自然災害科学特別号（特別号（）43）

A STUDY ON DEBRIS FLOWOUTFLOW DISCHARGE AT A
SERIES OF SABO DAMS
Namgyun Kim ＊・Hajime NAKAGAWA ＊＊・Kenji KAWAIKE ＊＊＊・
Hao ZHANG ＊＊＊＊A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE
AT A SERIES OF SABO DAMS
Namgyun KIM*, Hajime NAKAGAWA**,
Kenji KAWAIKE*** and Hao ZHANG****
Abstract
Debris flows are very dangerous phenomena in mountainous areas. Sabo dams arecommonly used to mitigate debris flows and they are effective countermeasures against
debris flow disasters. However, human life and property remain at risk off debris flows.
In order to develop measures to increase the effectiveness of a Sabo dam, its control
function and design have been reported. Nevertheless, few studies have discussed thecontrol functions of a series of Sabo dams. This paper estimates debris flow discharges
at a Sabo dam site using overflow equations. A 1-D numerical simulation method ofdebris flows is presented. Numerical simulations of debris flow were conducted
including overflow discharge at the dam point and laboratory experiments wereperformed to validate the simulation results. Comparisons between the numericalsimulation results and laboratory experimental results show reasonable agreement.
Application of the numerical model used here is recommended to calculate overflow
discharge at Sabo dam sites and to evaluate the sediment capturing effects of Sabo dam
arrangements.
Key words： debris flow, Sabo dam, overflow equation, deposition, numerical simulation

Student Member of JSNDS, Doctoral Student, Departmentof Civil and Earth Resources Engineering, Kyoto
University (Katsura Campus, Nishikyo-ku, Kyoto
615-8540, JAPAN)＊＊
Member of JSNDS, Dr. of Eng., Prof., DPRI, Kyoto
University (Yoko-oji, Fushimi, Kyoto 612-8235, JAPAN)

Member of JSNDS, Dr. of Eng., Assoc. Prof., DPRI,
Kyoto University (Yoko-oji, Fushimi, Kyoto 612-8235,
JAPAN)＊＊＊＊
Member of JSNDS, Dr. of Eng., Assist. Prof., DPRI,
Kyoto University (Yoko-oji, Fushimi, Kyoto 612-8235,JAPAN)

＊

＊＊＊43

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A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

1. INTRODUCTION

reinforcement of houses etc. Sabo dams are an

Many types of sediment-related disasters occur

effective structural countermeasure to controlin mountainous areas (Fig. 1). Sediment-related

debris flow. They play an important role in thedisasters are caused by localized torrential

management and development of a river basin.

downpours, earthquakes, volcanic eruption, and so

Sabo dams can be distinguished into two types:

forth. These are natural phenomena. However, asclosed and open dams (Di Silvio., 1990; Armanini eturbanization continues to expand in mountainousal., 1991). Closed-type Sabo dams intercept debris

areas, the risk of sediment-related disasters isflow to the downstream. In contrast, open-type

increasing. In particular, debris flows frequently

Sabo dams are constructed with suitable openings

cause extensive damage to property and loss of life.

in the body of the structure. Therefore part of theDebris flows are generally initiated fromsediment is allowed to pass through. These two

upstr eam of a mountainous ar ea whentypes of Sabo dams are constructed in series along

unconsolidated material becomes saturated andthe channel.

unstable or originate directly from landslides. They

The advance of science and technology has led tocan flow down several kilometers and damage themore advantageous counter measures forresidential areas at the foot of mountains. They

mitigating debris flow damage. To increase thecontain various particle sizes from fine material toeffectiveness of Sabo dams, the control functions oflarge boulders and these large boulders

such dams have been reported. Such Sabo dam

accumulate at the front part of the flow. Thus

functions have been described in many laboratory

damage caused by debris flow can be severe. In

experimental studies and numerical simulation

addition debris flows can cause morphologicalstudies (Honda et al., 1997; Imran, J. et al., 2001).

changes, serious casualties and damage toAlso, considerable theoretical and numerical works

property. Figure 2 shows the number of debris

have been performed on the size, shape andflow occurrences from 2000 to 2012 in Japan.

structure of Sabo dams (Mizuyama et al., 1988;

Countermeasures designed to reduce debris

Johnson et al., 1989). These studies contribute toflow disasters are classified into structural and non-technical standard guidelines on debris flows.

structural measures. Structural measures include

Thus, there are studies on methods of evaluating

Sabo dams, guide levees and training channels,

the control function of a series of Sabo dams (Osti

while non-structural measures include warninget al., 2008). However, further studies are required

systems, proper land use in the areas and theFig.1 Sediment-related disasters (Photo source :DPWH, Japan)

Fig.2 The number of debris flow occurrence in Japan(Data source : MLIT, Japan)

自然災害科学特別号（45）to develop general guidelines on a series of Sabo
dams. Few studies have reported about control(3)functions of a series of Sabo dams.
This paper describes a methodological approach

where, M (= uh) is the x components of the flowfor estimating debris flow discharge at a series offlux, x is the flow direction coordinate, t is time, β is

Sabo dams, and proposes equations for evaluating

the momentum correction factor equal to 1.25 for athe effectiveness of a series of closed-type Sabo

stony debris flow (Takahashi et al., 1992), u is thedams. A 1-D numerical model of debris flow iscomponents of mean velocity, g is the acceleration

presented. Numerical simulations were conductedof gravity, h is flow depth, θb is the bed slope, τb isincluding debris flow overflow at the dam point andcomponents of the resistance to flow, ρT is mixture

analyzed with boundary conditions. To verify thedensity (ρT=σC+(1-C)ρ), σ is density of the sedimentsuggested numerical model, laborator yparticle, ρ is density of the water, i is erosion (>0) orexperiments were performed.

deposition (≤0) velocity, C is the sediment

The numerical model is used to study the effectof Sabo dam arrangement. Through the proposed
calculation method of overflow discharge at thedam point, determination of optimal distanceconcentration in the flow, C* is maximum sedimentconcentration in the bed.
The equation of bed variation due to erosion ordeposition is described as follows:

between Sabo dams is expected.
(4)

2. NUMERICAL MODEL
where, zb is erosion or deposition thickness of the

2.1 Governing Equations(1) Transport and bed surface elevation equations

bed measured from the original bed surface

Debris flows are a fluid mixture that consists ofelevation. In the fixed bed, zb equals 0. Actually, thegranular materials and water. The equations used

sediment in the fixed bed should be contained inare the depth averaged one-dimensional

the flow parts when erosion occurs. However there

momentum and continuity equations. The

is no sediment in the fixed bed.

equations for the mass conservation of sedimentwater mixture and mass conservation of sediment(2) Erosion and deposition velocity equations
The erosion and deposition i are source terms.

are as follows.
Momentum equation of sediment and water flow

The velocity equations that have been given by
Takahashi et al. (1992) are described as follows:

mixture:(1)

Erosion velocity, if C < C∞;(5)

Continuity equation of flow mixture:(2)
Continuity equation of sediment particles:

Deposition velocity, if C ≥ C∞;(6)
where, δ is erosion coefficient, δ' is deposition

46

A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

coefficient, dm is mean diameter of sediment, andC∞ is the equilibrium sediment concentration(14)

described as follows (Nakagawa et al., 2003).
In the case of turbulent flow, the Manningʼs
If tanθw > 0.138, a stony type debris flow occurs,

equation is used to determine the bottom shearandstress. When C is less than 0.02,(7)

If 0.03< tanθw ≤ 0.138, an immature type of debris(15)
where, n is the Manning resistance coefficient.

flow occurs, and2.2 Conditions of Sabo Dam(8)The closed-type Sabo dam is set at the grid line
where discharge is calculated (Fig. 3). The gridIf tanθw ≤ 0.03, a turbulent water flow with bed loadsize is 5 cm. The flow surface gradient, θw, and bed

transport occurs, andgradient, θb, are calculated at the center of the cell.
The flow surface gradient θw and bed gradient θb are(9)calculated by the average of each value of θw, i+1,

(10)

the calculation method is changed as follows:(11)

Gradient at the dam point (zi < zdam);θb, i+1 and θw, i-1, θb, i-1. However, if there is a Sabo dam,

(12)

(16)

where, θw is water surface gradient, ρm is density(17)of the interstitial muddy fluid, ϕ is internal friction
angle of the sediment τ*c is the non-dimensional

Gradient at the dam point (zi ≥ zdam);critical shear stress and τ* is the non-dimensional(18)

shear stress.
(3) Bottom shear stress equations
The resistance terms are given by the following
equations for a stony debris flow:(13)
An immature debris flow occurs when C is lessthan 0.4C* and the bottom shear stress is describedas follows:
Fig.3 Definition of the variables

自然災害科学特別号（47）3. LABORATORY EXPERIMENTS(19)
Figure 4 shows the experimental flume setup.
The laboratory experiments were conducted using

2.3 Overflow Equations
Sabo dams involve obstructing the path of flow.

a rectangular flume, which is 6.5m long, 13 cm

This is a vertical obstruction over which the debris

high, 10 cm wide and has an incline of 18°. The

must flow such as a weir. At that time, outflow

flume is divided into two parts by an 8cm high sanddischarge at the dam point can be calculated using

stopper that is installed 1.5m from the upstream

cer tain equations. To calculate debris flow

end of the flume. The upstream part is filled with adischarge at the dam point, the overflow equation

movable bed that consists of silica sand and graveland free overfall equation are applied.
Table 1 Flow conditions at Sabo dam

Overflow equation (Complete flow):(20)
Overflow equation (Incomplete flow):(21)
Free overfall equation:(22)
where, M0 is debris flow discharge per unit width
at the dam point, and c is the overflow coefficient.
As the overflow equation and free overfall equation
are adjusted at the dam point, flow conditions arechanged by the bed elevation (Table 1).

Fig.4 Experimental flume setup

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A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

mixtures. The movable bed was set 20cm upstream

wide and 1 cm thick were used for thefrom the upstream end of the flume, length 150 cm,experiments. The lower Sabo dam was set 30 cm

8 cm high, and 10 cm wide. Sediment materials

upstream from the downstream end of the flumewith mean diameter d m=2.86mm, maximum

the upper Sabo dam was set 30 cm, 55 cm, 80 cm

diameter dmax=15mm and density σ=2.65g/cm ,upstream from the lower Sabo dam.

3

internal friction angle of a sediment tanϕ=0.7 were

Two runs were conducted under the sameused. The particle size distribution of the movable

experimental conditions in order to obtain reliable

bed is shown in Figure 5.

data. Debris flow discharge and sediment

To generate the debris flow, the movable bed isconcentration at each dam point were measured

saturated by seepage flow. After fully saturating theusing sampler. Debris flow deposition upstream ofmovable bed, the debris flow is generated throughthe Sabo dam was measured by video camera andsupplying clear water. The debris flow developed in

the images were analyzed over time.

the experiments is fully stony type debris flow andlarger particles are accumulated at the forefront of

4. RESULTS AND DISCUSSION

the debris flow. This debris flow, overtopping theThe numerical simulations were conducted tosand stopper, reaches the downstream part of thecalculate debris flow discharge at the dam point

flume. After overtopping the two Sabo dams, debris

and experiments were also performed to validate

flows are captured by the sampler.

the numerical model.

The experimental conditions are shown in Table

Figure 6 shows the simulated results and

2. Two closed-type Sabo dams 6 cm high, 10 cm

experimental results of debris flow discharge andsediment concentration. In this graph, time 0
means the start time to supply clear water. Thestart time of blue line means the time the debris
flow reached the upper Sabo dam. Table 3 shows
the time the debris flows reached each position.
In Case A, the overflow time of debris flow at thelower Sabo dam is earlier than in Case B and Case
C. The distance between two Sabo dams is not
sufficient capture debris flow. Sufficient distanceFig. 5 Particle size distribution of sediment materials
Table 3 Debris flow time
Table 2 Experimental conditions(unit : sec)

自然災害科学特別号（49）between two Sabo dams means that the length

deposition height is equal to 0.

between two Sabo dams is longer than theTable 4 shows the debris flow peak discharge.

deposition length upstream of one Sabo dam. ThisIn the experimental results, debris flow discharge

deposition starting from the Sabo dam to theis calculated at the downstream end of the flume

Fig .6 Debris flow discharge (a) and sediment concentration (b)Table 4 Debris flow peak discharge(unit : cm3/s)

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A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

under the no Sabo dam case. Simulated results ofthe shape of the deposition between the simulated

debris flow discharge are consistent with theresults and experimental results. The height ofexperimental results. Through the series of Sabo

deposition in the experimental results is higherdams, the total discharge of debris flow and peakthan that in the simulation results. The simulation

discharge is decreased.

results are underestimated. Therefore, a more

The total average peak discharge rate is 48.4% infeasible coef ficient of erosion velocity andthe experimental results and 48.1% in thecoefficient of deposition velocity are required.

simulation results. However, the longer theThrough adjusting the discharge coefficient anddistance between two Sabo dams, the higher theerosion, deposition coefficient, the debris flowrate of total discharge decrease. The situation isdeposition pattern could be further improved.

different in the lower Sabo dam. The longer theIn this study the debris flow overflow discharge

distance between two Sabo dams, the easier it is to

at a series of Sabo dams was evaluated. The

form a fully developed debris flow.

suggested simulation method for calculating debris

The average decrease rate of the upper Sabo
dam is 29.8% in the experimental results and 31.9%

flow discharge results in good agreement with theexperimental results.

in the simulation results. However, the averagedecrease rate of the lower Sabo dam is 18.6% in the

5. CONCLUSIONS

experimental results and 16.2% in the simulation

The numerical model was developed to simulate

results. The efficiency of the decrease rate ofthe debris flow discharge at the dam point.

debris flow peak discharge at the lower Sabo dam

Laboratory experiments were conducted and goodis less than the upper Sabo dam. The reason forresults of debris flow discharge as well as sediment

this is the sediment concentration. In the Figure

concentration were obtained. Debris flow

6(b), as debris flows pass the Sabo dam, sedimentdeposition will be further improved throughconcentration decreased. First, the sedimentadjustment of the coefficient.

concentration is consistent at around 35%. As theThrough considering the combination of Sabo

debris flows passed the upper Sabo dam, sedimentdams, elucidation of technical criteria on theconcentration decreased to around 30% and when

distance between Sabo dam is expected.

passing the lower Sabo dam, sedimentconcentration fur ther decreased. However,ACKNOWLEDGMENT

overflowed debris flow at the lower Sabo dam does

This research was supported by the JSPS AA

not have a consistent sediment concentration. TheScience Platform Program (Coordinator: H.

initial sediment concentration is lower than 5%.

Nakagawa) and support of the Wakate fundThis means that debris flow that is not fully

program by the Kyoto University Global COE

developed reaches the lower Sabo dam. As debris

Program (GCOE-ARS).

flows overflow the Sabo dam, sediment is capturedby the Sabo dam. Therefore, the forefront of thedebris flow has a low sediment concentration.
Figure 7 shows the debris flow deposition
upstream of the Sabo dam. In this graph, time 0means the start time of debris flow being capturedby the Sabo dam. Some discrepancies are found inREFERENCES
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Fig. 7 Debris flow deposition upstream of Sabo dam51

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A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

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