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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
143
DOI: 10.4408/IJEGE.2011-03.B-017
THE VARIABILITY IN TIME OF THE OCCURRENCE CONDITIONS OF DEBRIS FLOW
AFTER CATASTROPHIC TYPHOONS AND EARTHQUAKES: A THEORETICAL EX-
PLANATION WITH EXPERIMENTAL TESTS
Y.J. TSAI
(*)
, K.C. WANG
(*)
, Y.S. CHEN
(**)
& C.L. SHIEH
(*)
(*)
Department of Hydraulic and Ocean Engineering, National Cheng-Kun University, Taiwan
(**)
Disaster Prevention Research Center, National Cheng-Kun University, Taiwan
2000) of approximately 113 km
2
in total area were
triggered by the earthquake (H
unG
, 2000; l
in
, 2003,
2006). Sediment generated by these landslides was
deposited on slopes and riverbeds. In the following ty-
phoon seasons, heavy rainfalls readily mobilized the
sediment material and caused debris flows.
The significant increase in debris flow frequency
following the Chi-Chi earthquake and the strong
effect of rainfall on the generation of debris flows
prompted a re-evaluation and subsequent lowering
of the rainfall threshold for a valid debris-flow warn-
ing system (l
in
, 2003; s
HieH
, 2004; C
Hen
, 2006;
s
HieH
, 2009). Consequently, government and engi-
neers became increasingly interested in quantifying
and better understanding the variability in rainfall
triggering of debris flows.
The variation in the rainfall threshold for debris
ABSTRACT
In Taiwan, large and often catastrophic typhoons
and earthquakes are both factors to trigger seri-
ous landslides in mountains. The presences of large
amounts of sediments due to the landslides increase
the occurrence of debris flow. Base on post-event data,
the threshold of debris flow occurrence decreases soon
after an earthquake indicating a fast recovery. A re-
lationship of debris flow occurrence from e
GasHiRa
(1997) is applied, which shows fine sediment plays
an important role with debris-flow development and
occurrence. In this paper, a series mobile-bed experi-
ments were done to access the influence of the con-
centration change from upstream discharge with fine/
coarse particle. Two variables were recorded in the
experiment, which were depth-ratio (sediment layer
depth/ total depth), and the sediment discharge. With
comparison with theoretical relationship, the result
shows the occurrence condition varied with the ratio
of fine sediment.
K
ey
words
: debris flow occurrence, fine sediment, typhoons,
earthquakes, rainfall threshold
INTRODUCTION
The ML 7.3 Chi-Chi Earthquake (23.85°N,
120.81°E) that occurred on 21 September 1999 was
the largest earthquake on the island of Taiwan for the
past hundred years. In central Taiwan (a region of
around 2,400 km
2
), over 20,000 landslides (w
anG
,
Fig. 1 - The rainfall threshold from 1999 ~ 2009
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Y.J. TSAI, k.C. wANG, Y.S. CHEN & C.L. SHIEH
144
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
concentration profile, c(z) is the concentration of the
river bed, and θ is the slope of the river bed.
The depth-ratio of the moving sediment layer to
depth of flow, h
s
/ h
t
, is indicative of the type of sedi-
ment movement on or above the bed. When hs is simi-
lar to the diameter of the particles, transport is domi-
nantly within the bed-loads. Conversely, when h
s
/ h
t
is greater than 0.8, the water and sediment are almost
completely mixed, which indicates the occurrence of
a debris flow. Between these two types, it is a type of
motion referred to as sediment-laden flow (e
GasHiRa
,
1989, 1991, 1992 & 1997). e
GasHiRa
(2008) derived
this ratio from his model, which can be presented as
the following equation.
where c
s
is the depth-averaged concentration of the
moving sediment layer, σ is the density of sediment,
r
w
is the density of water, and f is the friction angle
of sediment. This relationship can be applied to the
continuum between debris flow and flow within bed
loads. According to the post-Chi-Chi-earthquake
monitoring results, multiple landslides contributed
new sediments. The new sediment contained a greater
proportion of fine particles and therefore the density
of flow increased rapidly because of the fine particles
in suspension. So, in the above relationship, the den-
sity of water including the suspended matter, r
m
can
be used instead of r
w
. Therefore, the original equation
can be modified as follow:
With parameters setting, the relationship between
depth-ratio and riverbed gradient can be plotted (Fig.
3). The figure shows that when the density of flow in-
creases, the depth-ratio of the moving sediment layer
to the flow depth also increases. For example, when r
w
is 1.0 and the riverbed gradient is 6°, the depth-ratio is
0.5. The flow type is sediment-laden flow only. When
r
m
increases to 1.3, however, the depth-ratio reaches
0.8 and the type of flow is a debris flow. Furthermore,
note that the lowest possible riverbed gradient for de-
flow triggering after the earthquake was analysed by
surveys in the earthquake area. Riverbed deposits,
particle-size distributions, and sediment concentra-
tions were monitored continuously at the field site
between 1999 and 2009. During the 10-year study
period, the data show that the rainfall threshold for
debris flow activity was remarkably decreased just af-
ter the Chi-Chi Earthquake, but gradually recovering
with time (Fig. 1).
In Fig. 1, the effective intensity means the max
effective rainfall intensity during a typhoon, and the
cumulative rainfall means the total rainfall during
the event. Each point in Fig. 1 means one event. The
reason for the variation is due to the fine particles
increased rapidly due to landslides triggered by the
earthquake. The fine sediment caused the flow den-
sity to increase, and lowered the debris flow triggering
criteria. With time, rainfall caused debris flows and
transported fine particles downstream, the flow den-
sity decreased, and the rainfall threshold is recovering
gradually over time (s
HieH
, 2009).
To investigate the variation in the rainfall threshold
for debris flow triggering, a move-bed experiment was
set and theory of mechanics of debris flow occurrence
by e
GasHiRa
et alii (1989) was modified in this paper.
METHODOLOGY
MECHANICS OF DEBRIS FLOw OCCURRENCE
e
GasHiRa
et alii (1989) developed constitutive
equations of debris flow. These results have been ap-
plied to a wide range of mass flows from debris flows
to the flow within general bed-loads, and the results
have been rational. From the theory, a debris flow oc-
currence condition could be derived as a simple equa-
tion, such as (1). Fig. 2 presents a schematic model of
such a debris flow.
In Fig. 2, hs is the sediment layer depth, ht, is total
depth), u (z) is the velocity profile in z-axis, c (z) is the
Fig.2 Schematic model of debris flow
(1)
(2)
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STUDY ON DEBRIS FLOW OCCURRENCE CONDITION VARIATION AFTER CATASTROPHIC TYPHOON AND EARTHQUAKE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
145
ment discharge. To measure the depth-ratio, a high-
speed camera was used and located near the end of
the flume (Fig. 4). Video speeds of 300 fps and 600
fps was selected for video recording. The sediment
discharge was measured by collecting the sand at the
downstream end of the flume. In all case, the follow-
ing variables were held const: slope of channel: 12°;
discharge of water: 410 cm
3
/sec.
The process of the experiments is description
as fallows:
1. Discharge of water and coarse sand were released.
2. When the space of the dam is filled with the sedi-
ment and the variation of bed is steady, the fine
sands would were added.
3. When the bed was near equilibrium, the flow was
recorded with camera, and sediment was collected
at the downstream end of the flume.
4. The depth-ratio was defined by each recorded
frame. Then the sediment discharges of coarse/fine
sand were calculated after a particle- size analysis.
5. The experiments were repeated for 3 runs of each
case.
bris flow decreases as the density of flow increases. In
Fig.3, when m ρ
m
increases to 1.5, a debris flow can
occur with a gradient as low as 4o. The result shows
that the increase of flow density not only lowers the
moving criteria for debris flows, but also increases the
distance of debris flow traveling.
EXPERIMENT SETTING
Base on the theory, a series mobile-bed experi-
ments were done to access and vaildate the relation-
ship of water density and debris flow occurrence. To
change m ρ
m
, two size particles were selected. For the
rough one, which is assumed as main part of sediment
movement, the size is 10 mm. On the other hand, a
fine particle which is 0.1 mm, is select for the change
of water density. Tab.1. is the parameter of sands. For
the channel, a 4.0 meter channel was selected, and
the slope of the channel could reach 12° (Fig. 4). In
the upstream end, water and sediment (both fine and
coarse sand) could be supplied for different discharge.
A dam with 10 cm was placed at the downstream of
the channel to catch the flow material.
To change the flow density m ρ
m
, the upstream
boundary was set as six different sediment supplies.
The discharge of water and rouse sediment was fix,
and the discharge of fine sediment was set from 0.0
to 48 cm
3
/s. Tab. 2 shows the input condition. The
fine sediment ratio range from zero to two times of
the coarse sediment, and the change of water density
range, from 1.0 to about 1.2.
In order to understand the phenomenon, two
variables were recorded, the depth-ratio and the sedi-
Fig. 3 - The relationship between depth-ratio and river-
bed gradient
Tab. 1 - Character of sediment
Tab. 2 - Upstream Condition of experiment
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Y.J. TSAI, k.C. wANG, Y.S. CHEN & C.L. SHIEH
146
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
Fig.6 shows the average data of each case, and
also thearison with theoretical line or relationship.
The experimental data plot very close to the theoreti-
cal line. So with fine sediment increasing, the bed-
load transform to debris flow gradually
On the other hand, the sediment volume was
record. Tab. 4 provides the result of the sediment
transportation. The input and output value of coarse/
fine sediment were listed in Tab. 4.
It shows the variation of discharge of coarse sand
would increase with the increasing of fine sand. In
Case0 and Case1, the discharge of coarse sand is equi-
librium, but increasing in Case 2 ~ Case4. In Case 5,
the coarse sand discharge is almost same with Case4.
The discharge of fine sediment was almost at equilib-
rium in each case. Fig.7 is draw According to the data
in Tab.4 to show the trend of sediment discharge. This
result could explan the increse of fine sediment would
result in more coarse sediment movement.
EXPERIMENT RESULT AND ANALYSIS
EXPERIMENT RESULT
Accord the experiment setting, the flow depth of
water is about 1 cm to 2 cm. Fig. 5 shows the image
took for depth-ratio analysis for Case0 ~ Case5 in the
figure, the size of grid is 5 mm.
In case0, the water density didn’t change, so the
depth-ratio is well recorded. With fine sand increas-
ing, the depth-ratio got increased. But in Case5, it is
very hard to define the hs and the depth-ratio. Tab.3
shows the defined depth-ratio of each experiment. “-”
is the table means the value couldn’t be defined by the
recorded flame.
Fig. 4 - Schematic diagram of the experiment al laboratory flume
Fig. 5 - Depth-ratio recorded in each case
Tab. 3 - Depth-ratio in each case for different runhs/
ht(Run1)
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STUDY ON DEBRIS FLOW OCCURRENCE CONDITION VARIATION AFTER CATASTROPHIC TYPHOON AND EARTHQUAKE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
147
DISCUSSION AND CONCLUDING RE-
MARKS
There was a significant variation of debris flow
occurrence after 921 Earthquake in Taiwan. Shieh
(2009) proposed the fine sediment played an impor-
tant role with the variation. After a catastrophic earth-
quake or typhoon, the large availability of sediment
due to landslides would lower the triggering rainfall
threshold. Then the threshold then increases in time
due to the washing out of the finer sediments provided
by mass transport.
This paper tries to reproduce the theoretical varia-
tion of debris flow occurrence with laboratory experi-
ments. According to a modified theory from e
GasHiRa
et alii (1989), the variation is supported due to the
change of water density. When the density increases
to 1.5, a debris flow could take place at a slope of 4°.
Through the experiment results, the depth-ratio of
sediment would increase with increasing density with
a constant slope. There are same trend by sediment
discharge analysis, the discharge increasing with the
increasing density. These both explain the decrease
of debris flow occurrence with the fine sediment in-
creasing. With comparing the sediment movement in
a watershed after earthquake, the variation of debris
flow occurrence condition could have a preliminary
understanding.
Tab. 4 - Sediment Discharge in each case
Fig. 6 - Comparison between experiment data with theo-
retical relationship
Fig. 7 - Sediment discharge change with percentage of
fine sediment
REFERENCES
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Hen
C.y. & y
u
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GasHiRa
s., a
sHida
k., y
aJima
H. & t
akaHama
J. (1989) - Constitutive equation of debris flow. Annuals Disaster Prevention
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unG
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in
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Hen
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anG
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in
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HieH
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Y.J. TSAI, k.C. wANG, Y.S. CHEN & C.L. SHIEH
148
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in
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ee
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