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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
477
DOI: 10.4408/IJEGE.2011-03.B-053
PREDICTION OF RUN-OUT PROCESS FOR A DEBRIS FLOW TRIGGERED
BY A DEEP RAPID LANDSLIDE
Y. NISHIGUCHI
(*)
, T. UCHIDA
(*)
, K. TAMURA
(*)
& Y. SATOFUKA
(**)
(*)
Public Works Research Institute, Ibaraki, Japan
(**)
Department of Civil Engineering, Ritsumeikan University, Shiga, Japan
INTRODUCTION
Landslides induced by rainstorms or earthquakes
often have disastrous implications for human society.
In particular, deep rapid landsides have triggered large-
scale debris flows that have had serious impacts on hu-
mans. Therefore, it is important to predict the run-out
process of debris flows and to identify debris flow haz-
ard areas. A number of numerical simulation models
have been developed to describe the propagation and
deposition of debris flows (e.g., e
GasHiRa
et alii, 1989;
o’b
Rien
et alii, 1993; t
akaHasHi
& k
uanG
, 1986;
i
veRson
& d
enlinGeR
, 2001; t
akaHama
et alii, 2002;
R
iCkenmann
et alii, 2006). However, useful techniques
for the prediction of run-out processes for large debris
flows have not yet been developed.
Most models used to describe stony debris flows
assume that they consist of solid and fluid phases
(t
akaHasHi
, 1977). In models of this type, if the river
bed or hill slope is stable, both sediments and intersti-
tial water are assumed to be stationary (Fig. 1a). When
sediments move in a debris flow, their motion under
these models is considered to be laminar, while that of
the interstitial water is turbulent (H
otta
et alii, 1998)
(Fig .1b), so these models comprise a “solid phase” of
sediments exhibiting laminar flow and a “fluid phase”
of interstitial water exhibiting turbulent flow.
Most of these models assume that all sediments
are the same size. However, real large-scale debris
flows have a broad grain size distribution; numerical
simulations based on these simplified models may be
ABSTRACT
Previous studies have shown that numerical simu-
lation models commonly used for debris flows may
not be applicable for large-scale debris flows. In this
study, we developed a technique for simulation of
large-scale stony debris flows. For this purpose, we
tested the hypothesis that the motion of fine sediment
in these debris flows is similar to that of the intersti-
tial water. We developed key parameters to simulate
large-scale debris flows, such as sediment concentra-
tion, fluid density, and representative particle diam-
eter based on the hypothesis. We also used a modified
version of the continuity equation for sediment in our
simulation. We conducted detailed field surveys of a
past debris flow in Japan and used topographic data
from LiDAR imagery, porosity measurements of soil
and weathered bedrock, and the grain size distribu-
tion of the debris flow sediments to test our model.
We also proposed a new process-based method for
determination of hydrographs at the lower end of the
landslide scar. Using these new data and methods, we
conducted numerical simulations of the past debris
flow, which reproduced well the observed erosional
and depositional pattern if when the concept of fine
sediment behaving like fluids was included in the nu-
merical simulation.
K
ey
words
: debris flow, deep rapid landside, numerical si-
mulation
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Y. NISHIGUCHI, T. UCHIDA, k. TAMURA, & Y. SATOFUkA
478
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
hypothesis that the motion of fine sediments in de-
bris flows is similar to that of interstitial water, and to
develop a valid technique for the simulation of large-
scale stony debris flows. To test our hypothesis, we
conducted detailed field surveys of debris flows by
using topographic measurements from LiDAR data,
measuring the porosity of soil and weathered bedrock
and measuring the grain size distributions of debris
flow sediments. Further, we proposed a new process-
based method for the determination of debris flow hy-
drographs at the lower end of the landslide scar. We
also considered the effects of the uncertainty of sev-
eral parameters on the simulated result.
THEORY
We assumed that the sediments in large-scale de-
bris flows comprise two types of sediments, a coarse
sediment and a fine sediment, and that the motion of
the fine sediment in a debris flow is similar to that of
the interstitial water. We therefore considered these
fine sediments as a fluid phase. Further, we defined
a maximum diameter D
c
for sediments that behave
like a fluid (Fig. 2; discussed later). On the basis of
this definition of D
c
we characterized the key param-
eters for our numerical simulation; these are sediment
concentration at the lower end of the landslide scar
(Cd, Eq. 1), fluid density of the debris flow averaged
in time and space (r, Eq. 2), and the representative
particle diameter of the debris flow (D, Eq. 3).
inappropriate for large-scale debris flows. a
sHida
&
e
GasHiRa
(1985) argued that the motion of fine sedi-
ments in a large-scale debris flow triggered by a large
landslide at Mt. Ontake in Nagano in 1984 could be
represented by a fluid phase, whereas the motion of
the coarse sediment was that of a solid phase. Thus,
for this large-scale debris flow, both the fine sediments
and the interstitial water exhibited turbulent flow, and
only the coarse sediment exhibited laminar flow (Fig.
1c). Further, n
akaGawa
et alii, (1998) and e
GasHiRa
et
alii, (1998) performed numerical simulations of past
large-scale debris flows with particular attention to the
motion of fine sediments. The results of their simula-
tions matched the observed deposited area and thick-
ness of the debris-flow deposits if it was assumed that
increases of fluid density were dependent on the pro-
portion of fine sediments considered as a fluid phase,
or when coarse and fine sediments were considered
independently to account for their different behaviour
and the different continuity equations between coarse
and fine sediments were presented.
Although these numerical simulations have pro-
vided powerful tools to describe the propagation and
deposition of debris flows, most parameters have been
determined by back-calculation or by calibration to
match field observations; in many cases, mean values
have been used. Consequently, the hypothesis that the
motion of fine sediments in debris flows is similar to
that of interstitial water has not been fully examined.
The objective of our study was to examine the
Fig. 1 - Conceptual diagram of static condition, small-
scale debris flow and large-scale debris flow
Fig. 2 - Definition of Dc
(1)
(2)
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PREDICTION OF RUN-OUT PROCESS FOR A DEBRIS FLOW TRIGGERED BY A DEEP RAPID LANDSLIDE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
479
weathered andesite and weathered tuff breccia.
A field survey immediately after the debris flow
identified two distinct types of debris flow deposits,
muddy deposits and stony deposits (Fig. 4). Local peo-
ple who were interviewed said that the muddy debris
flow occurred first and was followed by the stony de-
bris flow 10–20 min later. The distance from the lower
end of the landslide scar to the lower end of the debris
flow deposits was about 1,600 m.
According to aerial photographs, LiDAR data and
field survey data, the total volume of collapsed sedi-
ment was around 42,700 m
3
, including void volume
(hereafter, sediment volume includes void volume),
and the volume of collapsed sediment that remained
in the landslide scar was 12,220 m
3
. Therefore, the vol-
ume of sediment in the debris flow was about 30,500
m
3
. Moreover, the volume of sediment eroded from
the river bed within the run-out area was estimated to
be 59,100 m
3
. Therefore, the total volume of sediment
which reached deposited area was about 89,600 m
3
.
The total volume of the debris flow deposits was esti-
mated to be 76,500 m
3
, which suggests that 13,100 m
3
of sediment flowed further down the Hogawachi River.
Although the relative volumes of muddy debris flow
and stony debris flow were not measured, aerial pho-
tographs and field observations indicate that more than
half of the sediment volume was stony debris flow.
FIELD INVESTIGATION
TOPOGRAPHY
Before the debris flow, the run-out area was cov-
ered with vegetation, so the width of debris flow in the
run-out area was estimated by calculating the differ-
where P(D
c
) is the ratio of sediment smaller than D
c
to all sediment (Fig. 2), ρ
w
is water density, ρ
s
is the
solid density of sediment, d (D
c
) is the weighted aver-
age particle diameter greater than D
c
, w is the water
content of landslide soil and bedrock, w and is water
content of the debris flow averaged in time and space.
We also modified the continuity equation
based on our definition of Dc so that
where t is time, i is erosion and deposition rates, u and
v are velocities in the x and y direction, respectively, h
is flow depth of debris flow, and C
*
is volumetric sedi-
ment concentration in the river bed.
MATERIALS AND METHODS
STUDY SITE
The site of this study is Atsumari River in Ku-
mamoto Prefecture, Japan (Fig. 3). Heavy rain on
20 July 2003 induced a deep rapid landslide and the
resultant mass of collapsed sediments caused a large-
scale debris flow that hit the village along Atsumari
River, killing at least 15 people. The study area is un-
derlain by andesite and weathered tuff breccia. The
slip surface of the landslide was the interface between
Fig. 3 Location of our study site
(3)
(4)
(5)
Fig. 4 - Aerial photograph after the debris flow
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Y. NISHIGUCHI, T. UCHIDA, k. TAMURA, & Y. SATOFUkA
480
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
rock from ground surface to landslide slip surface
(i.e., the interface between weathered andesite and
weathered tuff breccia) was around 0.34.
PARTICLE SIZE DISTRIBUTION OF THE DE-
BRIS FLOw
We evaluated the particle size distribution of sedi-
ments between 7.5 cm and 30 cm from the cross- sec-
tional photograph of the deposits. We also identified
the proportions of sediments smaller than 7.5 cm and
larger than 30 cm by using the photograph. We com-
bined the sieve test result of sediments smaller than
7.5 cm and the observed result of particle size distri-
bution of sediments larger than 30 cm with the particle
size distribution of sediment between 7.5 cm and 30
cm at the rate of their respective proportions (Fig. 8).
NUMERICAL SIMULATION
MODEL
We used the “Kanako2D” debris flow simulator,
which can simulate 1D debris flows in gullies and 2D
debris flows in alluvial fans (n
akatani
et alii, 2008).
This simulator can be applied to transport of sedi-
ments ranging from bed load to stony debris flow. The
equations from Eq.6 to Eq.11 are governing equations
in the Kanako2D simulation. Eq.6 is continuation
ence between a digital surface model (DSM) and a
digital elevation model (DEM), both generated from
LiDAR data (Fig. 5). In the depositional area, it was
evaluated from aerial photography.
The elevations of the land surface along a lon-
gitudinal profile through the debris flow before and
after the debris flow were obtained from aerial pho-
tography and LiDAR data, respectively. The magni-
tude of the elevation change was calculated as the
difference of these (Fig. 6).
POROSITY OF SOIL AND BEDROCk
Porosity of soil and weathered bedrock of the
hill slope were determined from two boreholes near
the landslide scar. We measured bulk density and
soil water content using a gamma-radiation density
gauge and a nuclear radiation moisture gauge, re-
spectively (Fig. 7). Mean porosity of soil and bed-
Fig. 5 - Method for calculation of flow width from DEM
and DSM
Fig. 6 - Longitudinal profile and width of debris flow
Fig. 7 - Depth profiles of porosity from two boreholes near
the landslide scar
Fig. 8 - Particle size distribution of debris flow
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PREDICTION OF RUN-OUT PROCESS FOR A DEBRIS FLOW TRIGGERED BY A DEEP RAPID LANDSLIDE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
481
where C
is equilibrium sediment concentration in the
debris flow, δ
e
and δ
d
are coefficients of erosion and
deposition rates and q is discharge of debris flow per
unit width.
DATA PREPARATION
The simulation covered the area from the lower
end of the landslide scar to the lower end of the debris
flow deposits. How we determined the main simula-
tion parameters is provided in Table 1.
The longitudinal profile of the river bed and the
width of the debris flow were determined from field
survey data (Fig. 6). Our field survey data also showed
that the maximum erosion depth was 5 m, indicating
that the initial depth of the movable bed layer (D
s
) was
at least 5 m. Bedrock was exposed over much of the
eroded area, but movable sediment remained in some
areas after the debris flow, suggesting that the mean
initial depth of the movable bed layer might have been
more than 5 m. Consequently, we used two values (5
equation for the total volume of debris flow.
where i is erosion/deposition rate. Then, the continu-
ation equation for determining the debris flow is as
follow.
Eq.8 is the set of momentum equations for the
phenomenon of x-axis direction flow and y-axis direc-
tion flow.
where g is gravitational acceleration, θ
wx
and θ
wy
are
flow surface gradients in the x- and y-axis directions,
τ
x
and τ
y
are river bed shearing stresses in the x- and
y-axis directions. Then τ
x
is described as Eq. 9 (n
aka
-
Gawa
et alii, 2001).
where n
m
is Manning's coefficient. The river bed
shearing stress in y-axis direction is determined when
u is replaced by v in Eq.9. Equation for determining
change in bed surface elevation is as follow
Then, i is described as Eq.11. (n
akaGawa
et alii, 2001).
(6)
(7)
(8)
(9)
(10)
Tab. 1 - Determination of main simulation parameters
(11)
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Y. NISHIGUCHI, T. UCHIDA, k. TAMURA, & Y. SATOFUkA
482
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
and 10 m) for initial depth of the movable bed layer.
Sediment concentration at the lower end of the
landslide scar, fluid density and the representative par-
ticle diameter of the debris flow were determined from
Eqs. 1, 2, and 3, respectively. We assumed that the soil
and weathered bedrock of the landslide material were
water saturated. Our field investigations at boreholes
1 and 2 showed that porosity of landslide soil and bed-
rock was 0.34, so we used 0.34 for the water content
of soil and weathered bedrock. We determined C
d
at
the upper end of the simulation area (i.e., at the lower
end of the landslide scar) from Eq. 1 with w = 0.34.
For our first-order approximation, we assumed
that D
c
and ρ were constant in both space and time.
Therefore, the input value of ρ in the numerical simu-
lation represents the fluid density of the debris flow
in the run-out area. According to our field observa-
tions, the upper part of the river was eroded by the
debris flow, so we assumed that the debris flow was
composed of both collapsed sediments and river bed
sediments. Therefore, we decided to use an average of
the water content of the soil and weathered bedrock
that yielded the landslide and that of the river bed ma-
terials for w in Eq. 2. Although we did not measure the
water content of river bed material, previous studies
reported it to be around 0.4, so we used the average of
0.34 and 0.4 (i.e., 0.37) for w in Eq. 2.
We used the observed particle size distribution
(Fig. 8) to calculate sediment concentration, fluid
density, and the representative diameter of debris flow
particles. To ascertain the effect of different values for
the maximum diameter of sediment that behaves like
a fluid (Dc), we considered five cases (D
c
= 0, 10, 20,
30, and 100 mm). Grain size distribution of the debris
flow at Atsumari river showed that a large proportion
of fine material were included. Although these fine
materials might have colloidal properties, in this pa-
per, we did not consider these effects.
To construct a hydrograph at the lower end of the
landslide scar, we needed to determine the ratio by
volume of stony flow to total flow (k). We used aerial
photography and field data to determine that k was be-
tween 0.5 and 1.0. Therefore, we used values of 0.5,
0.7, and 0.9 for k in our simulations.
The hydrograph at the lower end of landslide scar
(i.e., the upper end of the simulation area) was esti-
mated as follows. Movement of a landslide mass can
be expressed as
where L is longitudinal length of the landslide scar
(120 m), v
m
is mean velocity at the lower end of the
landslide scar, and t
s
is the duration of the landslide at
the lower end of the landslide scar.
Mean flow depth at the lower end of the landslide
scar (h
m
) can be described as
where V
s
is total volume of stony debris flow at the
lower end of the landslide scar, and B
m
is flow width at
the lower end of the landslide scar.
Additionally, we assumed that the relationship be-
tween velocity and depth of debris flow at the lower
end of the landslide scar could be described by the
resistance law developed by t
akaHasHi
(2004):
where I
m
is slope angle at the lower end of the land-
slide scar, a
i
and α are constants (0.042 and 17.8°,
respectively) (t
akaHasHi
, 2004), and C
d*
is the maxi-
mum possible sediment concentration (0.65). Here,
ρ is fluid density at the lower end of landslide scar,
which can be described as
So, the duration of the hydrograph was
Fig. 9 shows hydrographs for D
c
equal to 0, 10,
20, 30, and 100 mm. At the precipitation station near
Atsumari River, maximum 10-minute rainfall of 26
mm has been recorded before the debris flows. The
water discharge attributed to the rainfall was esti-
mated at 30 m
3
/s at the upper end of the simulation
area, assuming a ratio of rainfall to runoff of 1.0. Dis-
charge of this volume is negligible in comparison to
the discharges presented by the hydrographs of Fig. 9.
Consequently, we didn’t include water discharge at-
tributed to rainfall in the upper drainage area with the
hydrographs of Fig. 9.
(12)
(13)
(14)
(15)
(16)
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PREDICTION OF RUN-OUT PROCESS FOR A DEBRIS FLOW TRIGGERED BY A DEEP RAPID LANDSLIDE
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
483
of the simulation.
Then, the calculated erosion depth was much
larger for D
s
of 10 m than for D
s
of 5 m and calculated
erosion depth well agreed with the observed depth
when D
s
was 5 m. However, travel and erosion dis-
tances were not affected by D
s
, although they were
influenced by D
c
. This indicates the simulated travel
and erosion distances for D
c
of 20 mm agreed well
with the observed result regardless of the value of D
s
in the range of 5-10 m. Therefore, the calibrations of
k and D
s
contributed little to the simulation matching
the observed travel and erosion distances.
Values of δ
e
and δ
d
in Eq. 11 were set as 0.0007
and 0.05 respectively, based on previous studies (n
a
-
katani
et alii, 2008; n
akatani
, 2010).
RESULTS
When all sediment particles in the debris flow
were considered to behave as solids (D
c
= 0), the sim-
ulated travel distance from the lower end of the land-
slide scar to the lower end of the debris flow deposits
was about 600 m, which is about 40% of the observed
travel distance. For this case, there was no erosion by
the debris flow and deposition started immediately
downstream of the landslide scar. As D
c
increased,
simulated travel distance of the debris flow increased
(Fig. 10). When D
c
was larger than 10 mm, the up-
per part of the stream was eroded. The distance from
the lower end of the landslide scar to the lower end
of the eroded area (hereafter referred to as “erosion
distance”) also increased with increasing D
c
. For D
c
of
20 mm, the simulated travel and erosion distances and
depths of erosion and deposition agreed well with our
observations (Fig. 10).
Figure 11 shows the results of simulations for
which the ratio of the volume of stony debris flow to
total volume (k) and initial depth of the movable bed
layer (D
s
) were changed, while D
c
was fixed at 20 mm.
When k is 0.7, the calculated volume and thickness
of the deposit well agreed with the observed volume
and thickness of the deposit. However, for k in the
range from 0.5 to 0.9, the differences of the simulated
travel and erosion distances were unremarkable (Fig.
11) which indicates that total volume of sediment at
the upper end of the simulation did not influence the
erosion and deposition distances of the debris flow, al-
though the erosion and deposition distance were influ-
enced by D
c
. Thus, even though there was uncertainty
regarding the total volume of sediment at the upper
end of the simulation, this uncertainty had little im-
pact on the results of erosion and deposition distances
Fig. 9 - Hydrographs for different values of Dc
Fig. 10 - Observed and calculated results for different val-
ues of Dc
Fig. 11 - Observed and simulated results for different val-
ues of k and Ds
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484
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
cally reasonable assumption.
CONCLUDING REMARKS
Our aim was to develop a technique to simulate
large-scale stony debris flows and to examine the hy-
pothesis that the fine sediments in such debris flows
behave as fluids. Focusing on the maximum diam-
eter of sediment particles that behave as fluids (D
c
),
we characterized the key parameters for numerical
simulation of the debris flow; these are sediment con-
centration, fluid density, and representative particle
diameter. We also used a modified version of the gen-
eral continuity equation for sediments. We conducted
detailed field surveys and used topographic data from
LiDAR imagery, porosity measurements of soil and
weathered bedrock, and the grain size distribution of
the debris flow sediments to test our model. Further,
we proposed a new process-based method for deter-
mination of hydrographs of a debris flow at the lower
end of the landslide scar. We also considered the effect
of the uncertainty of several parameters on the simula-
tion results. We then simulated the debris flow at the
Atsumari River on 20 July 2003. The conclusions of
this study can be summarized as follows:
- The simulated erosion and deposition distances of
the the debris flow agreed well with observed data
when the concept of D
c
was included in the simula-
tion. For simulations excluding this concept, there
was little agreement with the observed erosion and
deposition distances. Therefore, the hypothesis
that fine sediments in large-scale debris flows be-
have like fluids was confirmed for the July 2003
debris flow at the Atsumari River.
- The
D
c
of 20 mm that we used in our numerical sim-
ulation was verified as a reasonable estimate of the
particle size below which particles behaved like
fluids for the 2003 debris flow at Atsumari River
by comparison of the settling velocity of the D
c
fraction with the friction velocity of the debris flow
and the turbulent velocity of the interstitial water.
DISCUSSION
To verify the D
c
value of 20 mm, we compared the
friction velocity of the debris flow, turbulent velocity
of interstitial water, and the settling velocity of sedi-
ment of 20 mm diameter.
According to R
ubey
(1933), settling velocity (ω
0
)
can be expressed as
where v is kinematic viscosity (0.01 cm
2
/s). When D
c
is 20 mm, ω
0
is 37 cm/s (Table 2).
The friction velocity (U*) can be calculated from
river bed shear stress as
Here, we treated h
f
and I
f
as simulated mean flow
depth and mean slope angle, respectively, in the run-out
area. As a consequence, U* was 164 cm/s (Tab. 2).
The turbulent velocity (v
f
) can be calculated from
turbulent stress (H
otta
et alii, 1998).
where ρ
f
is turbulent shear stress, and ρ
f
can be ex-
pressed as
where u
f
and h
f
are simulated mean flow velocity and
simulated mean flow depth of debris flow, respec-
tively, when D
c
is 20 mm. z is bed elevation (here,
regarded as 0) and α can be expressed as
where k
f
is an empirical coefficient of 0.16 and C
df
is
the simulated mean sediment concentration of the de-
bris flow when D
c
is 20 mm. Then, ν
f
was determined
to be 80 cm/s (Tab. 2).
Consequently, the friction and turbulent velocities
were larger than the settling velocity for particles 20
mm in diameter, which verifies that a particle size of
20 mm can be suspended and in turbulent motion in a
debris flow. This means that D
c
= 20 mm was a physi-
(17)
(18)
(19)
(20)
Tab. 2 - Determination of settling, friction, and turbulent
velocities
(21)
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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
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