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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
725
DOI: 10.4408/IJEGE.2011-03.B-079
DEBRIS FLOWS PRODUCED BY HEAVY RAINS ON JULY 21, 2009 IN
HOFU CITY, JAPAN
H
iRoyuki
naGano
(*)
, H
aRuyuki
HasHimoto
(**)
, y
osHiaki
kuRoda
(**)
& H
iRoki
takaoka
(***)
(*)
Department of Civil Engineering, Yamaguchi University, Ube 755-8611, Japan
(**)
Department of Civil Engineering, Kyushu University, Fukuoka 819-0395, Japan
(***)
Department of Civil Engineering, Nagoya University, Nagoya 464-8601, Japan
district, 4 inhabitants were killed in a number of river
basins at Shimomigita district and 2 inhabitants were
killed in a few river basins at Ishihara district.
In order to consider the measures against the de-
bris flows in the mountain areas, it is important to
know the debris flow velocity and discharge.
The purpose of the present study is to estimate
velocity and discharge of the debris flows from the
field survey, the theoretical consideration and the nu-
merical simulation.
The rivers at Manao and Ishihara districts are se-
lected as the study rivers.
First, we visited these rivers in August, September
and October, 2009 to measure the cross-sectional pro-
files and know the river bed situation after the debris
ABSTRACT
In this paper, we examine the debris flows which
occurred in the mountain rivers in Hofu City, Japan
on July 21, 2009. We estimate velocity and discharge
of the debris flows in the rivers at Manao and Ishihara
districts from field survey and numerical simulation.
The numerical simulation indicates that the peak dis-
charge is 181 m
3
/s in the river at Manao district and
258 m
3
/s in the river at Ishihara district. It is found that
sediment yield volume by riverside erosion is larger
than landslide sediment volume in the both rivers. Al-
though the landslides triggered the debris flow initia-
tion, they did not play the major role for the sediment
outflow to the residential areas. The morphological
characteristics of the river at Ishihara district increase
debris flow discharge
K
ey
words
: debris flow, Hofu City, simulation, hydrograph,
discharge, velocity
INTRODUCTION
The Hofu City area in Yamaguchi Prefecture had
heavy rain on July 21, 2009. The accumulated rainfall
was 241mm and the largest hourly rainfall was 62mm/
hour at the downtown. This rainfall caused a large
number of shallow landslides on mountain slopes in
the Hofu City area. Most of the landslides changed into
debris flows and then moved downstream in rivers.
They resulted in 14 victims. For example, 7 inhabitants
were killed in the Ueda-minami river basin at Manao
Fig. 1 - Study area.
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
241mm from 4 a.m. to 1 p.m. The hourly rainfall had
two times of peak of 62 mm from 8 to 9 a.m. and 53
mm from 11 to 12 a.m. Corresponding to such rainfall
situation, flood flows arose in every river in Hofu City
area. Figure 3 illustrates the rainfall-runoff relation-
ship in a small-river basin at the downtown. In this
figure, the measurement of water level of the Mate-
gawa River at the downtown is plotted. We found that
the flood water level of the small rivers, such as the
Mate-gawa River, had also two times of peak.
OUTLINE OF THE DISASTER
This rainfall condition resulted in many shallow
landslides in the mountain areas. Most of the land-
slides changed into debris flows and then moved down
the mountain rivers. In their downstream areas, there
are villages, a nursing home for elderly people, and
roads. The impact of the debris flows produced 7 vic-
tims in Manao district and 2 victims in Ishihara dis-
trict. Figures 4 and 5 are photos of the nursing home
and the houses hit by the debris flows in Manao and
Ishihra districts, respectively. Some of the witness of
this event shows that most of the debris flows occurred
at around 12 a.m. Therefore, we can consider that the
second peak of the hourly rainfall initiated most of the
landslides. The landslide sediments moved into the
second peak flood flow. These transported a significant
flow event. Second, we simulated the debris flows in
the rivers at Manao and Ishihara districts with the meth-
od of Takaoka, H
asHimoto
& H
ikida
(2007). Finally,
we discussed the debris flow behaviour in the rivers.
OUTLINE OF THE DEBRIS FLOW DISA-
STER
STUDY AREA
The study area is located in Hofu City, Yamaguchi
Prefecture, Japan (Fig. 1). Geology of its mountain ar-
eas is mainly composed of fresh and weathered gran-
ite. Therefore, these areas are vulnerable to landslides
and debris flows. The government of Yamaguchi
Prefecture has made effort to prevent landslides and
debris flows. As a result, 23 check dams have been
installed to control river bed erosion and bed sedi-
ment runoff in the areas. However, Manao and Ishihra
district have no check dams in their mountain rivers.
These are selected as the study areas.
RAINFALL CONDITION
Hofu City area had heavy rain on July 21, 2009.
The situation of the rainfall at two hydrological sta-
tions is shown in Figure 2. Hofu station is located in
the downtown and Manao station is near the site of the
debris flow event. For example, Hofu station meas-
urement expresses that the accumulated rainfall was
Fig. 2 - Rainfall measured at the Manao and Hofu stations
on July 21, 2009
Fig. 3 - Rainfall-runoff relationship of the Mate-gawa
River basin
Fig. 4 - The nursing home damaged by the debris flow
(Manao district)
Fig. 5 - The house hit by the debris flow (Ishihara district)
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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
727
respectively. The main debris flow from O
2
moved
down the river with the slope of 17
o
and the width of 5
m to the confluence with the debris flow from O
1
. Fig-
ure 8 is the photo of the river bed at x
d
=1,420m. Here x
d
=distance measured in the upstream direction from the
confluence with the Manao River. This is the view from
the downstream to upstream direction; we can find the
confluence of the two rivers from locations O
1
and O
2
.
This photo shows the situation of river bed erosion.
Figures 9 and 10 are the photos of the river bed at
x
d
=1,260 m and 1000 m, respectively. These photos
express the situation of sediment deposition. River
amount of sediment to the downstream river reach.
FIELD INVESTIGATION INTO THE MA-
NAO AND ISHIHARA DISTRICT
Figure 6 depicts plan view of Manao and Ishihara
districts. At the Manao district, landslide-induced de-
bris flows occurred in the Ueda-minami River basin;
this is a tributary of the Manao River. At the Ishihara
district, the debris flows occurred in three mountain riv-
ers; for convenience, the first one is termed ‘the Ishihara
A River ’, and the second one ‘the Ishihara B River’ and
the third one ‘the Ishihara C River’. The morphological
characteristics of these rivers are shown in Table 1.
We visited Manao district on August 10 and 11,
2009 and also Ishihara district on September 4, 5 6 and
7, and on October 14. At these times, we took pictures
of river situation and measured the cross-sectional
profiles of the rivers at several sections. From these
measurements and the observation of flow tracks, we
obtained depth, width and area of debris flows during
the peak period.
MANAO DISTRICT
Figure 7 shows a longitudinal profile of the Ueda-
minami River and a longitudinal change of its river
width, respectively. The debris flows were initiated by
shallow landslides at locations O
1
and O
2
in this river
basin. The slope at locations O
1
and O
2
is 27
o
and 32
o
,
Fig. 6 - Landslides and debris flow channels at Manao
and Ishihara districts
Tab. 1 - Characteristics of the Ueda-minami River, and
Ishihara A, B and C River
Fig. 7 - Longitudinal river bed profile and change of river
bed width ( the Ueda-minami River)
F
ig. 8 - Eroded river bed and sides at Section 5 (xd =1,420
m)in the upper reach of the Ueda-minami River
Fig. 9 - The situation of erosion and deposition at Section
7 (xd =1,260 m)
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Ishihara B River and a longitudinal change of its river
width, respectively.
The debris flow was initiated by shallow land-
slides in this river. The slope at the landslide location
is 34
o
. The debris flow moved down the river reach (x
d
=1340~990m) with the average slope of 12
o
and the
width of 8~15m (Figure 13). Here xd =distance meas-
ured in the upstream direction from the street (Figure
6). Figure 13 shows the situation of sediment deposi-
tion on the river bed. At around x
d
=990m (Section
7), the river is curved significantly and then boulders
are deposited on the river bed, as shown in Figure 14.
The river reach such that 990m > x
d
>550m has
the average slope of 8.4o and the width of 6~10 m.
bed slope is 12
o
,10
o
and river width is from 9 m to 24
m between x
d
=1300 m and 870 m.
Figure 11 is the photo of the river bed at x
d
=460m.
The river bed around this position has the longitudinal
slope of 6.4
o
and the transverse width of 14 m to 42 m.
The photo shows the situation of boulder deposition
and driftwood accumulation on the river bed. Here it
is emphasized that river width does not always coin-
cide with that of debris flow. Especially in the case
of larger river width, it is possible that debris flow of
smaller width varies within larger river width.
ISHIHARA DISTRICT
Figure 12 depicts a longitudinal profile of the
Fig . 10 - Debris-flow deposit at Section 10 (xd =1000 m)
Fig. 11 - The situation of boulder deposition and driftwood
accumulation on the river bed at Section 14 (xd
=460 m)
Fig. 12 - Longitudinal river bed profile and change of river
bed width (Ishihara B River)
Fig. 13 - Debris-flow deposit at Section 3 (xd =1220m) in
the upper reach of the Ishihara B River
Fig. 14 - Boulder deposition in the river bend at Section 7
(xd =990 m)
Fig. 15 - Scoured river bed at Section 9(xd =830m)
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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
729
SIMULATION OF THE DEBRIS FLOW
EVENT
We simulate the behavior of the debris flows in
the Ueda-minami River at Manao district and the
Ishihara B River at Ishihara district. This simulation
is based on the model of t
akaoka
et alii (2007). It is
composed of two steps; the first one is transformation
of landslide into debris flow, and the second one is
numerical calculation of debris flow hydrograph along
the river reach. The first one becomes the boundary
condition for the second one.
TRANSFORMATION OF LANDSLIDE INTO DE-
BRIS FLOw
In order to know the transformation process of
landslide into debris flow, we use the simple model
proposed by t
akaoka
et alii (2007). When landslides
occur on mountain slopes, all sediments of landslide
do not change into debris flows. Since we can estimate
the sediment volume of landslide from the field sur-
vey or aerial photo analysis, we can know sediment
volume of initial debris flow by the concept of runoff
coefficient of landslide sediment.
From mass conservation of sediment before and
after the landslides, we obtain the relationship between
sediment volume V
s
of landslide and sediment discharge
Q
s0
(t) of initial debris flow at the landslide position:
where C
0
= sediment concentration in the initial
debris flow, Q
0
(t) = the initial debris flow discharge
and f
s
=sediment runoff coefficient. u(t) corresponds
to a response function for the transformation from
landslide into debris flow.
From Eq.(2), we have
No sediment deposition is found on the river bed, as
shown in Figure 15.
The river becomes abruptly narrow at around x
d
=410m (Section 13) and then wide at around x
d
= 340
m (Section 14). The river width varies rapidly from
15m to 40m and the river slope is 5.5 o on the average.
ESTIMATION OF PEAK DISCHARGE
H
asHimoto
& H
iRano
(1997) introduced a non-
dimensional parameter for sediment-water mixture
flow such as debris and mud flows. At smaller val-
ues of this parameter, intergranular-stress terms in the
momentum equation play major role compared with
the inertia terms; this shows that the effect of grain
collisions becomes major. At larger values of the pa-
rameter, on the other hand, the inertia terms in the mo-
mentum equation become important relatively to the
intergranular-stress terms; this means that turbulence
of the mixture flows becomes dominant. Therefore,
this parameter corresponds to Reynolds Number for
clear water. It is defined as
where h = flow depth; d = diameter of flowing sedi-
ment particles; C = sediment concentration in the
flow; σ =sediment particle density; ρ=water density;
ρt= σC+ρ(1-C) = density of sediment-water mixture;
and F(C)= a function of sediment concentration.
Assuming d =0.3m from the field survey, we can
obtain
N
h
=5~20 corresponding to the variation of C
from 0.2 to 0.5. The variation of C can be verified by
the simulation in the next chapter. The smaller values
of N
h
indicate that the debris flow is in the laminar-
flow type. From these values of N
h
, we can estimate
non-dimensional average velocity φ = v/u* as φ =2~8.
Here, v = cross-sectional average velocity and u* =
friction velocity. On the average, we obtain the value
of φ =5. Using the value of φ =5, we can estimate
average velocity and peak flow discharge under the
assumption of steady and uniform flow. The result
is presented in Table 2. Section 5 is selected as the
location for their estimate in the Ueda-minami River
and Section 9 is selected in the Ishihara B River. It
is found that the Ishihara B River had peak discharge
larger than the Ueda-minami River.
(1)
Tab. 2 - Estimated average velocity and peak discharge of
the debris flows
(2)
(3)
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
where the value of sediment runoff coefficient f
s
is
assumed equal to 1.0. The evaluation of response
function u(t) is very difficult. In this simulation, we
use the response function u(t) obtained by t
akaoka
et alii (2007):
where T = landslide duration time.
We have estimated landslide sediment volume
V
s
from the aerial photo analysis. On the basis of
the work of t
akaoka
et alii (2007), we have deter-
mined sediment concentration C
0
of the initial debris
flows and landslide duration time T by trial and error.
These parameters are summarized in Table 3.
CALCULATION OF DEBRIS FLOw HYDRO-
GRAPH
We assume that the cross sections of the river reach
are approximately rectangular and then the riversides
are eroded in lateral direction with constant angle of 90
degree. The equations of mass and momentum conser-
vation govern the flow in the river reach:
One-dimensional equation of motion
Continuity equation of sediment-water mixtures
Continuity equation of sediment
where t = time, x = distance measured in the down-
stream direction, ρt=σC+ρ(1-C) = density of sedi-
ment-water mixture; Q=discharge of the mixture flow;
v = average velocity; h = flow depth; z = bed level; B
= river bed width= debris flow width; φ = non-dimen-
sional average velocity; C = volumetric concentration
of sediment in flow; C
T
= flux-averaged sediment con-
centration; C
*
= 0.6 = the maximum possible sediment
concentration and qin= lateral inflow rate of water
from the slopes. Indicating friction velocity by u
*
, we
have φ = v/u
*
.
In the discussion we assume sediment concentra-
tion profile uniform. Therefore we can have the rela-
tion of C
T
= C.
Q, h, z, B and CT are unknowns in Eqs. (5), (6)
and (7). Solving theses equations requires two more
equations. t
akaoka
et alii (2005) derived the follow-
ing two equations from laboratory experiments
Riverside bed erosion rate equation
and
Riverside erosion rate equation
where C
T∞
=equilibrium sediment concentration; k
b
= coefficient for bed erosion rate and k
s
= coefficient
for side erosion rate. We can have the values of k
b
=
0.01 and p = 0.7 for Eqs. (8b) and (8c), and k
s
= 0.01
for Eq. (9b).
Denoting equilibrium sediment discharge by q
∞s
,
we can express the equilibrium sediment concentra-
tion as
Tab. 3 - Parameters on the transformation of landslide
into debris flow
(4)
(5)
(6)
(7)
(8 a)
(9 a)
(8 b)
(8 c)
(9 b)
(10)
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Initial condition
It is said that the debris flow event occurred at
around 12:00 on July 21, 2009 (f
uRukawa
et alii,
2009). Therefore, the numerical calculation is made
for the debris flow event from 11:00 to 13:00.
Initial river bed elevation data can be obtained
from the lasar measurement of land elevation by the
Ministry of Land, Infrastructure, Transport.
Initial river width can be given by that before the
debris flow event. However it is difficult to know the
mountainous river width before the debris flow event.
Therefore, initial river width B (m) can be estimated
by the empirical equation (H
asHimoto
et alii, 2001):
where k = coefficient and A (km
2
) = river basin area at
an arbitrary river section. P
aRk
& H
asHimoto
(2003)
reviewed the work of H
asHimoto
et alii (2001) and
then adopted k = 5.36 in runoff analysis of debris
flows. In the present calculation, we determine the
value of k, considering the river bed situation before
and after the debris flow event. As a result, we can
have k = 5.36 for the Ueda-minami River and k = 8.04
for the Ishihara B River.
The lateral inflow of rain water along the whole
river reach has to be considered, because flood flow
due to the heavy rainfall occurred immediately before
the debris flow event. The lateral inflow rate of rain
water can be evaluated by the rational equation.
Calculation condition
The calculation condition is summarized in Table
4. Time and distance step in the difference formulas of
Eqs. (5), (6) and (7) can be determined from stability
condition of numerical calculation. Diameter repre-
sentative of bed sediment grains was estimated from
the field survey. Non-dimensional average velocity φ
= v/u* was determined in the former chapter.
The equilibrium sediment discharge q
∞s
can be
evaluated by the formula of H
asHimoto
et alii (2003
& 2004); it is found appropriate for various kinds of
sediment transport in steep rivers:
where s = (σ - ρ)/ρ; d = sediment grain diameter; τ*=
the non-dimensional shear stress; τ*
c
= the critical
non-dimensional shear stress; θ = bed slope angle; I
f
= the friction slope; w
0
= the fall velocity of sediment
grains in water; α =0.875 and u
δ
/u* =4.7. According to
H
asHimoto
et alii (2003 & 2004), G is a function of If,
h/d and w0/u* and can be approximated as
In the field survey, we could not obtain infor-
mation about the thickness of river bed sediments.
Therefore, referring to P
aRk
& H
asHimoto
(2003), we
assume that river bed was composed of cohesionless
sediments 2.0 m thick.
Boundary condition
River reach for the numerical calculation is from
x
d
=1,552 m (x= 0) to x
d
= 302 m(x= 1,250) in the Ueda-
minami River and from x
d
= 1,440m (x=0 ) to x
d
=390m
(x= 1,050 ) in the Ishihara B River.
The boundary conditions at x = 0 (position down-
stream immediately from the landslide location) are
given by
and
where Q
0
(t)=initial flow discharge,C
0
=initial sediment
concentration and T=landslide duration. The value of
C
0
is assumed 0.4. Q
w0
(t) denotes flow discharge deter-
mined by runoff analysis.
(11)
(12)
(13)
(14)
(15)
Tab.4 - Conditions for numerical calculation
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
river width. This is due to the difference between river
width and flow width. In the Ishihara B River, on the
other hand, the calculation of river width agrees with
its field measurements. Therefore, a comparison be-
tween the calculation and field measurements of river
width shows the satisfactory agreement in the both
rivers except the region of larger river width.
The calculation of river bed change indicates
sediment deposition along the whole reach of the both
rivers. In the Ueda-minami River, the field survey
shows sediment deposition in the region of 460 m<
x
d
< 1,260 m except the small region of 1,320 m < x
d
< 1,470 m. In the Ishihara B River, on the other hand,
the field survey shows sediment deposition in the re-
gion of 1,040 m < x
d
<1,280 m and bed erosion in the
region of 350 m < x
d
<990 m. Therefore, a comparison
between the calculation and field observations of river
bed change shows agreement in the Ueda-minami
River and disagreement in the Ishihara B River.
Sediment budget within each river basin area is
also examined by numerical calculation. It is found
that sediment yield by riverside erosion is larger than
DISCUSSION
Figure 16 shows time-variation of flow discharge
Q at Section 5 (x
d
=1,420m) in the Ueda-minami River
and at Section 9 (x
d
=830m) in the Ishihara B River.
The peak discharge is found 181 m
3
/s in the Ueda-
minami River and 258 m
3
/s in the Ishihara B River.
Flow discharge in the Ishihara B River is found larger
than that in the Ueda-minami River. This simulation
corresponds to the field observations.
The flow velocity and discharge calculated nu-
merically are compared with their estimate based on
the field measurements and uniform-flow concept
(Tab. 5 (a) and (b)). The agreement between them is
excellent. Furthermore, it is confirmed that sediment
concentration C varies from 0.2 to 0.5.
Figures 17 and 18 express longitudinal change in
river bed elevation and river width during the debris
flow events. Here, it should be emphasized that calcu-
lated river width denotes flow width.
In the Ueda-minami River, the calculation of
river width disagrees with its field measurements af-
ter the debris flow event except the region of small
Fig. 16 - Time-variation of flow discharge
Tab. 5 - (a)Comparison between the simulation and field
measurement at Section 5 (xd=1,420m) in the
Ueda-minami River
Fig. 17 - Longitudinal change in river bed elevation and
river width(Ueda-minami River)
Fig. 18 - Longitudinal change in river bed elevation and
river width (Ishihara B River)
Tab. 5 - (b) Comparison between the simulation and field
measurement at Section 9 (xd=830m) in the Ishi-
hara B River
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733
3. The numerical calculation of river bed change
agrees with its field observations in the Ueda-minami
River and disagrees with those in the Ishihara B River.
4. The shallow landslides triggered debris flow
initiation, but the sediment outflow to the residential
areas was mainly attributed to the riverside erosion.
ACKNOWLEDGEMENTS
The laser measurement data of land elevation in the
mountainous region of Hofu City have been given by the
Ministry of Land, Infrastructure, Transport and Tourism.
Dr. Kiichirou Ogawa (Asia Air Survey Co., ltd.) gave us
the river profile data. The authors would like to appreci-
ate their supply of the data on this research.
landslide sediment volume in the both rivers, espe-
cially in the Ishihara B River. Although the shallow
landslides triggered debris flow initiation, they did
not play the major role for the sediment outflow to the
residential areas in the Ishihara B River.
CONCLUSIONS
The results obtained in this study are as follows:
1. Flow discharge in the Ishihara B River at Ishi-
hara district was larger than that in the Ueda-minami
River at Manao district.
2. The numerical calculation of river width agrees
with its field measurements in both rivers except the
region of larger river width.
REFERENCES
f
uRukawa
k., k
aiboRi
m., k
ubota
t., J
itouzono
t., G
onda
y., s
uGiHaRa
s., H
ayasHi
s., i
keda
a., a
Raki
y. & k
asHiwabaRa
y.
(2009) - Debris disasters caused by heavy rainfall around Hofu City in Yamaguchi Prefecture on July 21, 2009. Journal of
the Japan Society of Erosion Control Engineering, 62 (3): 62-73 (in Japanese).
H
asHimoto
H. & H
iRano
m. (1997) - A flow model of hyperconcentrated sand-water mixture.Proceedings of First International
Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment. Edited by C
Hen
C.L., ASCE:
464-473.
H
asHimoto
H., w
atanabe
k., J
un
b., u
eno
k., y
amanaka
m., k
asai
m., n
oGami
s. & o
Gata
t. (2001) – The investigation into
the land condition of kasegawa dam reservoir basin by using the remote-sensing data and the estimate of its sediment yield
volume
. Annual Journal of Hydraulic Engineering, JSCE 45: 805-810 (in Japanese).
H
asHimoto
H., P
aRk
k., i
kematsu
s. & t
asaki
n. (2003) - A sediment discharge formula for various types of sediment transport
in a steep open channel. Annual Journal of Hydraulic Engineering, JSCE 47: 571-576 (in Japanese).
H
asHimoto
H., t
akaoka
H. & P
aRk
k. (2004) - Sediment discharge formula for steep open channel. Proceedings of the 9
th
Inter-
national Symposium on River Sedimentation, Yichang, China, October 18-21: 1453-1461.
P
aRk
k. & H
asHimoto
H. (2003) - Runoff analysis of debris flows at Mt. Unzendake Volcano, Japan. Proceedings of the 3
rd
In-
ternational Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, Edited by R
iCkenmann
d. & C
Hen
C.l.: 695-704.
t
akaoka
H., H
asHimoto
H., P
aRk
k. & H
isaoka
n. (2005) – Bed and bank erosion rate equations for a steep mountain river.
Proceedings of the XXXI IAHR CONGRESS. Seoul, Korea, September 11-16: 3131-3143.
t
akaoka
H., H
asHimoto
H. & H
ikida
m. (2007) – Simulation of landslide-induced debris flow- The Atsumari debris flow disaster
in Minamata City, Japan. Proceedings of Fourth International Conference on Debris-Flow Hazards Mitigation: Mechanics,
Prediction, and Assessment, Edited by C
Hen
Cl. & m
aJoR
J.J.: 353-363.
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