Document Actions

IJEGE-11_BS-Yoshino-et-alii

background image
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
533
DOI: 10.4408/IJEGE.2011-03.B-059
APPLICATION OF A TWO LAYER MODEL WITH THE AID OF A SLOPE
COLLAPSE MODEL TO THE NATURAL LANDSLIDE DAM OUTBURST
PROCESS
K. YOSHINO
(*)
, J. TAKAHAMA
(**)
, T. MIZUYAMA
(***)
, K. OGAWA
(****)
& T. UCHIDA
(*)
(*)
Incorporated Administrative Agency, Public Works Research Institute, Japan
(**)
Graduate School of Life and Environmental Science, Kyoto Prefectural University, Japan
(***)
Graduate School of Agriculture, Kyoto University, Japan
(****)
Asia Air Survey Co., Ltd. Japan, Japan
INTRODUCTION
Outburst of a landslide dam that is formed after
an earthquake may cause catastrophic disasters on the
downstream area (e.g., C
osta
et alii., 1988; k
oRuP
,
2004). Estimation of the damage caused to the down-
stream area requires accurate prediction of the over-
topping erosion of the landslide dam and the down-
stream flood runoff.
By taking the outburst of the landslide dam and
downstream flow into consideration, one can predict
rapid changes in the sediment movement pattern, in-
cluding the transition from debris flow to sediment
sheet flow and bed load. Previously, a method based
on one-dimensional simulation was proposed for the
prediction and assessment of degree of erosion; this
model was used to estimate the peak discharge rate
and changes in the riverbed after the overtopping ero-
sion of the landslide dam (s
atofuka
et alii, 2007).
This method was successfully used for reproducing
the discharge rate and changes in a riverbed in the
event of a landslide dam outburst (e.g., m
oRi
et alii,
2010; s
atofuka
et alii, 2010). However, since this
method is based on one-dimensional analysis, it can-
not be used for obtaining data on the extended width
of the water channel during the overtopping erosion
of a landslide dam. Hence, a twodimensional simula-
tion model must be used for a detailed assessment of
the flow around a landslide dam and for predicting the
erosion process.
t
akaHasHi
et alii (1993) proposed a two-dimen-
ABSTRACT
Earthquakes and heavy rainfall result in the for-
mation of landslide dams following a massive collapse
or landslide. Landslide dams can result in catastrophic
outburst floods or debris flows when the dam breaches
with overtopping erosion. Therefore, it is important to
determine the discharge rate and area of flooding due
to overtopping erosion to mitigate disasters triggered
by landslide dams. This study applied a two-layer
model that incorporates a slope-collapse model to
the erosion process at landslide dams. The two-layer
model was proposed by Takahama and deals with the
process of deposition-erosion with fully dispersed de-
bris flow and sediment sheet flow. A two-layer model
is derived to unify these two kinds of flow. Moreover,
Takahama applied this model to a two-dimensional
numerical simulation of debris flow, and found that
the model can analyze phenomena in which the veloc-
ity direction of the upper-layer water flow differs from
that of the lower layer sediment-water mixture flow.
Furthermore, we introduced the slope-collapse model
proposed by Sekine to express gradual collapse of the
slope due to erosion in the riverbed. The model shows
the process that maintains a constant angle at the side
bank. We examined the erosion and deposit process of
a landslide dam with a numerical simulation.
K
ey
words
: landslide dam, outburst flood, numerical simula-
tion, and slope-collapse
background image
k. YOSHINO, J. TAkAHAMA, T. MIZUYAMA, k. OGAwA & T. UCHIDA
534
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
model into the two-dimensional model proposed by
t
akaHama
et alii (2004) and performed a two-dimen-
sional similation to study the overtopping erosion of
landslide dams.
CALCULATION MODEL
EQUATION FOR TwO-LAYER MODEL
In this analysis, the two-dimensional two-layer
model proposed by t
akaHama
et alii (2004) is used.
The model has been designed by taking into account
the essential differences in the constitutive laws for
the sediment moving layer and the water flow layer in
the sediment sheet flow, as shown in Figure 1. Further,
a governing equation based on the volume conser-
vation law and momentum conservation law is used
in this model. The conservation law is proposed by
taking into account the water flow flux (s
I
) and mo-
mentum flux at the interface between two layers; these
two fluxes are dependent on the velocity vector at the
interface. When this model is extended to two dimen-
sions in the horizontal plane by using the X-Y coor-
dinate system, the dominant equations can be given
as follows.
Equation of continuity for the water flow layer:
Equation of continuity for the sediment moving
layer:
Equation of continuity for the sediment:
Equation for the riverbed level:
sional method for assessing a landslide dam; this
method involves the classification of sediment trans-
portation patterns and the application of the friction
law to each pattern. This model takes into account the
side bank erosion caused by the shear stress. With this
method, the shear stress is estimated to be one-half of
that in the direction of the riverbed, and the erosion
velocity is assumed to decrease uniformly across the
calculated area because of the relative elevation of the
collapsed part of the dam on the side bank. On the
other hand, t
akaHama
et alii (2003) assumed that the
behavior of the sediment moving layer and water flow
layer under unsteady conditions is reflective of the
constitutive law for each layer and proposed an analy-
sis method based on a two-layer model. In this model,
a governing equation is considered for each layer, on
the basis of the volume conservation law and momen-
tum conservation law; further, it is assumed that the
sediment sheet flow comprises a low-concentration
layer (water flow layer) and a high-concentration lay-
er (sediment moving layer) separated by a interface.
t
akaHama
et alii (2004) extended this model to a two-
dimensional simulation. In this method, classification
of the sediment transportation patterns is not neces-
sary and direct calculation of the unsteady flow in the
sediment moving layer and water flow layer can be
carried out. s
ekine
(2003) took into account the proc-
ess of slope collapse and proposed for predicting the
degree of erosion, resulting in the same gradient of
slope; this method could be used for the accurate pre-
diction of the collapse of the side bank.
In this study, we incorporated the slope-collapse
Fig. 1 - Pattern diagram for thet wo layer model
(1)
(2)
(3)
(4)
background image
APPLICATION OF A TWO LAYER MODEL WITH THE AID OF A SLOPE COLLAPSE MODEL TO THE NATURAL LANDSLIDE DAM
OUTBURST PROCESS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
535
respectively. In this study, we use the equation (t
AKA
-
hAmA
et alii., 2004) obtained by extending the erosion
velocity equation proposed by e
GasHiRa
et alii. (1988)
to the two-layer model. Further, we use τ
wx
and τ
wy
as the x- and ydirection elements of the shear stress
at the interface.τ
bx
and τ
by
are the x- and y-direction
elements of the shear stress at the riverbed surface,
respectively, both of which are obtained from the con-
stitutive law proposed by e
GasHiRa
et alii (1997) un-
der conditions of uniform concentration. γ , γ' , and β
are correction coefficients based on the flow velocity
and concentrationdistribution and are set to 1 for the
all analyses in this study.
Details of the shear stress at the riverbed and the
interface and the formula for erosion-deposition ve-
locity used in this study can be found in t
akaHama
et
alii (2003). Note that in this study, we introduce the
following approximation and assumptions (t
akaHama
et alii, 2003):
1 The concentration of the sediment layer is uni-
form ( c
s
/ c
*
2 ).
2 The pressure at the riverbed is pd , which is
attributed to the pressure exerted by the particles; the
value of this parameter is zero. Thus, at equilibrium,
the stress in the riverbed is the same for the approxi-
mation solution and exact solution. The ratio of p
d
to the skeleton pressure ( p
s
) in the flow layer is not
constant and is given as a function of concentration
(e
GasHiRa
et alii, 1997): p
s
/ (p
s
+ p
d
)
1/5
= (c
s
/ c
*
)
1/5
3 When the sediment moving layer thickness cal-
culated by (1) is greater than the total flow thickness,
the sediment moving layer is considered as total sedi-
ment moving layer, with c
s
≥ c
*
/2 .
4 When the yield stress in the flow layer exceeds
the external force when calculating the flow velocity
distribution and friction coefficient of the sediment
moving layer, the friction coefficient is calculated by
using the equilibrium gradient corresponding to the
average concentration in the total layer (c
t
). This fric-
tion coefficient is the same as the equivalent friction
coefficient obtained by m
iyamoto
et alii (2002), who
carried out a numerical calculation of debris flow un-
der the condition that the yield stress is greater than
the external force.
In this study, we investigate the stopping and
remigration of the sediment layer by using the method
proposed by m
iyamoto
(2003) and carry out a two-
dimensional simulation of the soil mass movement.
Equation of motion for the water flow layer (x-
direction):
Equation of motion for the water flow layer (y-
direction):
Equation of motion for the sediment moving layer
(x-direction):
Equation of motion of the sediment moving layer
(y-direction):
where the indexes s,w denote the physical value of the
sediment moving layer and the water flow layer, re-
spectively. M = uh ; N = vh ;where u , and v denote the
average layer flow velocity in the x- and y-directions,
respectively. h denotes the flow layer thickness; ρ ,
the average layer density; and P , the integrated pres-
sure. p
I
and p
b
are the pressures at the interface and in
the riverbed, respectively. c
s
and c
*
denote the average
sediment concentration of the sediment moving layer
and sediment concentration of the deposit layer. z
b
and
s
T
represent the riverbed height and erosion velocity,
(5)
(6)
(7)
(8)
background image
k. YOSHINO, J. TAkAHAMA, T. MIZUYAMA, k. OGAwA & T. UCHIDA
536
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
The steepest slope denoted by tan ψ is calculated
from the slope angle in the horizontal and vertical di-
rections (denoted by tan α and tan ω , respectively):
According to s
ekine
(2003), side-bank collapse
occurs in the direction of the steepest gradient when
the gradient exceeds tanφ, which is determined from
the repose angle. In this study, we obtain the average
gradient by estimating the bank slope of the water
channel generated by the overtopping erosion of an
actual landslide dam.
In this study, we assume that slope collapse pro-
ceeds until the position indicated by point O is de-
creased by a factor of ε. The collapsing surface is
shown by the shaded ∆TAN in Figure 2 (a); ε denotes
the extent of decrease in the vertical direction at point
O and is given by
Ground level at the point O deducts that for ε.
Next, the collapse induced by changes in the ground
form during one calculation time step is similar to the
collapse that goes to completion within a time step
of the same duration. Here, the amount of sediment
The stopping conditions used in this study correspond
to the scenario where the momentum value calculated
by excluding the yield stress lies in a circle whose
radius is a product of the yield stress and pitch time
and whose center is the point of origin (m
iyamoto
,
2003). Further, when the momentum calculated in the
time step adjacent to the stopping step exceeds the
maximum stiction, remigration occurs in this model
(t
akaHama
, 2004).
SLOPE COLLAPSE MODEL
In this study, s
T
represents the changes occurring
in the riverbed in the vertical direction; in the two-
dimensional simulation, such changes do not occur in
the region where there is no flow at the horizontal sur-
face. For example, if a water channel, as in a natural
landslide dam, causes riverbed decrease (flat head of
landslide dam erosion) to such an extent that the rela-
tive height difference becomes very large and there
is no flow into the nearby mesh, no further decrease
occurs in the mesh, and a very steep gutter is gener-
ated in the water channel. For a simple representation
of the side-bank collapse caused by erosion in the flat
head of the landslide dam, we use the slope-collapse
model proposed by s
ekine
(2003) and generate a
mesh flow channel.
s
ekine
(2003) determined the value and direction
of the steepest slope among the four slopes around the
point of origin (O), as shown in Figure 2. When the
steepest slope is directed from point O to point S, the
vector for the point of appearance of this slope is as
shown below.
Fig. 2 - Conceptual diagram for slope-collapse model (S
eKiNe
, 2003)
(9)
(10)
(11)
background image
APPLICATION OF A TWO LAYER MODEL WITH THE AID OF A SLOPE COLLAPSE MODEL TO THE NATURAL LANDSLIDE DAM
OUTBURST PROCESS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
537
The equation of continuity for the riverbed level is
The equation of continuity for the total layer is
The equation of continuity for the sediment is
The degree of side-bank collapse is estimated for
the mesh in the vicinity of the mesh in which the flow
occurs, as shown in Figure 3. In other words, if a mesh
in which no flow occurs is lowered in height owing to
the side-bank collapse and a new flow is generated in
the process of calculation, the adjacent mesh is taken
into account for investigating the side-bank collapse
.
CONDITIONS FOR NUMERICAL CAL-
CULATION
DETERMINATION OF ANGLE OF THE SIDE
BANk
The slope at the beginning of the side bank collapse
is determined by examining the cross-sectional profile
of the actual landslide dam formed during the Iwate-Mi-
yagi inland earthquake (y
osHino
et alii, 2010). Figure 4
shows the relation between the relative height of the wa-
ter channel of the landslide dam and the slope of the side
supplied by the collapse per unit time is calculated as
follows:
The sediment discharge rate is different in the x-
and y-axis directions as shown in formula (9), and the
discharge is toward the steepest gradient; the vector
corresponding to the discharge rate is as shown be-
low.:
To solve the equation of continuity for the sedi-
ment, Sekine (2003) took into account the sediment
discharge rate (shown in formula (13) determined from
the sediment discharge function. We use this concept
to calculate the equilibrium of sediment caused by the
side-bank collapse from the summation ( Q
collapse IN
) of
q
collapse
, which flows into the rectangular Mesh A from
four directions. As the sediment is lost from Mesh A
( Q
collapse OUT
) Q
collapse
, the equilibrium ( Q
collapse
) is
calculated as follows:
Next, we consider the amount of sediment on the
collapsed side bank in each mesh and re-solve the fol-
lowing equations of continuity. Note that the sediment
amount on the side bank is considered to be com-
pletely included in the nearby mesh in the collapse
direction.
(12)
(13)
(14)
(15)
Fig. 3 - Placement of the calculation mesh
(16)
(17)
(18)
(19)
Fig. 4 - Relation between the relative height of the water
channel and the angle of inclination of the side
shore
background image
k. YOSHINO, J. TAkAHAMA, T. MIZUYAMA, k. OGAwA & T. UCHIDA
538
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
bank. The examination results indicate that the slope
varies by around 20 degree even for the same relative
height and that the slope increases with relative height of
the water channel. Therefore, it is necessary to consider
this effect when calculating the slope of the side bank;
however, for a simple representation of the model in this
study, we perform calculations by setting the minimum
angle required for the occurrence of the side bank col-
lapse to φc = 36 degree, which is the average angle of
the water channel after overtopping erosion.
CALCULATION CONDITIONS
The calculation conditions we used are as shown
in Table 1. Calculations were performed for the fol-
lowing three cases. The diagrams at the top in Figures
5and 6 show the cross-sectional profile of each side
bank, and the diagrams at the bottom show the longi-
tudinal profile. In addition, 1 shows the longitudinal
profile of the side bank, and 2 shows the longitudinal
profile of the water channel in each Figure.
(1) Case 1: Calculations are performed for the
water channel with a gradient changing point at 3°
on the upstream and 14° on the downstream. 2-cm-
high, 20-cm-wide water channel is form at the gradual
slope. In this case, the side bank collapse is taken into
account.
(2) Case 2: Calculations are performed under con-
ditions similar to those considered in Case I, except
that the side bank collapse in the water channel is not
taken into account.
(3) Case 3: Calculations are performed for the
water channel with a gradient changing point at 14°
on the upstream and 3° on the downstream. 2-cm-
high, 20-cm-wide water channel is formed at the
steep slope. In this case, the side bank collapse is
taken into account.
Note that the in the above-mentioned three cas-
es, the flow depth does not reach 2 cm, which is the
height of the water channel, at the given supply dis-
charge rate; further, there is no flow over the water
channel. Therefore, flow-induced riverbed erosion
does not result in any increase in the width of the
water channel.
Fig. 5. Case 1,3 (top: cross-sectional view bottom: longitu-
dinal section view)
Fig. 6 - Case 2 (top: cross-sectional view; bottom: longi-
tudinal section view)
Tab. 1 - Calculation conditions
Tab. 2 - Cases for calculation
background image
APPLICATION OF A TWO LAYER MODEL WITH THE AID OF A SLOPE COLLAPSE MODEL TO THE NATURAL LANDSLIDE DAM
OUTBURST PROCESS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
539
of landslide dam). The width of the upper part of the
water channel is maximum at the gradient changing
point. The water channel first becomes narrow in the
downstream direction and then becomes wide as we
proceed further downstream. As shown in Figure 10,
this is because riverbed erosion proceeds in the down-
stream direction, where the flow spreads over a wider
region in the transverse direction. On the other hand,
because side bank collapse is not taken into account in
RESULTS OF NUMERICAL SIMULATION
Figures 7, 8, and 9 show the riverbed level for
each case after T = 10, 30, and 60 s. Figure 10 shows
the riverbed level and water surface level determined
by our calculation.
In Case 1, side bank collapse occurs as riverbed
erosion advances from the gradient changing point.
Then, the riverbed erosion proceeds gradually to the
upstream to cause decrease at the upper end (flat head
Fig. 7 - Variation of riverbed level with time (Case 1)
Fig. 8 - Variation of riverbed level with time (Case 2)
Fig. 9 - Variation of riverbed level with time (Case 3)
background image
k. YOSHINO, J. TAkAHAMA, T. MIZUYAMA, k. OGAwA & T. UCHIDA
540
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
CONSIDERATIONS AND FUTURE CHAL-
LENGES
In this study, we developed a two-dimensional
two-layer model by taking into account side bank col-
lapse and used the model to carry out calculations by
assuming overtopping erosion of a landslide dam. We
simulated a side bank collapse process in which ero-
sion advances in the vertical direction. We also found
that the water flow layer is separated according to
the sedimentation pattern, resulting in a low-concen-
tration flow on the ground form after sedimentation;
this eventually leads to recurrence of erosion. Thus,
we could simulate the conditions under which a wa-
ter channel is formed. It has been reported that once
landslide dam breach occurs, a highconcentration flow
during which eroded sediment erosion occurs is usual-
ly induced; because of this type of flow, sediments are
often strong unsteady phenomenon property (t
akaHa
-
ma
et alii, 2004). In addition, we considered the side
bank collapse for a rational evaluation of the increase
in the water channel width in the erosion area.
In this study, we also determined the collapsing
slope of the side bank on the basis of the slope of the
water channel formed by overtopping erosion in the
case of the landslide dam, which in turn was formed
during the 2008 Iwate-Miyagi Nairiku Earthquake.
We also provided a simple method for calculating the
average gradient. In reality, this angle may vary with
the relative height of the water channel, materials that
make up the landslide dam, apparent cohesion,etc. In
the future, it is necessary to study multiple cases of
landslide dam breach by carrying out measurements
with the help of a LiDAR data set; in this case, empha-
sis should be laid on various factors such as the relative
height of the water channel, angle of the side bank, and
materials that make up the landslide dam.
Case 2, it is natural that the width of the water channel
does not increase.
Moreover, as there is no sediment intake from
the side bank, the extent of riverbed decrease at a
given time is greater than in Case 1. In Case 3, as
riverbed erosion advances from the upper end (flat
head of the landslide dam), the side bank collapses.
Then, the erosion advances gradually to the down-
stream. In addition to this, erosion occurs again in
the sediment deposited area, and the water channel
is gradually formed.
Fig. 10 - The riverbed level and water surface level (top:
Case 1; middle: Case 2; bottom: Case 3)
REFERENCES
C
osta
J.e. & s
CHusteR
R.l. (1988) - The formation and failure of natural dams. Geological Society of America Bulletin, 100:
1054-1068.
e
GasHiRa
s., a
sHida
k. & s
asaki
H. (1988) - Mechanics of Debris Flow in Open Channel. Annual Journal of Hydroscience
and Hydraulic Engineering, 32, : 485-490. (in Japanese)
e
GasHiRa
s., m
iyamoto
k. & i
to
t. (1997) - Bed- load Rate in View of Two Phase Flow Dynamics. Annual Journal of Hydro-
science and Hydraulic Engineering, 41: 789-794. (in Japanese)
k
oRuP
o. (2004) - Geomorphometric characteristics of New Zealand landslide dams. Engineering Geology, 73: 13-35.
m
iyamoto
k. & i
to
t. (2002) - Numerical Simulation Method of Debris Flow Introducing the Erosion Rate Equation. Journal
of the Japan Society of Erosion Control Engineering, 55(2), :.24-35. (in Japanese)
m
iyamoto
k. (2003) - Two Dimensional Numerical Simulation of Landslide Mass Movement. Journal of the Japan Society of
background image
APPLICATION OF A TWO LAYER MODEL WITH THE AID OF A SLOPE COLLAPSE MODEL TO THE NATURAL LANDSLIDE DAM
OUTBURST PROCESS
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
541
Erosion Control Engineering, 55(2):5-13. (in Japanese)
m
oRi
t., s
akaGuCHi
t., s
awa
y., m
izuyama
t., s
atofuka
y., o
Gawa
k., u
suki
n. & y
osHino
k. (2010) - Method of estimation
for flood discharges caused by overflow erosion of landslide dams and its application in as a countermeasure. Proceedings
of the INTERPRAEVENT International Symposium in Pacific Rim, Taipei, Taiwan, 293-302.
o
sanai
n., u
CHida
t. & i
to
H. (2007) - Real time Extraction Method for Natural dam Formation Triggered by Earthquake,
Using the Lazar Profiler Surveying. Civil Engineering Journal, 49(9): 42-47. (in Japanese)
s
atofuka
y., y
osHino
k., o
Gawa
k. & m
izuyama
t. (2007) – Prediction of Flood Peak Discharge at Landslide dam outburst.
Journal of the Japan Society of Erosion Control Engineering, 59(6): 55-59. (in Japanese)
s
atofuka
y., m
izuyama
t., o
Gawa
k. & y
osHino
k. (2010) - Prediction of Floods Caused by Landslide Dam Collapse. Journal
of Disaster Research: 288-295.
s
ekine
m. (2003) – Numerical Simulation of Brainded River with The Aid of Slope- Collapse Model. Annual Journal of Hydro-
science and Hydraulic Engineering, 47: 637-624. (in Japanese)
t
akaHama
J., f
uJita
y. & k
ondo
y. (2000) - Analysis Method of Transitional Flow From debris Flow to Sediment Sheet Flow.
Annual Journal of Hydraulic Engineering, 44: 683-686. (in Japanese)
t
akaHama
J., f
uJita
y., H
aCHiya
k. & y
osHino
k. (2003) – Application of Two Layer Simulation Model for Unifying Debris
Flow and Sediment Sheet Flow ans Its Improvement. In: R
iCkenmann
& C
Hen
(
eds
), Debris- flow Hazards Mitigation:
Prediction, and Assessment:515- 526.
t
akaHama
, J., f
uJita
, y. & y
osHino
, k. (2004) - Two-Dimensional Numerical Simulation Model for Unifying Debris Flow and
Sediment Sheet Flow. Annual Journal of Hydroscience and Hydraulic Engineering, 48: 919-924. (in Japanese)
t
akaHasHi
, t. & n
akaGawa
, H. (1993) - Flood and Debris Flow Hydrograph Deu to Collapse of a Natural Dam by Overtop-
ping. Annual Journal of Hydroscience and Hydraulic Engineering, 37: 699-704. (in Japanese)
Statistics