京都大学防災研究所年報 第 52 号 B 平成 21 年 6 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 52 B, 2009

Capturing Process of Debris Flow with Driftwood by an Open Type Check Dam

Badri Bhakta SHRESTHA*, Hajime NAKAGAWA, Kenji KAWAIKE, Yasuyuki BABA
and Hao ZHANG*Graduate School of Engineering, Kyoto University
Synopsis
A two-dimensional numerical model is developed for computing thecharacteristics of debris flow with driftwood and its capturing process by open typecheck dams such as grid or slit type check dam. A numerical model is developed with aninteracting combination of Eulerian expression of the debris flow and Lagrangian
expression of the driftwood, in which the fluctuation components of the position and therotational angular velocity of the driftwood are dealt with stochastically. The jammingof driftwood on grid or slit type check dam is evaluated based on the geometricconditions and probabilistic approaches. The simulated results of outflow discharge,
sediment discharge and the percentage of driftwood outflow at the downstream end of
the flume agree well with the experimental results.
Keywords: debris flow, driftwood, open type check dam, capturing process, simulation

Debris flow is a phenomenon that high-density
water with mud and big gravel flows down along a
stream at high speed, which occurs in a wide varietyof environments throughout the world. Because of
its high density and speed, it has huge destruction
power. Thus damages by debris flows are very
severe and sometimes tragic (Takahashi et al.,
1992; Hunt, 1994; Huang and Garcia, 1997;
Nakagawa et al., 2000; Shrestha et al., 2008). In
recent years much driftwood has combined withdebris flow. Such driftwood clogs narrows in theriver course or bridge or culvert sites giving rise toflooding, bridge/piers or embankments damage ordestruction (Shrestha et al., 2009). Fig. 1 shows theobserved yield quantities of driftwood carried bydebris flow in both coniferous and broadleaf forestsof Japan. Thus, the studies on behavior of debris
flow with driftwood and structural andnon-structural countermeasures against debris flow

disasters with driftwood are very important in orderto reduce the extensive property damage and loss oflife due to debris flow disasters with driftwood. It isalso necessary to understand the mechanism ofdebris flow with driftwood behavior to clarify thenature of debris flow disasters with driftwood.
10000
3

Introduction

Volume of Driftwood Vg (m )

1.

1000

1988 Hiroshima (C)Vg=1000Ab
Coniferous forest

1988 Hiroshima (B)1997 Yamagata (C)1997 Yamagata (B)100

Vg=100Ab
Broad
leaf forest

101982 Nagasaki (C)1982 Nagasaki (B)1989 Aichi (C)1989 Aichi (B)1993 Ohita (B)11994 Kagoshima (C)0.1

C=Coniferous forest
B=Broadleaf forest

1999 Hiroshima (C)

0.01

0.1

1

10
2

Basin Area Ab (km )Fig. 1 Basin area and volume of driftwood carried
by debris flow in both coniferous and broadleaf
forests of Japan (Source: Sabo Department,
Ministry of Construction, Japan, 2000)― 697 ―

Fig. 2 Debris flow and driftwood captured by griddam at Agi River, Nakatsugawa, Gifu Pref., Japan,
2000 (Source: Sabo Department, MLIT, Japan)

Fig. 3 Debris flow and driftwood captured by sabo
dam at Tenryu River, Okaya, Nagano Pref., Japan,
2006 (Source: Sabo Department, MLIT, Japan)
Many researchers such as Takahashi et al.
(1992), Egashira (1993), Nakagawa et al. (1996),
Honda and Egashira (1997), Inverson (2003) andothers have proposed numerical models of debris
flow as a mixture of sediment and water, but they
have not considered the behavior of debris flow
with driftwood. On the other hand, some numericalstudies to compute the behavior of driftwood onlywith clear water flow have been carried out by
Nakagawa et al. (1994, 1995), Gotoh et al. (2002),
Shimizu and Osada (2008) and few others, but they
have not focused on computing the behavior ofdriftwood with debris flow or sediment water
mixture flow.
Open type check dams such as grid type or slit
type check dams are commonly used for debris flow
control and capturing driftwood because they are
preferable over closed type check dams forconserving the natural environment and landscapeof mountain torrents as much as possible. In thedebris flow section where driftwood is assumed toflow down with a debris flow, both of them are
captured together by the open type check dam. Fig.
2 and Fig. 3 show the examples of debris flow anddriftwood captured by grid dam at Agi River, Gifu
Prefecture, Japan and by sabo dam at Tenryu River,
Nagano Prefecture, Japan, respectively. Many
researchers have investigated debris flow capturing
by check dams considering sediments of the flow
only (Takahashi et al., 2001; Satofuka andMizuyama, 2006; Shrestha et al., 2008). Only few
research works have been carried out on capturingof debris flow and driftwood by check dams (Ozaki
et al., 1998; Doi et al., 2000; Katatani and Yamada,2006). Furthermore, these studies are limited to theexperimental study only.
In this study, a two-dimensional numericalmodel is developed for computing the behavior ofdebris flow with driftwood and its capturing process
due to jamming of driftwood on open type checkdams such as grid or slit dam. A numerical model
has been developed with an interacting combinationof Eulerian expression of the debris flow andLagrangian expression of the driftwood, in which
the fluctuation components of the position and therotational angular velocity of the driftwood aredealt with stochastically as random variables basedon the results of a statistical analysis ofexperimental values. The motion of driftwood isrestricted near the flow surface. The simulated
results of outflow discharge and the percentage ofdriftwood outflow at the downstream end of the
flume are compared with those obtained fromhydraulic model experiments.
2.

Numerical model

2.1 Basic equations of debris flow motion
The basic equations used to compute thebehavior of flow motion of debris flow are thetwo-dimensional momentum equations, continuity
equation of flow, continuity equation of sedimentand river bed surface equation. The motion ofdriftwood is restricted near the flow surface and theshear stresses at the flow surface are generated as
the reaction of the drag force acting on thedriftwood. By introducing these shear stresses at theflow
surface,thedepth-wise
averaged
two-dimensional momentum equations of debris― 698 ―

flow for the x–wise (down valley) and y-wise(lateral) directions are described as follows.

∂(uM )∂(vM )∂M+β+β= gh sin θ bx 0∂t∂x∂y
∂ ( z b + h) τ bx τ sx
− gh cos θ bx 0
−
+
∂x
ρT ρT

(2)

(6)

τ sy =

1 Nt  1∑  ρT CDyWk (vk − Vk ) Aky 
A k =1  2(7)velocity components in x and y directions,U k and Vk are the respective local velocity
the position of the centroid of the driftwood,
Wk = (uk − U k ) 2 + (vk − Vk ) 2 , Akx and Aky are the

(3)

(4)

The equation for the change of bed surface
elevation is∂z b+ ib = 0∂t

1 Nt  1∑  ρT CDxWk (uk − U k ) Akx 
A k =1  2components of the fluid in x and y directions at

The continuity equation of the sediment particle
fraction is∂ (Ch ) ∂ (CM ) ∂ (CN )++= ibC*∂t∂x∂y

τ sx =

where u k and v k are the respective driftwood

The continuity equation of the total volume is∂h ∂M ∂N++= ib
∂t ∂x ∂ythe drag force acting on the driftwood as follows:(1)∂(uN )∂(vN )∂N+β+β= gh sin θ by 0
∂t
∂x
∂y

∂ ( z b + h) τ by τ sy
− gh cos θ by 0
−
+
ρT ρT
∂y

in x and y directions generated as the reaction of

(5)

where

M ( = uh) and N ( = vh) are the flow
discharge per unit width in x and y directions,u and v are the velocity components in x andy directions, h is the flow depth, z b is erosion or
deposition thickness of the bed measured from theoriginal bed surface elevation, θ bx 0 and θ by 0 are

respective projected areas of the submerged part ofthe driftwood in x and y directions, C Dx andC Dy are the drag coefficients in

A ( = ∆x∆y ) is the area of the flow
surface ( ∆x and ∆y are the grid sizes of the finite
difference equations), and N t is the number of total
pieces of driftwood in area A .
As the motion of the piece of driftwood isrestricted near the flow surface, the surface flow
velocity components are calculated as Takahashi(1991).
2.2 Basic equations of driftwood motion
It is assumed that the pieces of driftwood are
sufficiently dispersed so that collisions between
them are infrequent. The equations of motion ofeach piece of driftwood, individually labeled bysubscript k are expressed asdX k= uk ;
dt

as Takahashi et al. (1992), C is the sedimentconcentration in the flow, C * is the sediment

dYk
= vk
dt

( mk + mCM )concentration in the bed, β is the momentum
correction factor equal to 1.25 for a stony debris
flow (Takahashi et al., 1992) and to 1.0 for both animmature debris flow and a turbulent flow, g is theacceleration due to gravity, τ bx and τ by are the

duk
∂H k
= − mk g∂x
dt
1− ρT CDxWk (uk − U k ) Akx
2

dv k
∂H k
= − mk gdt∂y1− ρT C DyWk (vk − Vk ) Aky
2

(8)

(9)

( mk + mC M )bottom shear stresses in x and y directions used
as Takahashi (2007), ρT is mixture densityand τ sy are the shear stresses at the flow surfaceydirections,the x and y components of slope of the original
bed surface, i b is erosion/deposition velocity used

( ρT = σC + (1 − C ) ρ , σ is density of the sedimentparticle and ρ is density of the water), and τ sx

x and

(10)

where X k and Yk are the position of the centroid of
the driftwood, m k is the mass of the driftwood, m is

― 699 ―

the mass of the fluid occupied by volume of a pieceof driftwood, C M is the virtual mass coefficient, andH k is the flow level at centroid position of the

{

} (

)

∞
erf ( s ) = 1 − Φ ( 2 s ) = 1 / π ∫ exp( − ε 2 ) d ε ssΦ ( s ) = 1 / 2π ∫ exp( − ε 2 / 2 ) d ε
−∞


(

)

driftwood.
(14)

The rotational motion around the axis of thecentroid of the driftwood is described by evaluating
the moment N 0 produced by the hydrodynamic
force acting on the driftwood as

Id 2θ k / dt 2 = ∑ N0

The driftwood position is estimated by adding
the fluctuation value to the value obtained from theequations of motion deterministically as(11)

X kn +3 = X kn+1 + u kn+ 2 (2∆t ) + 4 K x (2∆t )erf −1 (α ' )(15)where θ k is the rotational angle of the piece ofdriftwood and I is the moment of inertia around the

Ykn+3 = Ykn+1 + vkn+ 2 (2∆t ) + 4 K y (2∆t )erf −1 ( β ' )centroid. The rotational motion of driftwood is also
supposed to be restricted on the flow surface and(16)

the rotation on the vertical plane is not considered.
2.3 Fluctuation of position and rotational angleof driftwood(1) Fluctuation of position of driftwood
Driftwood positions can be evaluated byintegrating Equation (8) deterministically undersuitable initial conditions, but they fluctuate due tothe collision of driftwood with boulders and(2) Fluctuation of rotational angle of driftwood
The rotational angle of a piece of driftwood canbe evaluated deterministically by solving Equation(11), but it also fluctuates due to the collision ofdriftwood with boulders and disturbances on theflow surface during the collision of the sedimentparticles. Therefore, the rotational angle ofdriftwood is evaluated by considering thefluctuation component as follows.

disturbances on the flow surface during thecollision of the sediment particles, which areconsidered in the diffusions coefficients. Thedθ k / dt = ω d + ω p(17)

θ kn+3 = θ kn+1 + 2∆t (ω d + ω p )(18)

diffusion coefficients are determined from thehydraulicmodel experiments with interacting

driftwood and sediment-water mixture flow. The
fluctuation components of driftwood position ∆X k
and ∆Yk are evaluated as Nakagawa et al. (1994,

where ω d is the angular velocity of the piece of1995).

driftwood obtained deterministically and ω p is
the fluctuation of the angular velocity of the∆X k = 4 K x ( 2∆t )erf

−1

'

(α )

(12)

driftwood evaluated stochastically. Assuming therotational angular velocity of the fluctuating
component of a piece of driftwood follows a normal∆Y k = 4 K y ( 2∆t ) erf −1 ( β ' )(13)

distribution, its distribution function, Φ , is given by

Φ(γ ) =

where K x and K y are the longitudinal and transverse
diffusion coefficients, α ' and β ' are randomvariables uniformly distributed in the range (0,1),
and erf −1 is the inverse of error function, erf ,given by1 γexp(−ε 2 / 2)dε
2π ∫−∞

where γ = (ω p − ω ) / σ w(19)

is obtained from theinverse function, Φ −1 , for uniformly distributed― 700 ―

SEDIMENT FEEDER

Q in

0 .8 m

Ѳ=18o

SIDE VIEW

x=0cm

m
0.45
x=180cm

0.3m

Qin
0.6m

2.6m

1.8m
MEASURING REACH
PLAN VIEW

Fig. 4 Experimental setup for determination of diffusion coefficients and rotational angular velocity ofdriftwood
Table 1 Experimental conditions and results of diffusion coefficient and rotational angle of driftwoodQin

Q flow

NO.

(cm3/sec)(cm3/sec)

1

646.020

2
3

Ky

σw

Kx
u* h

u* h

(deg/sec)(deg/sec)

1.188

0.856

0.487

-0.88128.89616.509

1.217

0.930

0.323

0.550

29.64516.601

1.261

0.278

0.389

0.727

38.97046.61918.252

1.420

0.709

0.293

-2.38541.1340.960

39.26217.051

1.280

0.543

0.408

-2.09927.268

0.270

0.990

40.93917.315

1.314

0.829

0.271

0.470

34.483

0.339

1.030

42.66517.661

1.343

0.774

0.244

1.518

33.945

0.269

1.020

41.97717.575

1.328

0.272

0.330

-2.61130.291

0.649

0.343

-0.58933.079

u*

h

u

C

(cm)

(cm/sec)(cm/sec)

Fr843.489

0.283

0.830

33.87515.854742.105

976.006

0.320

0.900

36.148888.5631028.305

0.323

0.910

37.6674

993.6441538.425

0.340

1.100

5

873.7291130.7340.265

6924.1461215.8977844.030

1318.3438

873.627

1284.487

EXP

Mean

ϖ

random numbers within (0,1), ω and σ w are the

45cm deep is used for the experiments. The slope ofmean and standard deviation of angular velocity ofdriftwood. After γ is obtained, ω p is estimatedthe flume is set at 18 degrees. To measure thefrom ω p = γσ w + ω .

pieces measuring rods having the same length as the

position and rotational angle of the driftwood, 19
flume width, are stretched across the flume at

3.

Determination of diffusion coefficients androtational angle of driftwoodintervals of 10cm in the downstream direction fromx = 0 cm (2.6m downstream from the upstream end)
along the 1.8m measuring reach (Fig. 4). Sediment

3.1 Laboratory experiments and method(mean size = 1.86mm, maximum size = 4.75mm) is

A rectangular flume of 5m long, 30cm wide andsupplied― 701 ―

withasediment

feeder

at

0.8m

15
10
5
0
-5
-10
-15

0.5
0.4
0.3
P
0.2
0.1
0

Y (cm)

EXP 1

0

50

100

150

200

0.5
0.4
0.3
P
0.2
0.1
0

EXP 2

5
0
-5
-10
-15
50

100

150

5

200

100

150

Y (cm)

X mean = 9.65cm

10

15

20

EXP 3
X mean = 9.85cm
X 2 = 1.54cm2

0
50

20

X (cm)
0.5
0.4
0.3
P
0.2
0.1
0

EXP 3

0

15

X 2 = 4.44cm2

X (cm)
15
10
5
0
-5
-10
-15

10

EXP 2

0
0

5

X (cm)

15

Y (cm)

X mean = 9.71cm
X 2 = 5.54cm 2

0

X (cm)

10

EXP 1

5

200

10
X (cm)

15

20

X (cm)

Fig. 5 Path lines of the centroid of the driftwood

Fig. 6 Frequency distribution of longitudinal
position of driftwood

downstream from the upstream end and water
discharge is supplied from the upstream end of theof the flow, u* = ghsinθ is the friction velocity

flume. A piece of driftwood is supplied at x= -10cm( θ = flume slope) and Fr = u / gh is the Froude

after supplying designated water and sediment

number. Eight experiments are carried out with

mixture flow discharge. The position and rotational

different hydraulic conditions.

angle of the moving driftwood are measured with avideo camera in each of the 19 sections for x = 0,
10, 20,…..180cm. Such measurement is repeated 30
times for each experiment under the same hydraulicconditions.
A 3.5cm long, cylindrical piece of driftwoodwith a diameter of 3mm and a massdensity ρ d = 0.785g/cm3 is used. The data obtainedin the experiments are analyzed statistically, after
which the diffusion coefficients and other hydraulicparameters are determined.
The experimental conditions and results areshown in Table 1, where Qin is the upstream end
inflow water discharge, Q flow is sediment-water

3.2 Diffusion coefficients of driftwood
Fig. 5 shows the path lines of centroids of thedriftwood of 30 pieces of driftwood and it
demonstrates statistical variety of them. The
scattering process of driftwood is described as adiffusion process and the diffusion coefficientsmight be defined. The frequency distributions of
longitudinal and transverse positions of driftwoodare shown in Fig. 6 and Fig. 7 respectively, inwhich solid line is calculated from the normal
distribution. The longitudinal and transverse
diffusion coefficients of the driftwood are evaluatedas follows:

mixture flow discharge in the flume, C is thesediment concentration in the flow, h is the flow
depth, u is the cross-sectional averaged velocity― 702 ―

K x = (1 / 2)(dX 2 / dt )(20)

X = 50cm

0.4
0.3
P 0.2
0.1
0

Y 2 = 2.9cm 2

X = 100cm

0.4

X = 160cm

Ymean = 0.41cm

0.3

Ymean = 1.017 cm

0.2

Y 2 = 18.035cm 2

0.4

Ymean = −0.018cm

EXP 1

0.3

Y 2 = 5.51cm 2

P 0.2

P

0.1

0.1

0

0

15

10

5

0

-5

-10 -15

15

10

5

0

X = 50cm

EXP 2

0.3

-10

15

-15

0.4

Y 2 = 1.24cm 2

0.3

Ymean = −0.03cm
2

Y = 3.86cm

20.3

Y 2 = 12.246cm 2

0.1

0

0
-10

0

15

-15

-15

0.4

P 0.2

-5

-10

X = 160cm

0.1
0

-5

Ymean = −0.36cm

P 0.2

5

0

X = 100cm

Ymean = −0.11cm

0.1

10

5

Y (cm)

P 0.2

15

10

Y (cm)Y (cm)

0.4

-5

10

5

Y (cm)

0

-5

-10

-15

15

10

5

Y (cm)

0

-5

-10

-15

Y (cm)

X = 50cm

EXP 3

0.4

X = 100cm

Ymean = −0.42cm

0.3

2

Y = 3.44cm

0.4

2

Ymean = −0.63cm

0.3

P 0.2

Y 2 = 9.37cm 2

P 0.2

0.1

P

15

10

5

0

-5

-10

0.3
0.2

Y 2 = 18.76cm 2

0

0

-15

X = 160cm
Ymean = −1.15cm

0.1

0.1

0

0.4

15

10

5

Y (cm)

0

-5

-10

15

-15

10

5

0

-5

-10

-15

Y (cm)Y (cm)

Fig. 7 Frequency distribution of transverse position of driftwood
EXP 1
EXP 4
EXP 7

1.0

EXP 2
EXP 5
EXP 8

EXP 3
EXP 6
Mean Value

0.8

Ky

Kx
0.6
u* h

u* h

0.4
0.2
0.0
1.150

1.250

1.350

1.450

0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.150

EXP 1
EXP 4
EXP 7

EXP 2
EXP 5
EXP 8

1.250

EXP 3
EXP 6
Mean Value

1.350

1.450

Fr

Fr

Fig. 8 Relation of non-dimensional diffusion coefficients and Froude number
1.0

K x 0.8
0.6
u* h

EXP 1

EXP 2

EXP 3

EXP 4

Ky

EXP 6

u*h

0.4

EXP 5

0.2

EXP 7

EXP 8

0.1

0.2

0.0
0.0

0.3

0.4

0.5

C

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

EXP 1

EXP 2

EXP 3

EXP 4

EXP 5

EXP 6

EXP 7

EXP 8

0.1

0.2

0.3

0.4

C

Fig. 9 Relation of non-dimensional diffusion coefficients and sediment concentration― 703 ―

0.5

0.4
0.3

w = −0.881o / sec

EXP 1

2
w

o

σ = 834.9( / sec)

45

2

σw

P 0.2

40

EXP 2
EXP 5
EXP 8

EXP 3
EXP 6
Calculatedo0.1( / sec) 35

030-90 -70 -50 -30 -10 10 30 50 70 90

25ow ( /sec)

20
1.15

0.4
0.3

EXP 1
EXP 4
EXP 7

w = 0.549 o / sec

EXP 2

1.25

1.35

1.45

Fr

σ w2 = 878.82( o / sec) 2

P 0.2

Fig. 11 Relation of Froude number, Fr , to standard
deviation, σ w , of the rotational angular velocities ofthe driftwood

0.1
0-90 -70 -50 -30 -10 10 30 50 70 90ow ( /sec)
0.4
0.3

appears to be prescribed by the hydraulicparameters, and it is related to the Froude number.
The relation between the Froude number, Fr , andthe standard deviation of the rotational angularvelocity of the driftwood, σ w , is shown in Fig. 11,ow = 0.727 / sec

EXP 3

σ w2 = 1518.65( o / sec) 2

P 0.2
0.1

and the relation is obtained as σ w = 25.61Fr .

0-90 -70 -50 -30 -10 10 30 50 70 90ow ( /sec)

4.

Fig. 10 Frequency distribution of the rotational
angular velocities of the driftwood

K y = (1 / 2)(dY 2 / dt )(21)

where X 2 and Y 2 are the longitudinal and transverse
variances. Table 1 shows the calculated results ofdiffusion coefficients. The average values of nondimensional diffusion coefficients K x / u*h = 0.649

and K y / u*h = 0.343 are obtained. The relations of

non-dimensional diffusion coefficients with Froudenumber and sediment concentration are shown in
Fig. 8 and Fig. 9, respectively.

Experiments of debris flow with driftwood

To investigate the capturing process of debris
flow with driftwood by open type check dams andthe verification of the model, a series ofexperiments are carried out. For the experiments, arectangular flume of 5m long, 10cm wide and 13cm
deep is used. The experiments are carried out forflume slope of 18 degrees. Fig. 12 shows the detailof experimental setup. Check dams are set at 20cm
upstream from the downstream end of the flume.
Fig. 13 shows the details of check dams. A
sediment bed of 1.9m long and 7cm deep ispositioned from 2.8m to 4.7m upstream measured
from the outlet of the flume. Sediment materials
with mean diameter d m = 2.39mm, maximum
diameter dmax = 11.2mm, tan φ = 0.7 ( φ =angle of

3.3 Rotational angle of driftwood

repose) and sediment density σ = 2.65g/cm3 are

Frequency distribution of the rotational angularvelocities of driftwood obtained experimentally isshown in Fig. 10, in which solid line is calculated
by assuming the normal distribution with values ofthe parameters determined from the experiments.
The mean value of the angular velocities isapproximately zero, ω ≈ 0 . The standard deviation

used. The sediment materials are prepared bymixing the uniformly distributed different sizes ofsilica sands and gravels. The particle size
distribution of sediment mixture is shown in Fig. 14.
Cylindrical pieces of 38 driftwood pieces (Raminwood, ρ d = 0.785g/cm3) are positioned on thesediment bed at intervals of 10cm c/c along the― 704 ―Q in

SIDE VIEW OF FLUMESEDIMENT BED

DOWNSTREAM
END

Ѳ
7cm

CHECK DAM

PLAN VIEW OF FLUME

10cm

7.5cm

30cm

4cm

Qin

10cm
4cm

20cm

1.9m, SEDIMENT BED
5m

Fig. 12 Experimental setup and positions of the driftwood for the experiments― 705 ―

26mm

26mm
(4mm column/beam diameter)(a) Grid dam
38mm

24mm

38mm

85mm

downstream direction from 7.5cm downstream fromthe upstream end of the sediment bed in twocolumns 2cm apart as shown in Fig. 12. The
sediment bed is saturated by water. Debris flow is
produced by supplying a constant water discharge
270cm3/sec for 10sec from the upstream end of the
flume. The experiments are carried out for
driftwood pieces of diameter 3mm and 4mm with
3.5cm, 4.0cm and 4.5cm in length.
The experiments are repeated three times under
the same identical conditions, because the sediment
composition and degree of saturation might not be
uniform throughout the sediment layer. The flow
discharge and driftwood at downstream end of the
flume are determined by collecting outflow
discharge using series of manually movable sampler
boxes. The jamming of driftwood and deposition
upstream of check dams are evaluated by capturing
the images shot by video cameras located at side,
front and above the downstream end of the flume.
The flow motion of driftwood at forefront of debris
flow in the experiment is shown in Fig. 15. Fig. 16
shows the flow motion of driftwood at upstream ofgrid and slit type check dams and sedimentdeposition behind check dams due to driftwood
jamming. Fig. 17 shows the final depth of debris(b) Slit dam
Fig. 13 Details of check dams (a) Grid dam, (b)Slit damP ercent F iner by W eight (% ) .

100
80
60
40
20
0
0.01

0.1

1

10

100

Diameter (mm)Fig. 14 Particle size distribution curve of bed
sediment

Fig. 15 Flow motion of driftwood at forefront ofdebris flow

Slit dam
Grid dam

Fig. 16 Flow motion of driftwood at upstream of check dams

Slit dam

Grid dam

Fig. 17 Final depth of sediment deposition upstream of grid and slit type check dams

flow deposition upstream of grid and slit type checkdams in the experiments.
5.

Driftwood
deposition

JamminganddebrisThe jamming of driftwood on open type check dams
is evaluated based on the geometric conditions andprobabilistic approaches as follows.

flow(1) Driftwood jamming on grid dam

5.1 Driftwood jamming

When the driftwood is jammed on open space ofopen type check dam such as grid or slit dam, thesediment is deposited upstream side of the dam.

Four cases are considered as conditions underwhich driftwood is jammed on open spaces of a griddam: (1) a piece of driftwood with a large rotational
angle (Fig. 18 (a)). On the basis of the experimental
results, it is considered that the rotational angle of― 706 ―

1.0

yd1
0.8

y d 1 < y g1

yd 2 > y g 2

0.6

p(n)

θk

Lg

Lg
y g1

yd 2

0.4

y

0.2

yg 2

(a)

Exp, Ld/(Lg-Dd)=1.52

Exp, Ld/(Lg-Dd)=1.73

Exp, Ld/(Lg-Dd)=1.95

Cal, Ld/(Lg-Dd)=1.52

Cal, Ld/(Lg-Dd)=1.73

Cal, Ld/(Lg-Dd)=1.95

0.0

(b)

0.0

1.0

2.0

3.0

4.0

n
n

Fig. 19 Plot of jamming probability, p (n ) , andGrid damcolumnnumber of driftwood arrival, n , using Equation(22) with experimental data for grid dam

Lg

Lg

(c)

(d)

This equation is represented in Fig. 19 withexperimental values. To determine which pieces ofdriftwood will be jammed, the random variable, q ,Fig. 18 Jamming of driftwood on grid dam

the driftwood to be in the range of 80 o ≤ θ k ≤ 90 o .
(2) A piece of driftwood will be jammed on a griddam due to geometric conditions as yd 1 < y g1 anduniformly distributed in the range (0,1), is
generated for each piece of driftwood flowing down
the flume. The driftwood is considered to be
jammed when the condition p(n) > q is satisfied.

y d 2 > y g 2 (Fig. 18 (b)). (3) A piece of driftwoodcoming from the rear will be also jammed by thepieces of driftwood already jammed on a grid dam(Fig. 18 (c)). It is considered that when more than
five pieces of driftwood already jammed at previous
time level of calculation, all pieces of driftwoodcoming from the rear are also considered to be
jammed on a grid dam. (4) The pieces of driftwood
will be jammed when the number of pieces ofdriftwood arrival at grid opening at same time (Fig.
18 (d)). In this case, the probability of a piece ofdriftwood jamming depends on the number ofdriftwood arrival at grid opening at same time. This
probability, p (n) , can be assessed in hydraulicexperiments with assuming the functions of length( Ld ) and diameter ( Dd ) of driftwood, clear spacing
between two columns of grid dam ( L g ) and numberof driftwood ( n ) arrival at same time. The
following relation isexperimental values as Ldp ( n) = 0.32
L −D d 
 gobtained

from

the

0.63

n 0.3

(22)

(2) Driftwood jamming on slit dam

Five cases are considered as conditions underwhich driftwood is jammed on a slit dam. The four
conditions of driftwood jamming on slit dam are
similar to as grid dam case (Fig. 20 (a), (b), (c) and(d)). In the case of slit dam, the relation of theprobability of a pieces of driftwood jamming, p( n) ,with the number of pieces of driftwood arrival atslit opening at a same time, n , is obtained as Ld p ( n) = 0.23
 b − Dd 

1.02

n 0.28(23)

where b is width of slit opening. Equation (23) isrepresented in Fig. 21. Another additional condition
for driftwood jamming on slit dam is described asfollows. A piece of driftwood will be jammed inimpermeable width ( b p ) of slit dam when thecentroid of the driftwood is located only inside deadzone of the flow as shown in Fig. 20 (e). When thecentroid of the driftwood is located outside of deadzone, it can be carried by coming flow from― 707 ―

yd1

1.0

yd 1 < yb1
y d 2 > yb 2

0.8

θk

yd 2

b

b

(a)

0.6

y

y b1

yb 2

p(n)

(b)

0.4
0.2

n

Exp, Ld/(b-Dd)=1.52

Exp, Ld/(b-Dd)=1.905

Exp, Ld/(b-Dd)=2.25

Cal, Ld/(b-Dd)=1.52

Cal, Ld/(b-Dd)=1.905

Cal, Ld/(b-Dd)=2.25

0.0
0.0
b

b

(c)

(d)

1.0

2.0

3.0

4.0

n

Fig. 21 Plot of jamming probability, p(n) , and numberof driftwood arrival, n , using Equation (23) withexperimental data for slit dam
Dead Zone

bp / 2bbp

bp / 2(e)θkFig. 20 Jamming of driftwood on slit dam
upstream. In this case, it is considered that when thecentroid of a piece of driftwood is located inside
half distance of impermeable width ( b p / 2) from thechannel wall, a piece of driftwood is considered tobe jammed on slit dam.
5.2 Debris flow deposition

Due to the jamming of driftwood on a grid dam,
sediment is deposited behind the grid dam. The
effects of the driftwood jamming on debris flow
deposition at grid dam is evaluated based on the
projected horizontal length of driftwood piece in ydirection with its rotational angle and clear spacingof column of grid dam, and the sediment passing
rate, Ps , through a grid dam is determined as
Ps = Lo / Lg (Fig. 22). The deposition velocity, idep ,is derived under the mass conservation law of
sediment discharge per unit width ( Qsed ) andsediment deposition as
idep = − ∆z / ∆t = −(1 − Ps )Qsed /(C*∆x) C*∆x∆z = (1 − Ps )Qsed ∆t

(24)

Lo
Lg

Fig. 22 Schematic diagram for sediment passing rate
through grid dam

In the case of slit dam, the deposition equation
due to jamming of driftwood on open space of slit
dam similar to as grid dam is described as
idep = −(1 − Ps )Qsed /(C* ∆x )(25)

in which Ps = Lo / b is the sediment passing rate
through open spacing of slit dam.
The open spaces of grid dam may be also
blockaded by large boulders, and growing rate
formula developed by Satofuka and Mizuyama(2006) is also considered. In the case of slit dam,the deposition velocity, idep , behind a slit dam
caused by clogging of open space due tosimultaneous arrival of two or more particles aredescribed as follows:i dep = − K sd (1 − Psd )where ∆x is the distance increment of calculating
point and ∆z is the thickness of the deposition.

― 708 ―

Q sed
C* ∆x

(26)

Flow Discharge (cm /sec)

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

0

2

4

6

8

10

12

14

1600
1400
1200
1000
800
600
400
200
0

3

3

Flow Discharge (cm /sec)

1600
1400
1200
1000
800
600
400
200
0

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

0

16

2

4

6

8

10

12

14

16

(a) Case with driftwood Dd=3mm and Ld =3.5cm(b) Case with driftwood Dd=3mm and Ld =4.0cm

2

4

6

8

10

12

14

3

1600
1400
1200
1000
800
600
400
200
0

16

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

0

2

4

6

8

10

12

14

16

Time (sec)Time (sec)(c) Case with driftwood Dd=3mm and Ld =4.5cm(d) Case with driftwood Dd=4mm and Ld =3.5cm

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

0

2

4

6

8

10

12

14

3

1600
1400
1200
1000
800
600
400
200
0

Flow Discharge (cm /sec)

3

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

0

Flow Discharge (cm /sec)

3

1600
1400
1200
1000
800
600
400
200
0

Flow Discharge (cm /sec)

Time (sec)

Flow Discharge (cm /sec)

Time (sec)

1600
1400
1200
1000
800
600
400
200
0

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

016Time (sec)

2

4

6

8

10

12

14

16

Time (sec)(e) Case with driftwood Dd=4mm and Ld =4.5cm(f) Flow without driftwood caseFig. 23 Flow discharge at downstream end of flume and discharge reduction by grid dam due to driftwood
jamming

where Psd = (b − d ) / b ( d is diameter of particle)
the sediment passing rate through slit dam, K sd isperformed to investigate the capturing process ofnumerical constant and Qsed is sediment discharge

dams such as grid or slit type check dams. The

per unit width.

jamming of driftwood on grid or slit dam isdebris flow with driftwood by open type check

The deposition velocity equation upstream of aevaluated based on the geometric conditions and thecheck dam developed by Shrestha et al. (2008) is

probabilistic approaches. The geometric conditions

also employed to calculate debris flow deposition inunder which jamming of driftwood on grid or slit

the upstream area of check dam.

dam are determined based on the evaluation of theexperimental results, and probabilistic approach is

6.

Results and discussions

developed from the regression analysis of thevalues obtained in the experiments. Debris flow

The numerical simulations and experiments aredeposition behind a grid or slit dam due to― 709 ―

Sediment Discharge (cm /sec)

600
400
200
0
0

2

4

6

8

10

12

800
Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

3

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

3

Sediment Discharge (cm /sec)

800

14

600
400
200
0

16

0

2

4

6

Time (sec)

200
0
0

2

4

6

8

10

12

14

800

16

600
400

2

4

6

4

6

8

10

12

14

800

12

14

16

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

3

0
2

10

(d) Case with driftwood Dd=4mm and Ld =3.5cm
Sediment Discharge (cm /sec)

3

Sediment Discharge (cm /sec)

200

0

8
Time (sec)

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

400

16

0
0

(c) Case with driftwood Dd=3mm and Ld =4.5cm

600

14

200

Time (sec)

800

12

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

3

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

400

10

(b) Case with driftwood Dd=3mm and Ld =4.0cm
Sediment Discharge (cm /sec)

800

3

Sediment Discharge (cm /sec)(a) Case with driftwood Dd=3mm and Ld =3.5cm

600

8Time (sec)

16

600
400
200
0
0

Time (sec)

2

4

6

8

10

12

14

16

Time (sec)(e) Case with driftwood Dd=4mm and Ld =4.5cm(f) Flow without driftwood caseFig. 24 Sediment discharge at downstream end and discharge reduction by grid dam due to driftwood
jammingdriftwood jamming is also developed. To simulate
the debris flow with driftwood capturing by grid orslit dam, a jamming model of driftwood and adeposition model behind a grid or slit dam areincorporated in a flow model of debris flow withdriftwood. The parameters of the numericalsimulation are as follows; ∆x =5cm, ∆y =1cm,∆t = 0.001sec, ρ = 1.0g/cm3, ρ m = 1.15g/cm3,2
g = 980cm/sec , C 3 = 0.48, n =0.04, C* =0.65,

C Dx =1.0, C Dy =1.0,
C M =1.0 and K sd =0.1.

δ e =0.0018, δ d =0.045,

Figs. 23 (a), (b), (c), (d) and (e) show the flow
discharge at downstream end of the flume andreduction of outflow discharge by grid dam withdebris flow capturing due to jamming of driftwood
on a grid dam for the cases with driftwood Dd=3mm
and Ld=3.5cm, Dd=3mm and Ld=4.0cm, Dd=3mm
and Ld=4.5cm, Dd=4mm and Ld=3.5cm, and
Dd=4mm and Ld=4.5cm, respectively. Debris flow
is captured effectively by a grid dam due to thedriftwood jamming. The simulated results of flow
discharge passed through a grid dam and flow
discharge without dam are quite close to the― 710 ―

Driftwood Outflow (%) .

Driftwood Outflow (%) .

100
Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

80
60
40
20

100

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

80
60
40
20
0

0
0

2

4

6

8

10

12

14

0

16

2

4

6

Time (sec)

12

14

16

.
Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

80
60
40
20
0
0

Driftwood Outflow (%).

10(a) With driftwood Dd=4mm and Ld =3.5cm

Driftwood Outflow (%)

Driftwood Outflow (%) .

(a) With driftwood Dd=3mm and Ld =3.5cm
100

8Time (sec)

2

4

6

8

10

12

14

16

100

Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

80
60
40
20
0
0

2

4

6

8

10

12

14

16

Time (sec)Time (sec)(b) With driftwood Dd=3mm and Ld =4.0cm(b) With driftwood Dd=4mm and Ld =4.5cm
Fig. 26 Accumulated driftwood outflow at outlet ofthe flume, with grid dam, driftwood diameter
Dd=4mm case100
Sim without grid dam
Exp without grid dam
Sim with grid dam
Exp with grid dam

80
60
40
20
0
0

2

4

6

8

10

12

14

16

Time (sec)(c) With driftwood Dd=3mm and Ld =4.5cm
Fig. 25 Accumulated driftwood outflow at outlet ofthe flume, with grid dam, driftwood diameter
Dd=3mm caseexperimental results. Fig. 23 (f) shows the flow
discharge without driftwood case, in which flow
discharge is not reduced effectively by a grid dam
with compared to the flow discharge with driftwoodcases. From the results, outflow discharge isreduced by a grid dam more effectively in the caseswith driftwood due to jamming of driftwood on agrid dam. The results of sediment discharge at
downstream end of the flume with different sizes ofdriftwood cases are shown in Figs. 24 (a), (b), (c),(d) and (e). The sediment discharge is reduced by
sediment deposition behind a grid dam due todriftwood jamming on a grid dam. Fig. 24 (f) shows
the sediment discharge at downstream end of the
flume without driftwood case. The simulated resultsof outflow sediment discharge from a grid dam arealso agreeable with the experimental results. The
effect of driftwood jamming on sediment deposition
behind a dam using developed deposition equation
is well explained in the simulations. In thecalculation, deposition due to blockage of grid damby large boulders is also considered.
The results of percentage of temporal driftwood
outflow at the downstream end of the flume in griddam case with different sizes of driftwood areshown in Fig. 25 and Fig. 26 for driftwood diameter
Dd=3mm and Dd=4mm cases, respectively. The
percentage of driftwood outflow is the ratio of thenumber of pieces of driftwood outflow at
downstream end to the total amount of driftwood
supplied at the inflow boundary. The driftwood
passed through a grid dam is reduced due to thedriftwood jamming on grid dam. The number ofpieces of the driftwood outflows from a grid dam― 711 ―

0

2

4

6

8

10

12

14

800

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

3

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

Sediment Discharge (cm /sec)

3

Flow Discharge (cm /sec)

1600
1400
1200
1000
800
600
400
200
0

16

Time (sec)

600
400
200
0
0

2

4

6

8

10

12

14

16

Time (sec)

1600
1400
1200
1000
800
600
400
200
0
0

2

4

6

8

10

12

14

800

16

600
400
200
0
0

Time (sec)

2

4

6

8

4

6

8

10

12

14

16

10

12

14

(b) Case with driftwood Dd=4mm and Ld =4.5cm
800
Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

3

Sediment Discharge (cm /sec)

3

Flow Discharge (cm /sec)

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

02Time (sec)(b) Case with driftwood Dd=4mm and Ld =4.5cm
1600
1400
1200
1000
800
600
400
200
0

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

3

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam(a) Case with driftwood Dd=3mm and Ld =4.5cm
Sediment Discharge (cm /sec)

3

Flow Discharge (cm /sec)(a) Case with driftwood Dd=3mm and Ld =4.5cm

16

600
400
200
0
0

Time (sec)

2

4

6

8

10

12

14

16

Time (sec)(c) Flow without driftwood case(c) Flow without driftwood caseFig. 27 Flow discharge at downstream end of the
flume with slit dam caseFig. 28 Sediment discharge at downstream end of
the flume with slit dam case

based on the developed driftwood jamming model
under the geometric conditions and probabilistic
approaches are well explained in the numericalsimulations. The simulated results of driftwood
outflow time at the downstream end of the flume
are also close to the results obtained from theexperiments.
The results of flow discharge and reduction offlow discharge by slit dam at downstream end of
the flume with and with out driftwood cases areshown in Fig. 27. Fig. 28 shows the results of

sediment discharge at downstream end of the flumein the case of slit dam. The simulated results offlow discharge and sediment discharge passing
through a slit dam are agreeable with theexperimental results. The debris flow deposition
behind a slit dam due to driftwood jamming is also
well explained in the numerical simulations.
The results of percentage of temporal driftwood
outflow at the downstream end of the flume in slit
dam case with driftwood Dd=3mm and Ld=4.5cm
and Dd=4mm and Ld=4.5cm are shown in Fig. 29.

― 712 ―

Driftwood Outflow (%) .

Driftwood Outflow (%) .

100

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

80
60
40
20
0
0

2

4

6

8

10

12

14

100

Sim without slit dam
Exp without slit dam
Sim with slit dam
Exp with slit dam

80
60
40
20
0
0

16

2

4

6

8

10

12

14

16

Time (sec)Time (sec)(b) With driftwood Dd=4mm and Ld =4.5cm(a) With driftwood Dd=3mm and Ld =4.5cm

Fig. 29 Accumulated driftwood outflow at outlet of the flume with slit dam

The driftwood passed through a slit dam is reduced
due to the driftwood jamming on slit dam. The
jamming of driftwood on slit dam is well explainedin the numerical simulations with compared to theexperimental results.
7.

Conclusions

A two-dimensional numerical model isdeveloped for computing the characteristics ofdebris flow with driftwood. Numerical simulations
and experimental works are carried out to determine
the characteristics of debris flow with driftwood.
Equations of the rotational motion and thetranslational motion of driftwood are evaluateddynamically in the Lagrangian form. A numericalmodel is developed with an interacting combinationof Eulerian expression of the debris flow andLagrangian expression of the driftwood, in which
the fluctuation components of the position and therotational angular velocity of the driftwood aredealt with stochastically. The position androtational angular velocity of the driftwoodfluctuate due to the collision of driftwood withboulders and disturbances on the flow surface
during the collision of the sediment particles, which
are considered in the diffusions coefficients. The
scattering process of driftwood is described as adiffusion process and the diffusion coefficients aredefined by the hydraulic experiments. The
calculated results of frequency distribution of thelongitudinal positions, the transverse positions andthe rotational angular velocities of the driftwood are
fairly good agreement with the experimental results.
The process of debris flow capturing by gridand slit dams due to jamming of driftwood isinvestigated. A numerical model is developed forcomputing the debris flow with driftwood capturingby open type check dams such as grid and slit dams.
The jamming of driftwood on open type check dams
is evaluated based on the geometric conditions andprobabilistic approaches. A deposition velocity
model is also developed to calculate the debris flow
deposition due to driftwood jamming on a grid orslit dam. The flow and sediment discharge passing
through a grid or slit dam are reduced due todriftwood jamming. The simulated results of flow
discharge, sediment discharge and percentage ofdriftwood passed through a grid or slit dam are ingood agreement with the experimental results.
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透過型砂防ダムによる流木を伴う土石流の捕捉過程

Badri Bhakta SHRESTHA*・中川一・川池健司・馬場康之・張浩*

京都大学大学院工学研究科

要 旨
流木を含む土石流の特性及び,グリッドダム・スリットダムに代表される透過型砂防ダムによるこれの捕捉過程をシ
ミュレートする二次元数値解析モデルを構築した。数値解析モデルは,土石流のオイラー的挙動解析法と流木のラグラ
ンジュ的運動追跡法の組み合わせにより構成しており,流木が存在する座標の変動成分及び流木の回転角速度については確率的にこれを与えた。透過型砂防ダムによる流木の阻害については,流木の幾何学的状態及び確率的手法により評価を行った。数値解析により, 実験結果と適合する流出量・堆積量・下流端での流木通過率を得た。

キーワード: 土石流, 流木, 透過型砂防ダム, 捕捉過程, 数値解析

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