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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
885
DOI: 10.4408/IJEGE.2011-03.B-096
NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE
DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AUGUST, 2009
k
o
-f
ei
liu
(*)
, y
u
-C
HaRn
HSU
(*)
, H
sin
-C
Hi
LI
(**)
& H
unG
-m
inG
SHU
(***)
(*)
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-Mail: d92521021@ntu.edu.tw
(**)
Socio-Economic System Division, National Science & Technology Center for Disaster Reduction, Taipei, Taiwan.
(***)
Graduate Institute of Disaster Prevention on Hillslopes and Water Resources Engineering, National Pingtung University
of Science and Technology, Pingtung, Taiwan
zone area and the path of debris flow. There are numer-
ous empirical formulas that can be used to obtain part
of the information needed in the designing process.
Nevertheless, empirical formulas can be inaccurate for
complicated geographic regions. Numerical simulation
is a better way to obtain the needed information.
In previous studies of debris flow, non-Newtonian
fluid models have often been used. Early analytical or
numerical studies of Bingham-like fluids have been
limited mainly to one- or twodimensional spreading
on an inclined plane. l
iu
& m
ei
(1989) presented a
two-dimensional theory for the unidirectional slow
flow of Bingham fluid on a slope. H
uanG
& G
aRCia
(1998) worked on the same problem for Herschel–
Bulkley fluid. For three-dimensional flows, the slow
and steady spreading of mud released from a point
source on a plane was investigated by H
ulme
(1974)
with a Bingham model, and by C
oussot
& P
Roust
(1996) and w
ilson
& b
uRGess
(1998) with a Her-
schel–Bulkley model. The static problem of the final
deposit on an inclined plane has been studied experi-
mentally by Coussot, P
Roust
& a
nCey
(1996) and by
o
smond
& G
RiffitHs
(2001). For a horizontal plane
bottom, b
almfoRtH
et alii (2000) derived analytical
and numerical solutions for the radically symmet-
ric evolution of isothermal lava domes. Reviews of
these topics can be found in C
oussot
(1997), G
Rif
-
fitHs
(2000) and m
ei
et alii (2001). b
almfoRtH
et alii
(2001) developed an analytical theory for the equilib-
rium shape of lava domes on an inclined plane.
ABSTRACT
In August 2009, Typhoon Morakot hit Taiwan and
induced tremendous disasters, including large-scale
landslides and debris flows. One of these debris flows
was suffered by the Daniao tribe in Taitung, eastern
Taiwan. The volume was in excesses of 500,000 m
3
,
much larger than the original design mitigation ca-
pacity. The DEBRIS-2D program developed by (l
iu
et alii, 2009) was applied in a hazard assessment at
this particular site two years before the disaster. The
model predicted a hazard zone that was close to the
real disaster. This successful prediction seems to sup-
port the usefulness of DEBRIS-2D. However, there
may be still factors that need to be discussed before
identifying the success of the program. One of the im-
portant factors discussed was the total volume and its
distribution. This paper showed that a 20 % variation
in estimating the total volume in this particular site,
would give rise to only a 2.75 % variation on the final
front position. Therefore, volume is not very sensitive
K
ey
words
: Typhoon Morakot, Numerical Simulation, Debris
flow, DEBRIS-2D, Hazards assessment.
INTRODUCTION
Debris flow is a mixture of water, gravel and soil.
The motion of the mixture is induced by gravity and
usually has high velocity, which causes catastrophic
destruction in Taiwan. The common uncertainties dur-
ing the planning of any countermeasures are the hazard
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k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU
886
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
tivity of three factors total volume, yield stress, and
bottom slope for debris flow spread in lab scale. The
paper concluded that total volume amount is more
important than the others. It was found that a 20%
change in total volume would induce 20% change for
the maximum depth. Therefore, this paper uses differ-
ent total volumes to simulate a real debris flow
DESCRIPTION OF DEBRIS-2D MODEL
The original DEBRIS-2D model was developed
by l
iu
& H
uanG
(2006). The governing equations of
the DEBRIS-2D model were adopted in the mass and
momentum conservation. The constitutive relation
proposed by J
ulien
&l
an
(1991) was used.
The original one-dimensional version was extend-
ed to a threedimensional version as.
where τ
ij
is the shear stress tensor and γ
ij
is the strain
rate tensor. τ 0 is the yield stress, μ
d
is the dynamic
viscosity and μc is the turbulent-dispersive coeffi-
cient. τ
ij
and γ
ij
represent the second invariant of the
shear stress and strain rate tensor, respectively. l
iu
& l
ai
(2000) defined the portion of debris flow with
stress greater than the yield stress as the boundary
layer. The depth ratio between the boundary layer
and the main debris flow could be proved to be small.
This implied that most of the flow region was in a
weak stress condition, i.e. the plug region. The corre-
sponding constitutive law is equation (2), which can
be expressed as
where the x-axis coincides with the averaged bottom
of the channel and is inclined at angle θ with respect
to the horizon. The y-axis is in the transverse direc-
tion and the z-axis is perpendicular to both the xand
y- axes. u, v, w are the velocity components in the x, y,
z
directions, respectively. Since debris flow in a lab or
in the field can usually be considered as long waves,
i.e. the depth scale is much smaller than the horizontal
For high-speed flows, l
iu
& m
ei
(1994) and n
G
&
m
ei
(1994) examined the nonlinear formation of roll
waves for a Bingham fluid and a power-law fluid, re-
spectively. Similar problems regarding the avalanche
of dry granules flowing down an inclined plane have
been reported by Wieland, G
Ray
& H
utteR
(1999) and
P
ouliQuen
& f
oRteRRe
(2002).
Most debris-flow models have focused on labora-
tory scale experiments or slow debris flow motion in
a regular channel. However, debris flows occurring in
the field are quite different from those in a control-
led environment. It is difficult to simulate debris flow
both numerically and experimentally. i
veRson
et alii
(2000) used a two-phase flow model to simulate de-
bris flows moving from a huge flume (5 m by 100 m)
to a wide deposition basin. o’b
Rien
& J
ulien
(1997)
used a quadratic constitute to simulate high concentra-
tion flows. The DEBRIS-2D program was developed
by l
iu
& H
uanG
(2006) for field debris flow simula-
tion. This model had already been verified by a 1-D
analysis solution, laboratory testing and a field case
(l
iu
& H
uanG
, 2006). Additionally, this model has
been used in many practical applications in Taiwan.
Debris flows at the Daniao tribe occurred during
typhoon Morakot in August 2009 in eastern Taiwan.
The typhoon dumped 740.5 mm of rainfall in 62
hours, and induced tremendous landslides and debris
flow with volume exceeding 500,000 m
3
. The authors
had performed a simulation for the Daniao tribe
using DEBRIS-2D in 2007 under different design ca-
pacities (l
iu
et alii, 2009). However, the area of influ-
ence for the present event, with mitigation measures
constructed, was almost the same as what was predict-
ed before with no countermeasures. This proved the
simulation ability of DEBRIS- 2D, but also induced
questions on why it was the same. The challenges for
finding the answers lie on the uncertainty of the input
data. The geographical data was available but was not
highly precise. The total amount of available soil that
could be eroded or mobilized during heavy rainfall and
the properties that could correctly represent the field
material were also two major problems. Strictly speak-
ing, if these parameters could not be precisely resolved,
any modelling results would have errors. Therefore,
this paper focused on only a few major factors.
R
iCkenmann
(1999) showed that in torrent hazard
assessment, the debris flow volume is one of most im-
portant parameters. l
iu
& H
su
(2008) studied sensi-
(1)
(2)
(3)
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NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AU-
GUST, 2009
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
887
field, it is usually necessary to find a computational
domain, which contains the whole reach of the de-
bris flows. In real applications, a large computation
domain could be selected, so that debris flows would
never reach the domain boundary. Thus the boundary
conditions are
If debris flows are restrained in a fixed domain
such as a flume, no normal flux condition will be used
on all physical boundaries. However, (12) still applies
to the front and tail of the debris flow. The tracking of
the points with a velocity near zero is important. Cor-
rections of overshooting the physical quantities are
performed during every time step. The initial condi-
tion is the depth contour in the computation domain
with all possible debris flow sources. The value of the
rheological properties is also needed, which must be
obtained from field sample measurements.
DESCRIOPTION OF DANIAO TRIBE DE-
BRIS FLOW
The Daniao tribe debris flow occurred in the de-
bris flow potential stream DF097 in Taitung (eastern
Taiwan). Stream DF097 has a high debris flow dis-
aster potential according to the information from the
Soil and Water Conservation Bureau in Taiwan. The
watershed area of DF097 is roughly 0.86 km
2
. A total
of 71.7% of area has a slope greater than 15°, 18.6%
of the area has a slope between 15°~6°, and only
28.3% has a slope less than 6° (see Fig. 1).
Field investigations in September 2006 discov-
length scales; it can be obtained from equation (4) by
neglecting the small terms
This implies that the portion of debris flow near
the free surface where the stress free condition ap-
plies is a two-dimensional plug flow [i.e. u≠u(z) and
v≠v(z)]. Substituting (4) into the momentum equations
obtains
The stress free condition is applied at the free
surface z = h(x, y,t) . The upper boundary of the thin
boundary layer near the bottom is defined as z = B(x,
y,t) +δ (x, y,t)
where the natural bottom of the debris
flow is z = B(x, y,t) . As the thickness of the bound-
ary layer is very small compared to the flow depth as
discussed above, the natural bottom can be used as the
boundary for the plug flow.
Equation (7) leads to static pressure in z
Integrating (5) and (6) in z from the bottom to the
free surface obtains the results in conservative form as
The depth integration of continuity equation gives
where H=h(x,y,t)-B(x,y,t) is the flow depth. Equations
(9), (10) and (11) could be used to solve the three un-
knowns H, u and v. This paper used the Adams-Bath-
forth 3
rd
order scheme for time and central differences
and the upwind scheme in space. The upwind method
is used for convective terms. The central difference
method is used for all other terms. Mathematically,
one condition each for H, u and v is needed in the
physical boundary. For debris flow simulations in the
(4)
(5)
(6)
(7)
(1)
(9)
(10)
(11)
(12)
Fig. 1 - Stream DF021 watershed where Daniao tribe de-
bris flow occurred
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k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
2009/8/7 9:00 AM to 2009/8/09 11:00 PM). The
annual record for the maximum rainfall accu-
mulated at 1, 2, 4, 6, 8, 12, 15, 24, 48 and 66 hours
duration are shown in Fig. 4. On 2009/8/9 at 3:00
PM (with a rainfall accumulation of 740.5 mm in 62
hours), the rainfall induced tremendous landslides
and debris flows. The aerial photo after the disaster is
show in Fig. 5. Field investigations after the disaster
revealed that almost 17.2 % (0.1485 km
2
) of the wa-
tershed was buried, the total volume of debris flow ex-
ceeded 500,000 m
3
and almost 200,000 m
3
flowed out
of the valley. The aerial photography before and after
Typhoon Morakotare compared in Fig. 6 and Fig. 7.
ered several locations with large amounts of deposit.
The total volume exceeded 19,943 m3 distributed on
the slopes and streambed. (Tab. 1 and Fig. 2, pictures
1~5). A total of 63.1% of this material was located in
regions with a slope greater than 15°, and only 7.8%
of the material was located in regions with slope less
than 6°. The formation of the mixture was composed
of slate, mudstone, sandstone and weathered gravel,
which are all easily movable under external forces.
In August 2009, typhoon Morakot hit Taiwan and
dumped heavy rainfall. The maximum rainfall inten-
sity of this event reached 45.5 mm/hour (see Fig. 3),
and accumulated 759 mm of rainfall in 66 hours (from
Tab. 1 . Field investigation in 2007 before typhoon Mora-
kot
Fig. 2 - Debris flow source location (before typhoon
Morakot)
Pic. 1 - Landslide deposition on upstream hill
Pic. 2 - Ground with serious erosion on left bank hill
Pic. 3 - Mass source deposition on streambed
Pic. 4 - Landslide deposition on right bank hill
Pic. 5 - Debris deposition on branch streambed
Fig. 3 - Rainfall intensity record for typhoon Morakot
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NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AU-
GUST, 2009
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
889
(see next page for volume estimation). A yield stress
of the debris flow of 250 dyne/cm
2
was measured in
the field. A time step of 0.01 seconds was set up, and
the computational grid size adopted was 5m x 5m
DTM of theDaniao tribe watershed. The initial debris
sources were distributed atthe head of Taitung DF097
creek. Fig. 8 shows the final simulated deposit con-
tour maps adopted in different volumes of debris flow
sources. This paper compared hazard zones in differ-
THE HAZARD ZONE ASSESSMENT OF
DANIAO TRIBE DEBRIS FLOW
R
iCkenmann
(1999) showed that in torrent haz-
ard assessment, the debris flow volume is one of the
most important parameters. In reality, it is difficult to
forecast real debris flow, as there are numerous uncer-
tainties in a watershed. The DEBRIS-2D model was
applied to assess a hazard zone with total amounts of
200,000 m
3
, 300,000 m
3
, 400,000 m
3
and 500,000 m
3
Fig. 4 - Annual record for maximum rainfall accumulated
for 1, 2, 4, 6, 8, 12, 15, 24, 4 and, 66 hours dura-
tion in the DF021 stream watershed
Fig. 5 - Aerial photograph of Daniao tribe debris flow in
Typhoon Morakot
Fig. 6 - Aerial photograph before Typhoon Morakot hit
Fig. 7 - Aerial photograph after Typhoon Morakot
Fig. 8 - Final deposition contour maps adopt in different
volume; (1)The maximum depth all almost equal
to 15 m deposited on a watershed gap in medi-
um stream; (2)The front peak all almost equal to
12~13 m deposited on the ran out of valley region
of the watershed in down stream
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k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
ent volumes as shown in Fig. 9.
Form 2006 surveyed, we found there were at least
20,000 m
3
solid sources of debris flow deposited on
the triggering areas of the Daniao tribe watershed.
However, for heavy rainfall event, there should be
more loose material can be created. Therefore, we
adopt a different approach using accumulated rainfall
to estimate the volume of debris flow in this site.
An equilibrium concentration conceptual of
t
akaHasHi
(1980) was applied to estimate the debris
flow volume amount. t
akaHasHi
(1980) derived the
equilibrium concentration, which is
where C
is the equilibrium concentration, ρ
s
is the sol-
id density of debris, ρ
w
is the liquid density of debris, φ
is the rest angle of solids, and θ is the slope. In general,
ρ
w
is the water density, ρ
s
and φ could be measured from
field samples, and θ could bem calculated from the Dig-
ital Topographic Map (DTM). In the Daniao tribe debris
flow watershed (Taitung DF097 watershed), the slope
was calculated from the average creek bottom slope to
be 23.2% ( ≈ 13
o
), as shown in Fig. 10. From the field
samples, the solid density was ρ
s
= 2.6 g/cm
3
, and φ
30
o
. With the liquid density ρ
w
= 1.0 g/cm
3,
the equilib-
rium concentration was calculated as C
= 41.6% from
equation (13). With this equilibrium concentration, the
amount of water needed to induce debris flow in this
watershed could be estimated. If the amount of water
was not enough to mobilize all the source material to
form a debris flow, then the volume of the debris flows
would be smaller.
This study assumes that water that can induce de-
bris flow must come from rainfall in the area with loose
deposition and in the correct flow direction. After slope
and direction analysis, we found 71.7% of the Daniao
tribe watershed (equal to 0.63 km
2
as shown in Fig.1)
satisfies this requirement. For the particular event, a
rainfall accumulated to 740.5 mm in 62 hours before
the debris flow occurred. The last 12 years of records
showed this value was satisfied in 22.3 return years
from frequency analysis showed. Therefore, a water
volume accumulation of about 296,916 m
3
occurring
in 62 hours using rational formula can be found from
the flow duration curve, and the debris flow volume of
508,417 m
3
could be found from the water volume di-
vided by (1- C
). With all the uncertainties, 508,417 m
3
can be considered as the maximum possible amount.
Therefore, 200,000 m
3
, 300,000 m
3
, 400,000 m
3
and
500,000 m
3
four cases are simulated. It happened that in
2006, we were using 50 year return frequency as design
basis and these volumes are also cases we simulated.
The following simulation results are for total volume
500,000 m
3
.
The simulated debris flow depth contour and veloc-
ity vector at 1, 3, 6, 10, 50 and 100 minutes are shown
in Fig. 11 and Fig. 12. The maximum depth of the de-
posits was in excess of 15 m. The sources of debris
flows were distributed in the gap of the watershed (in
the medium stream) and ran out of the valley region (in
the down stream), as shown in Fig. 11 (a) and (b). The
maximum velocity was in excess of 20 m/sec during
the start of the debris flow, but began to slow rapidly
when the debris flow passed the watershed gap (maxi-
mum velocity less than 3 m/sec), as shown in Fig. 12
(b), (c), (d) and (e).
The results showed that around 10 minutes, the
Fig. 9 - Compared hazard zones in difference volumes
(13)
Fig. 10 - Average slope of debris flow path
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NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AU-
GUST, 2009
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
891
The final deposition area for both the simulation
and the real event are shown in Fig. 13. The simulation
results were very close to the field measurements. How-
ever, drainage ditches were constructed on both sides
of the village after the simulation in 2006, so part of
the debris flow spread along the ditches (see Fig. 13).
As a result, the front travelled a shorter distance than
debris flow reached upstream of the Daniao tribe, as
shown in Fig. 11 (d) and Fig. 12 (d). As the velocity of
the debris flow slowed to less than 0.5 m/sec, as shown
in Fig. 12 (f), and the debris flow front peak continued
to maintain the same depth ( ≈ 15 m), as shown in Fig.
11 (d), (e) and (f). The final deposition fronts for all 4
cases are almost identical.
Fig. 11 - The debris flow depth contour maps at different time
Fig. 12 - The debris flow velocity vector maps at different time
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k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU
892
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
estimated is between 12 m and 13 m at the location
marked by red star in Fig. 13. The simulation result is
13.06 m for 500,000 m
3
and 11.74 m for 200,000 m
3
.
CONCLUSION
This study used a DEBRIS-2D model to simulate
a real debris flow event before it occurs. The loca-
tion of loose deposits was found through a field in-
vestigation. The total volume was obtained through
hydrological methods and was verified with field
estimation. The simulated result done in 2006 had a
deposition area very close to the real event in 2009.
Maximum depth and its location have practically no
meaningful error between numerical result and real
event. One reason for this successful prediction is
due to the relatively insensitivity from volume es-
timation. This paper found that a 20 % variation in
estimating the volume would only give rise to a 2.76
% variation on the final deposition front. This case
study of Daniao tribe debris flow would give a sup-
port for the usability of numerical simulations in real
engineering detailed designs.
what was simulated. Since the only difference for dif-
ferent total volume is the front location. Therefore, this
means the spread of the simulation from all 4 different
total volumes are equally good. However, the maxi-
mum depth of debris flow for the final deposition was
15 m measured in the field and is 15.14 m for 500,000
m3 simulation and 15.02 m for 200,000 m
3
simulation.
The location for the maximum predicted by numerical
simulation is only 3 m away from the real location as
shown in Fig. 8. One depth near the front in the field
is available by the estimation from rescuers. The depth
Fig. 13 - Region in red is area affected by Typhoon Morakot, and the blue region is the simulation result. The red star in-
dicates where field depth estimation is available. The depth estimated by rescuer is between 12 m and 13 m. The
simulated result for 50,000 m
3
is 13 m
Tab. 2 - Changes in front positions for different volumes
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NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AU-
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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
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