E3S Web of Conferences 415, 04004 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341504004

Study on the relationship between rainfall, topography andlandslide volume in the recent debris flow disasters inHiroshima, Japan
Tomoaki Eguchi1* , Hiroya Umemura1, Mizuho Arai1, Atsushi Okamoto1, Yusuke Sakai2, Taro Uchida3, Shinichiro
Hayashi4, and Makoto Ohyama5
1

Asia Air Survey Co., Ltd., Manpukuji 1-2-2, Asao-ku, Kawasaki, 215-0004, Japan
National Institute for Land and Infrastructure Management, Asahi 1, Tsukuba, 305-0804, Japan3Tsukuba University, Tennodai 1-1-1, Tsukuba, 305-8572, Japan
4
Sabo & Landslide Technical Centre, Hirakawacho 2-7-5, Chiyoda-ku, Tokyo, 102-0093, Japan
5
Hiroshima West-Mountains Sabo Office, MLIT, Hatchobori 3-20, Naka-ku, Hiroshima, 730-0013, Japan
2

Abstract. Three types of sediment volume estimation equations were developed by analyzing therelationship between rainfall, topography (e.g. slope gradient, relative height) and the volume of collapsed
sediment in 1 km grid for heavy rainfall events (2014 and 2018 events) in Hiroshima Prefecture whereintensive slope failures and debris flows occurred. All three equations showed a tendency for the volume ofcollapsed sediment per unit area to increase with increasing rainfall. However, some equations showed therate of increase tends to gradually plateau.

1 Introduction
Slope failures are considered to be closely related to theamount of rainfall (triggering factor) and the amount oftopography (predisposing factor). Many studies havebeen conducted in this field, and various prediction
equations [1-3] have been proposed to predict the areaof slope failures. On the other hand, caused by recent
global warming, large-scale landslides associated withan unprecedented record-breaking heavy rainfall havebeen occurring in many regions of Japan. Therefore, it
is important to predict the amount of sediment yield
during extreme weather events associated with climatechange.
In this study, we analyzed the relationship between
predisposing factors and triggering factors with theamount of sediment yield for two torrential rainfall
occurred in August 2014 (hereinafter referred to as"2014 disaster") and July 2018 (hereinafter referred toas "2018 disaster"), which caused significant damage in
Hiroshima Prefecture. Then we formulated therelationship among rainfall, topographic characteristics
and amount of sediment yield.

was given to ensure that triggering factors andpredisposing factors such as rainfall and geology(granite, rhyolite, etc.) were no biased in specific areas
during the 2014 and 2018 disasters.

Fig. 1. Study area.

2 Study area
The study area is a 596 km2 area in Hiroshima Prefecture
shown in Fig.1. In this study area, slope failures anddebris flows occurred extensively during the 2014 and2018 disasters. For setting the study area, consideration* Corresponding author:

3 Landslide area classification andsediment volume calculation

tma.eguchi@ajiko.co.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, 04004 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341504004

5.1 Expression typeestimation equations

Landslide areas (1,463 sites) within the study area fromthe 2014 and 2018 disasters were classified into
collapsed, transported and deposited areas based on
photographic interpretation using aerial orthophoto
imagery and difference analysis of airborne laser
measurements at two different periods (before/afterevents), and then the volume of collapsed sediment andtransported sediment was calculated (Fig. 2).
The volume of collapsed sediment is expressed as thevolume of sediment discharged in downstream from theend of the collapsed area (originated zone), and thevolume of transported sediment is expressed as thevolume of sediment discharged in downstream from theend of the transported area.

ofsedimentvolumeThree types of equations were used in the sedimentvolume estimation equation: "power function" and"multinomial power function," in which the Unit
collapsed sediment increases cumulatively withincreasing rainfall, and "logistic function," in which theUnit collapsed sediment reaches its peak when rainfall
becomes extremely large. The reason why these 3
equations are selected are as follows:
Power function and multinominal power function wereadopted because previous studies have proposed thesefunctions to express the relationship between landslidevolume and rainfall and topography. On the other hand,logistic function was adopted because the sedimentvolume is not expected to increase without limit as
rainfall increases. This is because the landslide length
does not exceed the slope length and there is an upper
limit to the sediment volume. In view of this, logistic
function was adopted as the function that causes thesediment yield to reach a ceiling when the rainfall isvery large.
V=a(R-Rmin)b
V=a(R-Rmin)bSc
V=Vmax/[1+exp{-(c0+c1R+c2S)}]

Fig. 2. Schematic map of landslide area classification andsediment volume calculation

(1)
(2)
(3)

Where, V: Sediment volume, R: Rainfall, Rmin:
Minimum rainfall, S: Topographic characteristics, a,b,c:
Regression coefficient, Vmax: Maximum sedimentvolume4 Creating grid unit area

The power function(1) is only for rainfall factors only,
while the multinomial power function(2) and logistic
function(3) are functions of rainfall and topographicfactors.

The basic unit for calculating the volume of collapsed
sediment is the 1 km grid shown in Figure 1. Thefollowing attributes were given to each grid as basic data
for the analysis.
Sediment volume: Volume of collapsed sediment per
1km2, volume of transported sediment per 1km2
(hereinafter Unit collapsed sediment and Unit
transported sediment）
Rainfall amount: Maximum rainfall of 1, 3, 6, 12, and24 hours, maximum soil water index [4], and cumulative
rainfall at the time of the 2014 disaster and 2018 disaster
Topographic characteristics: Maximum slope gradient,
average gradient, relative height, percentage of area
where the gradient more than 5°, 10°, 20°and 30°Geology: Granite, rhyolite, others

5.2 Result of Sediment Volume Estimation
Equation
The SVEEs were developed using multivariate analysis
by combining the sediment volume, rainfall andtopography by grid organized in Section 4 (480 cases intotal). Based on the evaluation method shown in Table
1, the most appropriate estimation equations were thenselected for each sediment quantity (Unit collapsedsediment, Unit transported sediment), geology (granite,rhyolite, others) and equation type (power function,multinomial power function, logistic function). As anexample, the equations and graphs for estimating theUnit collapsed sediment of granite are shown in Fig. 3.

5 Analysis of the relationship between
rainfall, topography and collapsed
sediment
Based on the results of the previous section, equations
relating the amount of rainfall and topography to thevolume of Unit collapsed sediment and the volume ofUnit transported sediment (hereafter referred to as"Sediment Volume Estimation Equations, SVEEs")
were developed.

2

E3S Web of Conferences 415, 04004 (2023)
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https://doi.org/10.1051/e3sconf/202341504004

The rainfall factors employed were maximum 12-hour
rainfall for the power and multinomial power functions
and maximum soil water index for the logistic
function, both of which were considered as long term
rainfall. The topography factor employed was therelative height in areas with a slope of 10° or more forthe multinomial power function and the percentage ofarea with a slope of 10° or more for the logistic
function. The equations obtained show that the Unit
collapsed sediment reached a ceiling at 33,000 m3/km2
for the logistic function, and that the power exponentsof rainfall and topography were less than 1 for thepower function and multinomial power function,
resulting in the Unit collapsed sediment graduallyreaching a ceiling as rainfall increased.

Table 1. Evaluation methods for SVEEs.

Signs ofregression
coefficients
Coefficient ofdetermination
Residual
standard
deviationa)

Evaluation approach
Qualitatively uninterpretable
equations with negative regression
coefficients (e.g. the smaller therainfall, the larger the sedimentvolume) are excluded.
Adopt a formula with a coefficient ofdetermination of 0.5 or more andsignificance of the correlation at least
at a risk rate of 5% in a t-test.
Adopt a formula with the smallest
residual standard deviation among theformulae satisfying the above twoitems.

5.3 Verification of the accuracy of the SVEEs

Power function
V=0.3615(R-143)0.8470

To verify the accuracy of the SVEEs, a scatter diagram(Fig.4) was created with the measured values (truevalues) from the airborne laser survey data on thehorizontal axis and the estimated values obtained fromthe SVEEs on the vertical axis. Both values are close toa 1:1 straight line, indicating good estimation accuracy.
The mean absolute error (Fig.5) was also relatively
small, ranging from about 3,000 to 7,000 m3 per km2.
These results indicate that under the conditions ofrainfall (maximum 12-hour rainfall: less than 300mm,maximum soil water index: less than 260mm) andcollapsed sediment volume (less than 33,000m3/km2)
experienced during the 2014 and 2018 disasters,
relatively similar results can be obtained using powerfunction, multinomial power function and logisticfunction.

b) Multinomial power function
V=0.0310(R-143)0.7503S0.5200

100

Rhyolite

OthersOthers80

6040

Multinomial
power function

GraniteRhyolite

Estimated value (103m3/km2)

Estimated value (103m3/km2)

8020c) Logistic function
V=33/[1+exp{-(-3.2402+0.0319(R-195)+0.6830S}]

100

100

Power function

GraniteGranite40204060

80

100

Measured value (103m3/km2)

40

00060

20200Others

8060

Logistic function

Rhyolite

Estimated value (103m3/km2)

Evaluation
items

020

406080100

Measured value (103m3/km2)

020406080

100

Measured value (103m3/km2)

Fig. 4. Comparison results between measured and estimatedvalues.

Mean absolute error(m3/km2)

Power function

Multinomial power function

8,000
6,000
4,0002,0000Granite

Fig. 5. Mean absolute error.

Fig. 3. Unit collapsed sediment estimation equation (examplefor granite).

3

Logistic function

10,000Rhyolite

OthersE3S Web of Conferences 415, 04004 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341504004

6 Conclusions
In this study, SVEEs (Sediment Volume Estimation
Equations) were developed to calculate Unit collapsed
sediment (collapsed sediment volume per 1km2) fromrainfall and topographic factors using three equation
types with different characteristics (power function,multinomial power function and logistic function). This
study showed the possibility of estimating the volume ofcollapsed sediment per 1km2 according to amount of
rainfall by analysing the difference analysis data fromairborne laser surveys before and after a disaster and thespatiotemporal distribution data of rainfall in detail. In
the future, it is important to further improve the accuracy
by selecting an equation type that assumes an increasein rainfall due to climate change and by analysing morevarious types of disasters.

References
1.
2.
3.
4.

T. Uchiogi, Journal of Japan Society of Erosion
Control Eng., 79-23, 21-34 (1971)
H. Yoshimatsu, Journal of JSECE, 29-3, 1-9(1977)
Chun-Yi Wu and Po-Kai Chou, Open
Geosciences, 13, 944-962 (2021)
N. Osanai, T. Shimizu, K.Kuramoto, S.Kojima,
T.Noro, Landslides, 7, 325-338 (2010)4