# IJEGE-11_BS-Li-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*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**

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.

numerical studies of Bingham-like fluids have been

limited mainly to one- or twodimensional spreading

on an inclined plane. l

flow of Bingham fluid on a slope. H

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

deposit on an inclined plane has been studied experi-

mentally by Coussot, P

*et alii*(2000) derived analytical

ric evolution of isothermal lava domes. Reviews of

these topics can be found in C

*et alii*(2001). b

*et alii*

rium shape of lava domes on an inclined plane.

**ABSTRACT**

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

pacity. The DEBRIS-2D program developed by (l

*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**

usually has high velocity, which causes catastrophic

destruction in Taiwan. The common uncertainties dur-

ing the planning of any countermeasures are the hazard

*k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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**

momentum conservation. The constitutive relation

proposed by J

*τ*

*ij*

*γ*

*ij*

*τ 0*is the yield stress,

*μ*

*d*

*is the dynamic*

cient.

*τ*

*ij*

*and*

*γ*

*ij*

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

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,*

zdirections, respectively. Since debris flow in a lab or

z

in the field can usually be considered as long waves,

i.e. the depth scale is much smaller than the horizontal

spectively. Similar problems regarding the avalanche

of dry granules flowing down an inclined plane have

been reported by Wieland, G

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

*et alii*

bris flows moving from a huge flume (5 m by 100 m)

to a wide deposition basin. o’b

tion flows. The DEBRIS-2D program was developed

by l

analysis solution, laboratory testing and a field case

(l

The typhoon dumped 740.5 mm of rainfall in 62

hours, and induced tremendous landslides and debris

flow with volume exceeding 500,000 m

pacities (l

*et alii*, 2009). However, the area of influ-

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.

portant parameters. l

**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*

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

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**

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

of the area has a slope between 15°~6°, and only

28.3% has a slope less than 6° (see Fig. 1).

neglecting the small terms

plies is a two-dimensional plug flow [i.e.

*u≠u(z*) and

*v≠v(z)*]. Substituting (4) into the momentum equations

obtains

*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

y,t) +δ (x, y,t)

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.

(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

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

*Fig. 1 - Stream DF021 watershed where Daniao tribe de-*

*bris flow occurred*

*k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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

ceeded 500,000 m

Typhoon Morakotare compared in Fig. 6 and Fig. 7.

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.

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*

**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*

of the debris flow of 250 dyne/cm

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**

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

*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*

*k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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.

*ρ*

*s*

*ρ*

*w*

*is the liquid density of debris,*

*φ*

*θ*is the slope. In general,

*ρ*

*w*

*ρ*

*s*

*φ*could be measured from

*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

*ρ*

*s*

*φ*≈

*ρ*

*w*

*C*

*∞*

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.

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

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

the flow duration curve, and the debris flow volume of

508,417 m

*1- C*

*∞*

*). With all the uncertainties, 508,417 m*

Therefore, 200,000 m

basis and these volumes are also cases we simulated.

The following simulation results are for total volume

500,000 m

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).

*Fig. 9 - Compared hazard zones in difference volumes*

*Fig. 10 - Average slope of debris flow path*

**NUMERICAL SIMULATION OF DEBRIS FLOW: A CASE STUDY OF THE DANIAO TRIBE DEBRIS FLOW IN EASTERN TAIWAN IN AU-**

**GUST, 2009**

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

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*

*k.-F. LIU, Y.-C. HSU, H.-C. LI & H.-M. SHU*

marked by red star in Fig. 13. The simulation result is

13.06 m for 500,000 m

**CONCLUSION**

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.

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

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*

**REFERENCES**

*Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear.*Proc.

*Visco-plastic models of isothermal lava domes.*

**403:**37-65.

*Rheological interpretation of deposits of yield stress fluids*. Journal of Non-Newto-

**66**(1)

**:**55-70.

*Mudflow Rheology and Dynamics.*Publisher: Taylor & Francis Group.

*Slow, unconfined spreading of a mud flow.*J. Geophys. Res., 101(B11): 25217-25229.

*The dynamics of lava flow.*Annual Review of Fluid Mechanics,

**32:**477-518.

*. &*Garcia m.H.

*(1998) -*

*A Herschel–Bulkley model for mud flow down a slope.*Journal of Fluid Mechanics,

**374:**

**GUST, 2009**

*The interpretation of lava flow morphology.*Geophysical Journal of the Royal Astronomical Society,

**39**(2)

**:**

*Landslide triggering by rain infiltration.*Water Resources Research,

**36**(7): 1897-1910.

*Rheology of Hyperconcentrations*. J. Hydr. Engrg.,

**117**(3)

**:**346-353.

*Numerical simulation of two-dimensional debris flows.*Proceedings of the 2

*Study on the sensitivity of parameters relating to debris flow spread.*Proceedings of the International

*Numerical simulation of debris flow with application on hazard area mapping*. Computational

**10**(2)

**:**221-240.

*Slow spreading of the sheet of Bingham fluid on an incline plane.*Journal of Fluid Mechanics,

**207:**505-529.

*Roll waves on a layer of a muddy fluid flowing down a gentle slope - A Bingham model.*Physics

**6**(8)

**:**2577-2590.

*Debris flow hazard assessment with numerical simulation.*Natural Hazards,

**49**(1)

**:**137-

*Mud flow-slow and fast.*Geomorphological Fluid Mechanics,

**582:**548-577.

*Roll waves on a shallow layer of mud modelled as a power-law fluid.*Journal of Fluid Mechanics,

**263:**151-184.

*On the importance of mudflow routing*. Proc. 1

*The static shape of yield strength fluids slowly emplace on slope*. J. Geophys. Res.,

**106**(B8)

**:**16241-16250.

*Friction law for dense granular flows: application to the motion of a mass down a rough*

*inclined plane.*Journal of Fluid Mechanics,

**453:**133-151.

*Empirical Relationships for Debris Flows*. Natural Hazards,

**19**(1)

**:**47-77.

*Shear stress developed during rapid shear of concentrated suspension of large spherical*

*particles between concentric cylinders.*Journal of Fluid Mechanics

**, 127:**453-472.

*Debris flow on prismatic open channel.*J. Hydr. Div.,

**106**(3)

**:**381-396.

*Study on the configuration of debris-flow fan*. PhD Dissertation, Department of Hydraulic and Ocean Engineer-

*Channelized free-surface flow of cohesionless granular avalanches in a chute*

*with shallow lateral curvature.*Journal of Fluid Mechanics,

**392:**73-100.

*The steady, spreading flow of a rivulet of mud*. Journal of Non-Newtonian Fluid Mechan-

**79**(1)

**:**77-85