# IJEGE-11_BS-Nakatani-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-080*

**DEVELOPMENT AND APPLICATION OF GUI EQUIPPED 1-D AND 2-D**

**DEBRIS FLOW SIMULATOR, APPLIED TO MIXED-SIZE GRAINS**

understand the results instinctively from the animated

graphical results. Thus, the interface enables users to

run high-quality debris-flow simulations easily and

leads them to better solutions for sabo engineering.

**K**

**ey**

**words***: debris flow, numerical simulation, mixed-size*

*grains, sediment sorting, two-layer model, GUI, Miyajima area*

**INTRODUCTION**

be effectively reduced using numerical simulation

models, which can describe the debris-flow process

(e.g., e

*et alii*, 1997; t

s

bris-flow numerical simulations do not have efficient

graphical user interfaces (GUIs). Therefore, we devel-

oped KANAKO and KANAKO 2D (n

*et alii*,

packages equipped with efficient GUIs, and applied

them to real disasters and debris-flow torrents (n

*et alii*, 2009, 2010). However, actual debris flows

causes sediment sorting (t

*et alii*, 2001).

d

**ABSTRACT**

be effectively reduced using numerical simulation

models, which can describe the debris-flow process and

determine the possible effects of sabo dams or erosion

and sediment control dams. Although various models

have been developed, many existing debris-flow nu-

merical simulations do not have efficient graphical

user interfaces (GUIs). In addition, actual debris flows

are composed of mixed grain-size sediment, which

causes sediment sorting, while many simulation mod-

els have been developed only for uniform-sized gravel.

Here, we report the development of a GUI-equipped

oneand two-dimensional (1D and 2D, respectively)

debris-flow simulation system for mixed-size gravel.

The model uses two layers in 1D simulations to ac-

count for debris-flow sediment sorting, and can also

examine the effect of closed, slit, and grid sabo dams.

The model can incorporate multiple dams and combi-

nations of different types of sabo dams. We simulated

a debris-flow disaster that occurred on September 6,

2005, in Miyajima, Hiroshima Prefecture. Although

two sabo dams were present along the torrent, a large

amount of damage was caused in the nearby residential

area. We considered these existing dams in our simula-

tion. Our results demonstrated that applying the mixed

grain-size sediment model provided a more realistic

description of the debris-flow deposition than uniform-

sized gravel models. Furthermore, our GUIequipped

*k. NAkATANI, T. wADA, N. MATSUMOTO, Y. SATOFUkA & T. MIZUYAMA*

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

*TwO-LAYER MODEL FOR 1D SIMULATION AREAS*

phenomena. This model uses the basic equations for a

one-layer debris-flow model with mixed materials, but

the vertical change in the sediment concentration is also

considered. The flow is divided into two vertical layers

(see Fig. 1), and the proportion of each grain-size cat-

egory of flowing sediment at each point is considered.

Inverse gradient or sediment sorting is modeled by ex-

changing particles between layers. The process is calcu-

lated using parameters obtained from laboratory experi-

ment results (see details from s

*et alii*, 2007).

*k*to indicate the

*k*

*d*

*k*

*C*

*k*

*k*

*d*

*m*

*ke*is the largest grain-size category. Here,

*C*

*k*

*d*

*k*

*d*

*m*

*p*

*k*

category of flowing particles. Given the exchange of

particles between the two layers, this proportion will

respectively) debris-flow simulation system “KANA-

KO 2D Ver. 2.1” for mixed grain-size sediment. The

model uses two layers in 1D simulations to account

for debrisflow sediment sorting, and it can also exam-

ine the effect of sabo dams. We used the developed

software package to simulate the debris-flow disaster

that occurred on September 6, 2005, in Miyajima, Hi-

roshima Prefecture, and compared the results obtained

using mixed and uniform grain-size sediment.

**METHODS**

tains two parts: a user interface that manages the data

input and displays the output, and a simulation model.

For the user interface, we applied and extended KANA-

KO 2D, which can simulate uniform-sized gravel. For

the simulation model, we applied and modified an inte-

grated model (w

*et alii*, 2008) so that we could ob-

1D simulation areas, such as gullies, and 2D simulation

areas, such as alluvial fans. We also modified a mixed

grain-size gravel model (m

*et alii*, 2008).

slit, and grid sabo dams.

**1D AND 2D DEBRIS-FLOW SIMULATION**

**MODEL APPLIED TO MIXED GRAIN-SI-**

**ZE SEDIMENT**

tion areas. In 1D simulation areas, we applied a mixed

grain-size gravel erosion/deposition process, and also

considered sediment sorting and the concentration of

coarse particles at the front of the debris flow (s

*et alii*, 2007). In 2D simulation areas, the vertical

the cross-flow direction. Therefore, since the exchange

of particles in the vertical direction decreases, we ex-

cluded the process of sediment sorting and the concen-

tration of coarse particles at the front of the debris flow.

the following sections.

*Fig. 1 - Velocity distribution in the debris flow (u*

*0*

*: aver-*

*age flow velocity for the total flow depth)*

*Fig. 2 - Outline of particle proportion p*

*k*

*in the upper layer*

**DEVELOPMENT AND APPLICATION OF GUI EQUIPPED 1-D AND 2-D DEBRIS FLOW SIMULATOR, APPLIED TO MIXED-SIZE GRAINS**

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

*k*

the size distribution of debris flow in the vertical di-

rection, we set

*k*

*k*

*GOVERNING EQUATIONS FOR 1D SIMULA-*

TION AREAS

TION AREAS

entire debris-flow volume is:

*k*

*k*

*i*

*k*

*k*

*u*is the x-axis flow velocity,

*z*is the bed elevation,

*t*is time,

*g*is the acceleration due

to gravity,

*H*is the flow surface elevation (

*H*=

*h*+

*z*),

*ρ*

is the interstitial fluid density,

*C*

*τ*

*x*

*x*-axis direction.

*U*and

*L*indicate the upper

*k*

*q*

*bk*

*p*

*k*

*q*

*bk*

0.5 to 1.5 times that of the uniform case. When we

use Eq. (3) to solve the continuity equations for each

grain-size category instead of the standard sediment

flux formula, we can reproduce the concentration of

larger particles at the front of the flow.

*R*

*m*

Fig. 3. m

openings between large particles (dynamic sieving).

We considered that this is the main factor producing

vertical sediment sorting. The average opening size of

the lower layer can be expressed as follows using the

average particle diameter in the lower layer:

*d*

*Lm*

*k*

layer is thought to increase when the proportion of small

particles in the upper layer is large and the velocity is

high. Therefore, the rate

*r*

*k*

*k*

*d*

*k*

*R*

*m*

*d*

*k*

*R*

*m*

because of the assumption that the sediment is distrib-

uted homogeneously over the entire flow.

These movements cause the exchange of particles

and vertical sorting in the debris flow. The rate

*r'*

*k*

*Fig. 3 - Settling condition of small particles and large*

*particles, depending on the opening space in*

*the lower layer*

*k. NAkATANI, T. wADA, N. MATSUMOTO, Y. SATOFUkA & T. MIZUYAMA*

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

*C*>

*C*

*i*> 0, the erosion velocity is:

*δ*

*e*

*d*

*mbed*

*d*

*k*

ment. The deposition velocity for the

*k*

*i*

*k*

*d*

*k*

*f*

*bk*

*k*

*u*

***

*θ*

*w*

*u*

**ck*

*k*

*EQUILIBRIUM SEDIMENT CONCENTRATION*

AND RIVERBED SHEARING STRESS

AND RIVERBED SHEARING STRESS

vious research (n

sediment sheet flow, or bed load transport based on the

slope gradient and sediment concentration of the flow.

*GRAIN SIZE DISTRIBUTION ON A RIVERBED*

SURFACE

SURFACE

how the grain-size distribution of a riverbed sur-

face varies with time. Therefore, we define a par-

ticleexchange layer

*δ*

*m*

and consider that the grain-size distribution changes

only in this layer. When erosion/deposition occurs

and the riverbed surface changes, the particle-ex-

change layer will also change. On the upper surface

of the particle-exchange layer, particle exchanges

will occur through the fluid-phase erosion/deposi-

tion volume. On the lower surface of the particleex-

change layer, particle exchange will occur through

*k*

then we calculate the continuity equation for the upper

layer. We determine the lower layer volume from the

difference between the entire flow and the upper layer

volumes. When sediment sorting does not occur, we

set the falling rate and rising rate to 0; thus, we don’t

need to consider the continuity equation for the upper

layer, and just model one layer of flow. Such a situation

can occur when applying this model to uniform-sized

grains or to bed load transport in mild-slope areas.

calculate the flow motion of the upper and lower lay-

ers separately. Instead, we assume that the sediment

concentration is distributed homogeneously in the

flow depth direction, and we use the entire flow sedi-

ment concentration when calculating the momentum

equation and the erosion/deposition process.

*EROSION / DEPOSITON VELOCITY*

centration

*C*

*et alii*, 1991a). If

*C*<

*C*

*i*< 0, the

*q*is a unit sediment discharge,

*C*

*C*is the sediment con-

centration of all the grain sizes in the flow, and

*δ*

*d*

*k*

*i*

*k*

settling is neglected, even in low gradient and velocity

areas, such as the mouth of a river or upstream of a dam.

Therefore, when the sediment diameter (

*k*

tion so that the friction velocity

*u*

**ck*

*w*

*0k*

*w*

*0k*

**DEVELOPMENT AND APPLICATION OF GUI EQUIPPED 1-D AND 2-D DEBRIS FLOW SIMULATOR, APPLIED TO MIXED-SIZE GRAINS**

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

cle-exchange layer elevations have moved.

*k*

bed surface, or the riverbed surface ratio

*f*

*bk*

*f*

*0k*

*k*

*EFFECT OF A SABO DAM*

sabo dams for a 1D simulation area: closed, slit, or

grid. For detail information of deposition process up-

stream to the sabo dam, see the following references

(s

*et alii*,

composed of several grain-size classes, but we only

consider the largest class of sediment, which blocks the

grid dam opening and increases the dam height. In the

future, we may divide the grain-size classes into two

groups for grid sabo dams, and consider that the mean

diameter of the larger group affects the dam blockage.

*2D SIMULATION AREAS*

direction. Therefore, since the exchange of particles

in the vertical direction decreases, we excluded the

process of sediment sorting and the concentration of

coarse particles at the front of the debris flow. We ap-

ply the particle-number conservation law (t

*et alii*, 1991b) to calculate the change in time and

space of the mean particle size

*d*

*m*

size and making use of the calculated

*d*

*m*

they consider the cross (

*y*-axis) direction as well as

the flow (

*x*-axis) direction. We only modeled uniform

grain-size and one layer flow in 2D simulation areas,

calculated using Eq. (17).

**KANAKO 2D VER. 2.10: A GUI-EQUIPPED**

**1D AND 2D DEBRIS-FLOW SIMULATOR AP-**

**PLIED TO MIXED GRAIN-SIZE SEDIMENT**

figure representing the 1D riverbed profile, and a plane

figure displaying the 1D river width and 2D landform

plane appears. The debris flow first passes through the

1D simulation area, and then through the 2D simulations

area. The KANAKO 2D GUI system is also easy to use

for beginners because the required simulation data sets

can be input using a mouse and viewed on a monitor. A

new function for mixed grain-size sediment is the grain-

size detail-setting screen, which is used to set the grain-

size classifications, grain diameter, and concentration of

particles in the supplied hydrograph. A data file is used

to set the volume ratio of riverbed particles.

2D landform screen. On the main screen, the user can

see real-time images of the flow depth and riverbed vari-

ation in the longitudinal and plane plots. Users can also

visualize the flow and sediment discharge at each calcu-

lation point. The new mixed grain-size sediment func-

tion allows the user to visualize the discharge of each

grain-size classification of sediment along with the entire

sediment discharge. Users can also view real-time im-

ages of the average particle diameter on the 2D landform

screen during the simulations, as it is shown in Figs. 8.

Other functions are the same as those in the existing

KANAKO 2D interface (see n

*et alii*, 2010).

**SYSTEM APPLICATION TO A REAL DE-**

**BRIS-FLOW DISASTER**

pan (k

*et alii*, 2006). Landslides followed heavy

gathered and flowed down about 2.6 km, destroying

*Fig. 4 - Particle exchange layer for riverbed surfaces*

*k. NAkATANI, T. wADA, N. MATSUMOTO, Y. SATOFUkA & T. MIZUYAMA*

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

m

Fig. 5. Reportedly, 13,000 m

ported downstream. Therefore, we placed 13,000 m

the riverbed. Using the landform data, the calculated

thickness was 0.7 m. The landform conditions were

obtained from topographic maps and reports, and were

prescribed in KANAKO 2D as shown in Fig. 6. We set

the river width for the 1D landform area at a constant

15 m. Other parameters were set as listed in Table 1.

In Case 1, we used ten grain-size classifications with

equal proportions. In Case 2, we set a uniform grain

size of 0.55 m, which was the average diameter for

to overflow downstream. We simulated this event us-

ing the developed KANAKO 2D Ver. 2.10 package by

modeling the mixed grain-size sediment debris flow.

*SIMULATION CONDITIONS*

volume from the upstream end of the simulation. We

then calculated the sediment concentration of the slope

after applying the Takahashi equation (t

*et alii*,

*σ*is the mass density of the bed material (= 2550

kg/m

*ρ*is the mass density of the fluid phase includ-

*f*is the inter-

*θ*is the angle of the 100-m

slope area (= 4.93°);

*Cd*is the concentration of the

debris flow (0.3 ≤

*Cd*≤ 0.9

*C*

***

*C*

***

discharge using the following equations from the Sabo

Master Plan for Debris Flow (NILIM Japan, 2007):

*Q*

*sp*

*Q*

sediment (m

*Vdqp*is the sediment volume (m

*Tab. 2 - Simulation cases*

*Fig. 5 - Supplied hydrograph for Cases 1 and 2 (left figure) and supplied material conditions for Case 1 (right figure)*

*Tab. 1 - Simulation parameters*

**DEVELOPMENT AND APPLICATION OF GUI EQUIPPED 1-D AND 2-D DEBRIS FLOW SIMULATOR, APPLIED TO MIXED-SIZE GRAINS**

Therefore, sediment sorting occurred at Obs. 2.

and 3. This dam was not large enough for the amount of

sediment and was located on a steep gradient, so it was

not very effective. Due to erosion of the initial riverbed

and the sediments flowing over the sabo dam, both Cases

1 and 2 predicted more sediment discharge and total flow

at Obs. 3 than at Obs. 2. The trends for total sediment

discharge, amount of flow, and sediment sorting were

the same as seen at Obs. 2. A 8-m-high closed sabo dam

was located between Obs. 3 and 4. This dam was also

not large enough to catch all the sediment. However, the

dam was located on a small gradient and its capacity was

larger than the upper sabo dam, so it did trap some sedi-

ment. The slope gradient at this point was decreasing;

thus, the sediment discharge and total flow were less at

Obs. 4 compared to Obs. 3. As before, Case 1 predicted

more total sediment discharge and total flow than Case

2, and the peak arrival time was slightly earlier.

time, as observed at Obs. 2 and 3. However, medium-

sized sediments 0.3-0.5 m in diameter had a higher

discharge peak than larger sediments over a short pe-

riod of time. For smaller sediments 0.1-0.2 m in diam-

eter, the amount of discharge was initially small, but

this increased after the discharge of the larger and me-

dium-sized sediments decreased and the duration of

the discharge was longer. These phenomena occurred

due to sediment sorting as the debris flow traveled

down the slope, and due to deposition caused by the

sabo dam and the decreasing slope gradient.

simulations, and assumed that both dams were empty.

*SIMULATION RESULTS FOR 1D AREA*

labeled in Fig. 8 as Obs. 1-4. We also examined each

grain size sediment discharge for Case 1 (see Fig.6).

At Obs. 1, the difference between the total flow and

total sediment discharge for the two cases was small.

The grain size distribution for Case 1 indicated that

the discharge of smaller sediments that were 0.1 and

0.2 m in diameter was higher than that of larger diam-

eter sediments due to the selective transport caused by

the flow velocity and flow depth.

not large, so the amount of flow was small and the flow

depth was low, therefore sediment sorting did not occur.

large, so the type of sediment transport was debris

flow. Due to erosion of the initial riverbed, the sedi-

ment discharge in both Cases 1 and 2 increased com-

pared to Obs. 1, and the amount of flow increased.

Case 1 showed slightly more total sediment discharge

and total flow, and the peak arrival time was slightly

earlier than in Case 2. For Case 1, for larger sediments

0.5-1.0 m in diameter, the amount of discharge of

each grain size was initially large over short periods

of time. For smaller sediments 0.1-0.4 m in diameter,

the amount of discharge was initially small, but this

increased after the discharge of larger sediments de-

creased, and the duration of the discharge was longer

*Fig. 6 - Miyajima simulation*

*area shown on kANA-*

*kO 2D (1D area in the*

*lower right, 2D area*

*in the upper right) and*

*corresponding topog-*

*raphy map (left)*

*k. NAkATANI, T. wADA, N. MATSUMOTO, Y. SATOFUkA & T. MIZUYAMA*

*SIMULATION RESULTS FOR 2D AREA*

er and right), at 301 s, 426 s, 645 s, and 1799 s. Case 1

with mixed grain-size sediment covered a wider area

and the sediment deposition was thicker. This tenden-

cy was seen all through the simulation period 1800 s.

and 1799 s (shown in Fig. 8 left). The average grain-

size diameter decreased with time due to sediment

sorting. Also, the coarse particles were concentrated

which affected the discharge flowing to the 2D area.

**CONCLUSION**

and erosion/deposition process of debris flows con-

sidering granularity characteristics. By equipping the

mixed grain-size sediment simulation model with an

efficient GUI, users can run more reasonable debris-

flow simulations without difficulty, and are able to

plan better sabo engineering solutions. We applied our

*Fig. 7 - Total flow and total sediment discharge for Cases 1 and 2 (left) and grain size sediment discharge for Case 1 (right)*

iment model is limited by the conditions of laboratory

experiments; further studies are required to improve the

parameters we used and check our assumptions. The

proposed model should also be applied to other real

disasters to ensure its accuracy. Furthermore, we must

consider more userfriendly GUIs for the simulations.

Japan and compared the results obtained using mixed

and uniform grain-size sediment.

and earlier peak arrival times.

*Fig. 8 - Transitional change of average grain-size diameter in the 2D landform area for Case 1(left), riverbed variation in the*

*2D landform area for Case 1 (center) and Case 2 (right)*

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