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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
947
DOI: 10.4408/IJEGE.2011-03.B-103
AN APPLICATION OF THE FLO-2D MODEL TO DEBRIS-FLOW
SIMULATION - A CASE STUDY OF SONG-HER DISTRICT IN TAIWAN
P
inG
-s
ien
LIN
(*)
, J
ie
-H
ua
LEE
(**)
& C
Hi
-w
en
CHANG
(***)
National Chung-Hsing University, Taiwan, R.O.C.
(*)
Email: pslin@dragon.nchu.edu.tw 886-4-2287-2221 ext.229
(**)
Email: wayne.chihua@msa.hinet.net 886-987-826-881
(***)
Email: cwchang@dragon.nchu.edu.tw 886-4-2287-2221 ext.232
simulation was performed using FLO-2D with the
results presented as area of debris-flow inundation,
maximum deposit depth, and deposit volume. The
simulation results were then compared with the aerial
photos and the micro geomorphological study. Final-
ly, suitable conditions for using this model, and the
suggestions for future research are discussed.
K
ey
words
: Debris Flow, FLO-2D, Rheological Parameters,
Micro geomorphology
INTRODUCTION
Due to the extrusion of Philippine Sea Plate and
the Eurasian Plate, the island of Taiwan was formed
with one third of its area located in mountainous zones
higher than 1000m. Owing to the scarcity of usable
land, many housing units and farmhouses are built
at the hillsides and on the hills. Earthquakes and ty-
phoons occur frequently in Taiwan because it is on the
Circum-Pacific Earthquakes Belt and Western-Pacific
Typhoon Path. The average annual rainfall is more than
2500 mm and is due to severe rainstorms caused by
typhoons. Moreover, after the 921 Chi-Chi earthquake,
weak geology, steep topography, and land use in steep
terrain has caused frequent debris flow in mountain
areas, in which people also suffered from debris flow
during plum rains and typhoon seasons. In recent years,
natural disasters such as landslides, debris flows, and
mudflows usually occur in mountainous areas during
and after typhoons and rainstorms in Taiwan.
ABSTRACT
Taiwan is an island located in the subtropical zone
where typhoons often bring heavy rainfall. In addition,
streams and geology results in a high susceptibility to
debris flow. Especially after the Chi-Chi earthquake
on September 21, 1999, the geological condition of
the mountain area located in the central part of Taiwan
has been more susceptible to natural disasters of debris
flow. Fractured geological units and landslides caused
by frequent earthquakes provide abundant source ma-
terial for debris flow. Following a typhoon or heavy
storms, debris mixed with water form debris flows.
Many studies have examined the triggering criteria,
flow routing and deposition of debris flow in order to
reduce the impact and losses caused by debris flow.
In this research, parameters and processes needed
for a numerical simulation method for debris flow
routing and depositions are formulated to provide a
reference for hazard zone mapping. A two-dimension-
al model (FLO-2D software) was used to simulate a
debris flow and flood, and the accuracy of the simu-
lation, including flow depth, velocity and volumetric
sediment, was analyzed using data collected on the
rainfall and terrain. The case study in this research
consists of three phases. In the first phase, debris flow
data, including information on topography and rainfall
from typhoon Mindulle in 2004 collected from First
River Basin of Song-Her District in Taiwan, were
compiled to establish a database of factors that influ-
ence debris flow. For the second phase, a numerical
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P.-S. LIN, J.-H. LEE & C.-w. CHANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
rule, to interchange the order of integration and
differentiation to simplify the continuity and the
momentum equations;
2 steady flow;
3 hydrostatic pressure distribution;
4 steady flow resistance equation.
There are two restrictions in this model.
1 The model cannot modify scoured depth.
2 The model cannot simulate shock wave and
hydraulic jumps.
Although FLO-2D model has some assumptions
and restrictions. s
u
(2002) used the model for debris-
flow routing in Da-Xing in Taiwan and found that the
down-stream deposit and velocity distribution were
accurately estimated using the FLO-2D model.
FLO-2D CONTROL FORMULA
Using the notation and coordinate system given in
Fig. 1, the governing equations are shown as follows:
The continuity equation is:
h: depth of debris flow
u: velocity components in the x-direction
v: velocity components in the y-direction
i: rainfall intensity
t: time
The momentum equations is:
S
fx
, S
fy
: friction slope;
S
bx
, S
by
: bed slope;
Debris-flow deposition is greatly influenced by
material parameters. Time consuming and expensive
sampling and laboratory experiments are needed to
model debris-flow deposition.. The maximum particle
size of a field sample needs to be reduced so that the
material properties can be performed in the laboratory
experiments. Numerical simulation was performed
using FLO-2D on the results presented as area, maxi-
mum deposition depth, and deposition volume.
In June, 2004, Typhoon Mindulle caused 72 seri-
ous floods in the central Taiwan, bringing about an ac-
cumulated rainfall of 1670 mm. There were also several
serious debris-flow disasters in mountainous regions of
Song-Her District. This study used the FLO-2D Model,
developed by O’Brien and Julian in 1998, which coordi-
nates rainfall data and a digital terrain model (DTM) to
predict debris-flow properties of volumetric sediment,
flow depth and rate of debris-flow deposition. Actual
rainfall data was gathered during Typhoon Mindulle to
simulate debris flows in the Song-Her District using the
FLO-2D model, and the results were compared to data
on the actual area of debris-flow deposition determined
by aerial photography and the micro-topography.
Results from this research will determine the area
of influence from the First River Basin of Song-Her
District debris flow to provide basic information for
the local evacuation and rescue route planning for
debris flows. The methodology developed in this re-
search may be used to determine hazardous zones, to
estimate the effectiveness of the Flo-2D model, and
provide guidelines for future construction.
METHODOLOGY
INTRODUCTION OF FLO-2D MODEL THEORY
o’b
Rien
et alii (1993) developed a two-dimen-
sional flooding routing model (FLO-2D), which is a
valuable tool for delineating flood hazards and simu-
lating flood wave attenuation and debris flows.
Simulation of debris flows requires rheological
models (or constitutive equations) for solid-liquid
mixtures. The rheological property of a debris flow
depends on a variety of factors, such as water concen-
tration, solid concentration, cohesive properties of the
fine material, particle size distribution, particle shape
and grain friction (i
mRan
et alii, 2001).
The following conditions are assumed in order to
simplify the model operation of FLO-2D:
1 using the shallow water equation, the Leibnitz
(1)
(3)
(2)
Fig. 1 - Definition of coordinate system for two-dimen-
sional governing equations
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AN APPLICATION OF THE FLO-2D MODEL TO DEBRIS-FLOW SIMULATION - A CASE STUDY OF SONG-HER DISTRICT IN TAIWAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
949
REGIONAL OVERVIEWS
REGIONAL INVESTIGATION
Topography and stream
This study investigates the potential debris flows of
First River Basin. The first River Basin of Song-Her Dis-
trict is located in Herping in Taiwan. Herping is a moun-
tainous township located in eastern Taichung County,
and occupies the largest part of the county by area (half
of the entire county). The height in the township is about
2230 m. There are approximately 1000 km
2
in Herping.
The geography of this study in the region is shown in
Fig. 2 (f
u
-x
ionG
e
nGineeRinG
C
onsultants
, i
nC
., 2005).
Wingrid software on a DTM (digital terrain model)
grid system was used to obtain the watershed used in the
simulation. It shows that basin of Song-Her Districtin is
flat, long and narrow (Fig. 3). It is easy to deposit quanti-
ties of earth and stones because the topography is long and
narrow, when the sediment transporting along the stream.
First River Basin of Song-Her is classified as
having debris-flow potential. The river basin number
003 has an area of 375 hectares and a length of 4430
m. After the 921 Chi-Chi earthquake in 1999, many
landslides have occurred in the First River basin of
Song-Her watershed area. According to the investi-
gation, the landslides are still active due to abundant
rainfall provided by typhoons. The unstable soils in
the landslide initiation areas are the main soil sourc-
es of debris-flow. Recent observation there is a high
possibility that more debris flows will happen again.
g: gravitational acceleration.
Equations (2) and (3) represent the momentum
equations of the force equilibrium on the X- and Y
axes, respectively. This non-dimensional implication
further discusses the effects of acceleration involving
friction slope affected by material intensity on contact
(rheological model), bed slope of gravity, pressure gra-
dient, local acceleration and convective acceleration.
The dynamic wave model is an intact momentum
equation as shown in Eq. (2) and (3). However, the
diffusion wave model is obtained when ignoring the
items 3 through 5 after the equal sign in Eq.(2) and (3),
whereas the kinematical wave model ignores the items
2 through 5 in the same equations. While FLO-2D is
available for the analysis of the above three models,
only the diffusion wave model was used in this study.
RHEOLOGICAL EQUATION
The FLO-2D numerical code is used to simulate
debris-flow deposition, velocity and area of inundation.
This model uses the quadratic rheological model pre-
sented by o’b
Rien
& J
ulien
(1988), which includes yield
shear stress, viscous shear stress, cohesive yield stress,
and turbulent shear stress. Five important parameters are
chosen, including the slope of channels, concentration by
volume, yield stress, viscosity, and density of sediment.
The analysis result shows that the slope of channels and
the concentration by volume are the most important pa-
rameters of the debris flow routing in FLO-2D.
where:
S
y
: yield slope; S
v
: viscous slope; S
td
: turbulent-dis-
persive slope; τ
y
: Bingham yield stress; η: Bingham
dynamic viscosity; γ
m
: unit weight of debris flow; k:
resistance parameters for Laminar flow; n: Manning’s
roughness coefficient; h: depth of debris flow; u: ve-
locity components
INTERPRETATION OF MICRO-GEOMORPHOLOGY
The DEM data for the First River Basin of Song-
Her District were obtained big disaster caused by
typhoon Mindulle in 2004. If a value of pre-disaster
DEM is less than the value of the post-disaster DEM
deposition has occurred. The depositional area, maxi-
mum depositional depth, and depositional volume at
the basin can thus be defined. Simulation results are
compared with aerial photos and micro-topography.
(4)
Fig. 2 - The geography of
First River Basin of
Song-Her District site
(intergrated planning
and designing for the Song-Her District of Herping townshipe in
Taiwan, f
u
-X
ioNG
e
NGiNeeriNG
c
oNSultANtS
,i
Nc
., 2005)
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P.-S. LIN, J.-H. LEE & C.-w. CHANG
950
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
DATA OF RAINFALL
Typhoon Mindulle caused 72 serious floods in
central Taiwan in June, 2004. The path of the typhoon
is shown in Fig. 7. The rainfall distribution from 7/2 to
7/3 in 2004 at Song-Her raingauge station is shown in
Fig. 8. The observation of the maximum hourly rain-
fall at Song-her workstation is shown in Table 1.
RESULTS AND DISCUSSIONS
This study investigates the potential debris flows
of First River Basin (No. 003) in Herping, Taichung
during rainfalls due to typhoon Mindulle to simulate
stream discharge and debris-flow occurrence. The fol-
lowing sections present the results of this study.
DATA PRETREATMENT
Digital elevation model, DEM
DEM data for the First River Basin of Song-Her Dis-
Due to the minimal distance between the river and
village, future debris flows in this area may dam the
river and cause a serious disaster. On July 2, 2004,
heavy flooding from typhoon Mindulle caused seri-
ous disaster in both Song-Her and Boh-Ai villages as
shown in Fig. 4.
Stratigraphy in the First River Basin of Song-Her
According to the 1:500,000 scale geologic map pub-
lished by Central Geological Survey, MOEA (Central
Geological Survey, Ministry Of Economic Affairs, 1986),
synclines and anticlines of Da-jian Sandstone and Paileng
formation constitute the strata in this watershed (Fig. 5).
Surface soils in the First River Basin of Song-Her
There are two different kinds of colluvial soils
and lithosols in this area. Lithosols compose the main
soil of the upper stratum. The soil distribution in this
study area is shown in Fig. 6 (s
oil
and
w
ateR
C
onseR
-
vation
b
uReau
C
ounCil
of
a
GRiCultuRe
, 2005).
Fig. 3 - The watershed region of First River
Basin of Song-Her (The plan debris
flow-003 designated soil and water
conservation area of Herping town-
ship in Taiwan, S
oil
AND
w
Ater
c
oN
-
ServAtioN
B
ureAu
c
ouNcil
of
A
Gricul
-
ture
, 2005)
Fig. 4 - Aerial photography on Song-Her District site (af-
ter typhoon Mindulle in 2004)
Fig. 5 - The stratigraphy of debris flow-003 designated by
the soil and water conservation area of Herping
township in Taiwan (S
oil
AND
w
Ater
c
oNServAtioN
B
ureAu
c
ouNcil
of
A
Griculture
, 2005)
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AN APPLICATION OF THE FLO-2D MODEL TO DEBRIS-FLOW SIMULATION - A CASE STUDY OF SONG-HER DISTRICT IN TAIWAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
951
trict were obtained after the debris-flow disaster caused
by typhoon Mindulle in 2004 from the Agricultural and
Forestry Aerial Survey. The DEM has a 20m resolution
and was used simulate the debris flow using FLO-2D.
watershed delineation
The DEM data encompassed the entirety of the
studied watersheds, and a database of factors that
influence debris flows was compiled to aid in digital
simulation of the debris flows.
The DEM was analzyed as follows:
1 The vector form of digital elevation for each basin
is converted to gridded data.
2 A grid-based unit flow direction was determined
by ArcView spatial analyst- hydrologic modules.
3 A flow accumulation grid was calculated.
4 The watershed was delineated.
Finally, the shape of the watershed is determined.
The Fig. 9 shows the watershed outline of the First
River Basin at Song-Her District.
Flow Outlet
In this study, it was found that debris flow main-
ly scoured and deposited material above the water-
shed outlet. Below the wathershed outlet, only depo-
sition occurred. The location of the waterhsed outlet
is very important in the application of the FLO-2D
debris-flow simulation model.
Guidelines for locating the watershed outlet was
provided by H
ui
(2006), which shows that the First
River Basin at Song-Her District was interpreted by
micro-topography. If the value of pre-disaster DEM
minus disaster DEM is negative, it indicates an area of
deposition, whereas if it is positive, it reflects an area
of erosion. The range selected in the balanced area of
the deposition and erosion is the outlet of flow at the
Fig. 6 - The Surface soils of debris flow project 003 in
the soil and water conservation area of Herp-
ing township, Taiwan (S
oil
AND
w
Ater
c
oNSer
-
vAtioN
B
ureAu
c
ouNcil
of
A
Griculture
, 2005)
Fig. 7 - The path of typhoon Mindulle (Typhoon Database,
c
eNtrAl
w
eAther
B
ureAu
, 2004)
Fig. 8 - Rainfall distribution from 7/2 to 7/3 in 2004 at
Song-Her workstation
Tab. 1 - Observation of the maximum hourly rainfall at
Song-Her workstation
Fig. 9 - First River Basin at Song-Her District
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
concentration by volume, C
v
, is shown in eq.(6)
From the rheological coefficient test in the field
and referring to FLO-2D Users Manual (o’b
Rien
,
2004), as well as substituting the α
1
, β
1
, α
2
, β
2
, and
C
v
values into the equations (5) and (6). Then the
initial value (τ
y
, η) of rheological coefficient of si-
mulation can be obtained.
3 Manning’s n value:
Both the parameter of the field test and the curve of
particle size distribution can be obtained as shown
in Table 2, and Fig. 12, respectively. Another curve
of particle size distribution by f
u
-x
ionG
e
nGine
-
eRinG
C
onsultants
, i
nC
. (2005) can be found in
Fig. 13. The results of the sediment collected in
the field are then analyzed as shown in Table 3.
The result of Manning’s value, n, which is 0.032
is shown in Table 4.
4 Specific gravity:
s
Him
(1999) indicates that the specific gravity of
sedimentary rocks between 2.01~2.78. The specific
gravity with high block content was determined to
basin (Fig. 10). The areas of erosion and deposition
and the watershed outlet is shown in Fig. 10 and 11.
After the hydrologic analysis of the DEMs of
Song-Her District, it was automatically divided into
functional divisions of watershed areas using WinGrid
software, and also for basic analysis of the study area
by using ArcView software’s contour lines, aspect,
slope and other functions. The DEM data were then
transferred into a word file using FLO-2D software
program to determine the Manning coefficient n val-
ue, and the output of the FLO-2D program.
PARAMETRIC STUDY ON THE DEBRIS FLOw
SIMULATION
1 Volumetric Concentration of Sediment:
The volumetric concentration of 70% was used in the
study based on the field investigation after the debris
flow disaster. Samples of the debris-flow deposit con-
tained higher gravel content and larger gravel size.
2 Rheological coefficients:
Both τy, η, and C
v
can be obtained using equation
5 and 6.
The relationship between yield stress, τy, and con-
centration by volume, C
v
, is shown in eq.(5)
The relationship between dynamic visosity, η and
Fig. 10 - Debris-flow erosion and deposition of the
First River Basin at Song Her District
Fig. 11 - Outlet of the First River Basin at
Song Her District
(5)
(6)
Tab. 2 - The parameter of field test
Fig. 12 - Curve of particle size distribution for sieve analy-
sis of the field sample
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AN APPLICATION OF THE FLO-2D MODEL TO DEBRIS-FLOW SIMULATION - A CASE STUDY OF SONG-HER DISTRICT IN TAIWAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
953
greater than 40, the maximum flow depth incre-
ases (Fig. 14), but the maximum flow velocity
decreases with higher volumetric concentration
as shown in Fig.
(c) Many factors in the FLO-2D simulation model
are influenced by volumetric concentration of se-
diment.
2 The influence of Manning’s Roughness Coeffi-
cient, n. The effects of Manning’s Roughness Co-
efficient on the depth and the velocity of debris
flow are shown in Table 6 and 7 and Fig. 16. The
tables and figures show that as Manning’s Rough-
ness Coefficient, n, increases, the debris flow depth
increases, whereas the flow velocity decreases.
SIMULATION RESULTS
Simulation results are compared with aerial pho-
tos and micro-topography study. The result of micro-
be 2.70 in this study. The parameters of initial value
of simulation by FLO-2D are shown in Table 5.
Sensitivity Analysis
The data and parameters collected in the field
from the First River Basin at Song-Her District in Tai-
chung after typhoon Mindulle were adopted to con-
duct a sensitivity analysis with FLO-2D.
The results are shown as follows:
1 The influence of volumetric concentration.
The effects of volumetric concentration on maxi-
mum depth are shown in Fig. 14 and 15, respectively.
(a) When volumetric concentration of sediment is
less than 50, maximum debris-flow velocity was
found to increase. This is due to resistance force
being smaller than the driving force of the debris
flow.
(b) When volumetric concentration of sediment is
Tab. 3 - The investigate and analyze result of sediment in
the field
Fig. 13 - Curve of particle size distribution around the First
River Basin at Song-Her District (Fu-Xiong Engi-
neering Consultants, Inc., 2005)
Tab. 4 - The result of Manning’s n value
Tab. 5 - Parameters of initial value simulated by FLO-2D
Fig. 14 - The relationship of volume concentration and
maximum depth with the debris flow
Fig. 15 - The relationship of volume concentration and
maximum speed with the debris flow
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P.-S. LIN, J.-H. LEE & C.-w. CHANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
topography is shown in Fig. 17.
The depositional area, maximum depositional
depth, and depositional volume are shown in Table 8,
and the comparison of depositional volume is shown
in Table 9. The depositional volume is 798,800 m
3
as
shown in Fig. 18. There is a minimum of 5% differ-
ence in depositional volume between micro-topogra-
phy and the simulation result with yield stress of 2,500
Pa and Bingham dynamic viscosity (n) of 10 Pa-s by
FLO-2D.
CONCLUSIONS
1 Manning’s Roughness Coefficient has an extre-
mely significant effect on debris-flow processes
and final deposition morphology. An increase of
Manning’s Roughness Coefficient would lead to
a decrease of the distances of debris-flow runout
and an increase of the maximum deposition depth.
However, during the flow process, debris-flow ve-
locity would be decreased.
2 The specific gravity of debris-flow materials had a
lesser effect on the success of the FLO-2D simu-
Tab. 6 - The relationship of Manning’s n value and the
depth of debris flow
Tab. 7 - The relationship of Manning’s n value and the ve-
locity of debris flow
Fig. 16a - Manning’s n value =0.4
Fig. 16b - Manning’s n value =0.2
Fig. 16c - Manning’s n value =0.1
Fig. 16d - Manning’s n value =0.05
Fig. 16e - Manning’s n value =0.025
Fig. 17 - Result of micro-geomorphology
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AN APPLICATION OF THE FLO-2D MODEL TO DEBRIS-FLOW SIMULATION - A CASE STUDY OF SONG-HER DISTRICT IN TAIWAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
955
deposition; however, the differences in debris-
flow deposition volume and maximum deposition
depth between the simulation study and the in situ
condition were still present.
ACKNOWLEDGEMENTS
Finanical support from National Science Council,
Republic of China (NSC-96-2625 -Z -005-002-MY3)
is gratefully acknowledged. Special thanks are ex-
tended to Professor Chao-Yuan Lin for offering GIS
software program. The graduate student Sung-Tsuen
Chen was helpful in reorganizing the data of FLO-2D.
lation. An increase of specific gravity of debris-
flow material granules caused an increases of the
debris-flow runout and debris-flow velocity.
3 Volume concentration is found to have affected
the material parameters (e.g. yielding stress and
viscosity coefficient) of debris fluid and amplifi-
cation of debris flow. An increase of the volume
concentration leads to elevated sediment volu-
mes, and therefore these parameters need to be
simplified in order to do the digital simulation of
the debris flow.
4 The results of the simulation and the micro-topo-
graphy features in the present study suggested that
the closest parameterizations of debris flow ma-
terials were as follows: a yielding stress of 2500
Pa, a viscosity coefficient of 10 Pa-s, a Manning’s
Roughness Coefficient of 0.0312, laminar flow re-
tarded coefficient of 2285 and a specific gravity of
debris-flow material of 2.7.
5 A case study was performed to progress the digital
simulation through the model and the parameters
of the present study. At the same time, simula-
tion results were compared to aerial photos and a
micro-topography study. The results suggest that
the simulation adequately modeled debris-flow
Fig. 18 - Simulation with yield stress 2500 Pa
Tab. 8 - Simulation Results
Tab. 9 - Comparison of Deposition Volume
Note: Difference of deposition volume (%) = (the
results of micro-geomorphology - the results of
simulation) / the results of micro-geomorphology
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u
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P.-S. LIN, J.-H. LEE & C.-w. CHANG
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oil
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ateR
C
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