M. Iverson, C. Ouyang, Reviews ofGeophysics, 53 (2015)
11. Lai. G-C, Tai. Y-C, Cai. Y-J, Kuo. C-Y,
INTERPRAEVENT 2018 in the Pacific Rim
Symposium Proceedings (2018)
12. K. Miyamoto, T. Itoh, H. Kisa, Proceedings of
DFHM7 (2019)4