Progress on numerical model development of 1D debris flow using Langrangian Galerkin Method - repository civitas UGM
ISBN: 978-602-95687-8-3
The 4th-International Workshop on
MULTIMODAL SEDIMENT DISASTER
"Disaster Mitigation through
Partnership-Based Knowledge Sharing"
September 8-9,2013
Civil and Environmental Erlgineering Department, Faculty of Engineering,
Universitas Gadjah Mada, Indonesia
Editors
Djoko legono
Teuku Faisal Fathani
Rachmad Jayadi
Jazaullkhsan
Puji Harsanto
Muhammad Sulaiman
Civil al'ld fl'lvirol'lmental
Rese.,ch Cel'lter for Fluvial ill'ld Coastal Disaster,
El'llIll'leeril'l8 Departmel'lt,
DI$ilster Prevel'ltlol'l Research Institute,
F.culty of Enail'leerin&,
Kyoto Ul'liversity
Ul'llversit.s Gadjah Mada
.
•
UniVt!rsity ofTsukuba
~ J
MSD
NetWork
Proudly co-organize
The 4th International Workshop on Multimodal Sediment Disaster {4th-IWMSDJ
Disaster Mitigation Through Partnership-Based Knowledge Shoring
Published by
Department of Civil and Environmental Engineering
Faculty of Engineering, Universitas Gadjah Mada
Jalan Grafika No.2, Yogyakarta 55281, INDONESIA
Tel: +62·274-545675
Fax: +62·274·545676
Website: http://msd2013.cee-ugm .com/
E-mail: msd2013@cee-ugm.com
ISBN : 978-602-95687.8·3
The teKts of the papers in thiS volume were set individually by the authors or under their supervision.
Only minor correaions to the text may have been carried out by the publisher. By submitting the
paper in the The 4t1'1lnternational Workshop on Multimodal Sedtment Disaster (4th-IWMSD)-Disaster
Mitigation Through Partnership-Based Knowledge Sharing. the authors agree that they are fully
responsible to obtain all the written permission to reproduce figures, tables and text from
copyrighted material. The authors are also fully responsible to give sufficient credit included in the
figures, legends or tables. The organizer of the workshop, reviewers of the papers, editors ilnd the
publisher of the proceedings are not respons ible for any copyright Infringements ilnd the damage
they may cause.
LIST OF PAPERS
PREFACE
LIST OF PAPERS
1.
Predicting the Bed Material Load of Non-uniform Sediment using Selected Transport
Formulas ............................................................................................................................. .
Wan Hanna Melini WAN MOHTAR, JUNAIDI and Muhammad MUKHLISIN
2.
Morphological Changes of Riverbed Induced by Channel's Cross Section and
Discharge Variation ............................................................................................................. 7
Endro P. W AHONO, Djoko LEGONO, ISTIARTO, Bambang YULISTIY ANTO and Gcrrit J.
KLAASSEN
3.
A Practical Idea for Disaster Prevention in the Areas around Active Volcanoes such as
Mt. Merapi, Y ogyakarta, Indonesia - A Preliminary Research ......................................... 13
Masayuki WATANABE
4.
Hydrological Characteristic and Simulation of the Jakarta 2013 Flood, Indonesia
19
Ratih Indri HAPSARI, Satoru OISHI, Sri WAHYUNI, Dian SISINGGIH and Reni SULISTYOWATI
5.
Debris Force on Rectangular Column due to Tsunami ...................................................... 25
Maulina INDRIYANI, Radianta TRIATMADJA, KUSWANDI
6.
Simulation of Sediment Runoff Following Landslides ..................................................... 31
Masaharu FUJITA, Chen-Yu CHEN, Daizo TSUTSUMI and Kazuki YAMANOI
7.
Slope Management Survey using SMART Method at Precint 20 Putrajaya Malaysia ..... 37
Muhammad MUKHLISIN, Nur Syahira ZAINAL and Wan Hanna Melini Wan MOKHTAR
8.
The Investigation of Sediment Accumulation and Its Distribution over Sentani Lake,
Jayapura ............................................................................................................................. 45
YusufBUNGKANG and SOEMARNO
9.
Study on Surge Triggered by Debris flow Plunging into River ........................................ 51
Hideaki MIZUNO and Takaaki ANKAI
10. Prediction of Lahar Triggered by Snowmelt using Numerical Simulations Involving
Snowmelt and Drainage Processes ..................................................................................... 57
Shusuke MIY A T A, Daizo TSUTSUMI, Keiki MURASHIGE and Masaharu FUJITA
11. Lift up Force on Concrete Blocks due to Tsunami ............................................................ 65
Nurul AZIZAH, Radianta TRIATMADJA, KUSW ANDI
12. EFDC Three Dimensional Model Assumption for Sediment Deposition in Wonogiri
Reservoir ............................................................................................................................ 71
Dyah Ari WULANDARI, Djoko LEGONO and Suseno DARSONO
13. Community-based Approach on Flood Disaster Risk Reduction ....................................... 77
Agus SUHARY ANTO
14. Time-prediction Method of Upset of Landslides based on the Stress-dilatancy Relation
for Early Warning against Shallow Landslides .................................................................. 83
Katsuo SASAHARA
15. Community Based Disaster Risk Reduction: lember Debris Flow Experiences ............... 91
M. Farid MA'RUF and Evita S. HANI
16. Community Awareness and Attitudes to Urban Floods: Findings from Questionnaire
Survey of Flooding and Non-Flooding Areas in East lava, Indonesia .............................. 97
Dian SISINGGIH, Ichiko INAGAKI, Sri WAHYUNI and Ratih Indri HAPSARI
17. Influence of the Correction Factors in Simulating Debris Flows .................................... 103
Yih-Chin TAl and Chia-Chi SHEN
18. Bridges Condition in the Rivers of Boyong-Code, Kuning and Gendol in the Post 2010
Merapi Eruption.......... ............ ......... ........... ............................... ................................. ...... 109
Iman SATY ARNO, Andreas TRIWIYONO, Ali AKBAR, Mega A. WIDIASTUTI and Ulil M.
MUSAKKIR
19. Influence of Past Landslides and Resulting Sedimentation in a Sediment Disaster at
Hsiaolin Village, Taiwan, during Typhoon Morakot, 2009 ....... ............ .......................... 117
Norifumi HOTT A, Tomoharu KUBO, Fumitoshi IMAIZUMI, Kuniaki MIYAMOTO, Shin-Ping LEE,
Yuan-Jung TSAI and Chjeng-Lun SHIEH
20. Progress on Numerical Model Development of ID Debris Flow using Lagrangian
Galerkin Method ............................................................................................................... 125
Adam Pamudji RAHARDJO and Beni Zakaria AR RIDLO
21. Effect of Debris Flows Post the 2010 Eruption of Mount Merapi on Environment and
Socio-Economic Condition In Progo River and Its Tributaries ....................................... 133
Jazaul IKHSAN, Puji HARSANTO and Muhammad SULAlMAN
22. Experimental Study of Pore Water Pressure in Multi-layer Soil Structure ..................... 141
Fumitoshi IMAIZUMI, Kuniaki MIYAMOTO and Yuta MATSUMURA
23. Debris Flow and Flash Flood at Putih River after the 2010 Eruption of Mt. Merapi,
Indonesia ....... .................. ..... ................ .... ... ... ........... .................... .......... ......................... 147
Yutaka GONDA, Djoko LEGONO, Bambang SUKA TJA and Untung Budi SANTOSA
24. An Evaluation of River Bank Erosion in Volcanic Rivers Post Eruption 2010 of Mount
Merapi .............................................................................................................................. 153
Puji HARSANTO, Jazaul IKHSAN and Hiroshi TAKEBA Y ASH I
25. Tools of Prediction of Lahar Occurrence after Volcanic Eruption .................................. 161
Kouji MORITA, Nagazumi TAKEZA WA, Tadanori ISHIZUKA, Takao Y AMAKOSHI, Hiroshi KISA,
Toshiki Y ANAGIMACHI and Yukinori NOWA
The 4th International Workshop on Multimodal Sediment Disaster (4th_IWMSD)
Disaster Mitigation Through Partnership-Based Knowledge Sharing
Progress on Numerical Model Development of ID Debris
Flow using Lagrangian Galerkin Method
I
Adam Pamudji RAHARDJO ,and Beni Zakaria AR RIDLO
I
1 Civil and Environmental Engineering Dept., Universitas Gadjah Mada (J1. Grafika 2, Yogyakarta, 55281, Indonesia)
E-mail: adam@tsipil.ugm.ac.id;adam.pamudji.r@gmail.com
The Lagrangian Finite Element Galerkin Method is implemented for modeling ID debris flow model. This
approach is expected will provide better simulation result for the fast moving abrupt front modeling than
that of the most of Eulerian based numerical methods that face difficulties in handling phase elTor of higher
frequency components. Semi two-phase flow equations for debris flow model are adopted. There are two
conservation of mass equations that are for the mixture and for the solid phase. However, there is only one
equation for momentum conservation. The Galerkin formulation is applied for the matrix-vector form
equations. Issues on numerical stability and boundary treatment are discussed. The CUlTent progress shows
promising results for the expected improvement of the debris flow model performance.
Key words: debris flow model, Lagrangian, finite element Galerkin method
1. INTRODUCTION
2. DEBRIS FLOW MODEL
In order to supp0l1 development of warning systems
and hazard maps for debris flow, a numerical model
of debris flow is developed. The model would be lD
and 2D models or an integrated one. Since the
nature of debris flow is strongly convection,
especially the front of the debris flow, the Eulerian
approach that is popular in surface flow modeling
has some drawback and difficulties.
Eulerian approach is preferred in modeling
studies of flow in a fixed region such as flow around
structures within the channels or flow in a certain
river reach, or flow around a moving vessel with
constant speed. For the case of debris flow or flash
flood in river reaches, Eulerian approach has been
used, however, it has been facing difficulties
concerning with numerical stability in modeling
water surface discontinuity and drying wetting.
There is a challenge in using the Lagrangian
approach in solving the stability and wetting drying
problems and having better simulation results.
This paper presents the early stage progress of the
development of the ID debris flow model.
Numerical schemes have been developed and the
evaluation of the performance of the schemes will
be presented.
The debris flow model implemented is semi-two
phase model. The equation of mass conservation is
for the mixture of water and solid particles and the
conservation of solid particles in form of
concentration. It assumed that the debris flow is of
the turbulent muddy type. In Eulerian coordinate
system the debris flow equations of [Takahashi,
2007] are as follows.
The equation of conservation of the mixture
ah + a(uh) =i[C.+(l-C,)sh]+r
at ax
The equation of conservation
particles
of the
a(Ch) a(Cuh)
iC.
at
ax
(1)
solid
--+
(2)
The equation of conservation of flow momentum
and forces is only for the mixture. The fonn
equation form is combined from [Takahashi, 2007]
and [Shrestha et al., 2008] as follows,
2
auh
au
h.
ah [,
- + - - = ghsmB- ghcosB- --'
at ax
ax Pr
wi th h is depth of the mixture flow,
125
1I
(3)
is the depth
The 4th International Workshop on Multimodal Sediment Disaster (4 th -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
averaged velocity, t is time coordinate, x is space
coordinate, f) is bed slope angle, g is the
gravitational acceleration, i is erosion or deposition
rate, C is solid volume to volume concentration, C.
is the maximum solid concentration of the bed, Sb is
degree of saturation in the bed sediment. As for the
other symbols, P is density of water, Pr is the
mixture density and r is lateral water discharge. The
symbol Th accounts for the bed shear stress that
depends on the constitutive relation related to the
debris flow type as in Eq.(6), (8) and (10).
The are several source terms in the right hand
side of Eq.(3), namely the projection of gravitational
force (first term), the hydrostatic pressure gradient
(second term) and the friction force from bed (third
term). The friction forces from the deposition and
erosion processes, from the lateral inflow and also
drag force from the air is neglected.
The erosion and deposition rate follows these
conditions [Takahashi, et al., 1992] in [Shrestha, et
al.,2008].
For C < Ch , erosion takes place and
Ch-C
i=6
e
uh
C. -Cb d
(4)
Ch is the equilibrium concentration that its value
depends on the bed slope and internal friction angle
as follows.
F or stony type debris flow (C > 0.4 C. or tan f) >
0.138):
C _
b -
T
tanB
(a/ p - 1Xtan ¢ - tan B)
=p , tan-h+ P
hI
'f'
8
(5)
r
(al p) (dlll)2Ulul
[(C. /C)'(3 -1 h
(6)
where,
PI' = f(CXCJ- p)CghcosB
C-C3
f( C) =
•
C. - C3 '
0;
C::;C3
C is the limitative concentration which Ps
(static pressure) affects.
For immature debris flow (0.01 < C < 0.4c. or
0.03 < tan f)~
0.138):
tan B
Cb = 6 7[
. (CJ/ p - 1Xtan ¢ -
T=
b
tan e)
]2
(7)
1!L(d )2 ulul
ll1
0.49
h
(8)
For bed load transport flow (C
0.03 or hid? 30):
~
0.01 or tan
T'''][I-a;t'J
Ch = (I+Stane)(I_ag
(CJ/ p -1)
T.
T.
()~
(9)
(10)
For C> CI" deposition takes place and
•
l=UJ~-
where,
nM
s:'
Cb -C uh
C. d
( 11)
is Manning bed roughness coefficient,
Pill is apparent density of the institial fluid, (J'is the
specific density of the bed material, () is the bed
slope angle, ¢ is the internal friction angle of the bed
material, be is the erosion coefficient (=0.0007) and
6d is the deposition coefficient (=0.01).
[Nakatani, et aI., 2011] in developing the 1D-2D
debris flow, Kanako v 2.0 software implements the
above debris flow erosion and deposition model.
The Eulerian Finite Difference Method is used for
the discretization.
3. LAGRANGIAN APPROACH
The drawback of Eulerian approach in modeling
flow phenomena for certain cases especially
convection dominated problem with moving abrupt
change has been being concerned by many
researchers. In the Finite Element Methods there are
some efforts to encounter such drawback. In the
early period, there were proposed methods such as
the Petrov-Galerkin (up-wind method) [Brooks and
Hughes, 1982], the Taylor-Galerkin (second order in
time) [Donea, 1984] and the Characteristic-Galerkin
[Zienkiewics and Taylor, 1991] methods. Recently,
there are other methods proposed such as the multi
scale approach that use the bubble function enriched
elements to encounter the high order polynomial
present in the element containing abrupt change
[Nasehi and Parvazinia, 2011]. Those efforts have
delivered satisfied result for some cases such as
steady state problems and stand still abrupt change
("shock") problems. However, for moving abrupt
change cases and cases with strong source tenns,
instability or too diffused results are still
experienced.
There are other effort in increasing accuracy and
minimizing wiggles around the stand still "shock"
by adaptive mesh refinement strategy [Lohner,
1987] or by moving mesh strategy [Miller, 1981].
Lagrangian
approach
has
been
studied
126
th
The 4th International Workshop on Multimodal Sediment Disaster (4 -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
intensively for modeling flow of 20 vertical and 3D
problems [Shakibaeinia and Jin, 2009, Padova, et
al., 2013, Fu and Jin, 2013,]. The one for ID and
20 horizontal (depth averaged) surface flow model
is hardly to find.
In the Lagrangian approach, the equations
represent the condition of a certain particle that are
moving. The particle position coordinate is also a
dependent variable.
where: V is volume of the control volume, h is the
depth of the control volume and I is the length of the
control volume.
\
\ \,
'.
\.
'~
Figure 2. Forces acting on the moving control volume.
The rate of momentum change is equal to the
resultant of all forces acting on the moving control
volume (see Fig. 2). Therefore, the equation of
momentum conservation of the mixture is
Dl
1=10 +-dt
Dt
x
D(u V) = g V sin e _ g V cos ah _ IT b
Figure 1. Sketch of a moving control volume of 10 debris flow.
A moving control volume as shown in Fig. 1 has
initial position at Xo. After an elapse time of dt, the
position became X. Since by definition the velocity
of the moving control volume is the rate of position
coordinate change, therefore, there is a total
differential equation for the control volume position
coordinate rate of change as follows.
DX
--=U
Dt
(12)
where,
-D· = -a· + -a·
Dt
ax
at
is the total differential operator.
There are two things to be described related to
the mass balance of the moving control volume. The
first is that the mass balance of the moving control
volume depends on the erosion or deposition rate
and the lateral inflow or outflow. The second is that
the control volume defonns so that the depth and the
length are changing while the control volume is
moving. Therefore the mass balance equations are
DV = if[ C. +(l-C. )s/ J+r1
)
Dt
Dt
The governing equations can be packed into a vector
form equation as follows.
DU =aF +R
Dt ax
ax
uT=(X
FT
(15)
ax
( 18)
where,
(13)
Dl =1 all = a(lu)
Dt
(17)
4. NUMERICAL DISCRETIZATION
(14)
V=h·l
PT
The first tenn of the right hand side terms of
Eq.17 comes from F3 in Fig. 2. The second tenn
comes from FJ and F] together and the last tenn
comes from F 4 . The convection term in Eulerian
equation (Eq.3) is replaced by the equation of the
position coordinate rate of change (Eq.12).
At this development stage, the bed change
process has not been included, since the
concentration is still set to constant. The bed change
equation is based on the mass conservation principle
of the bed surface. Therefore, the deposition rate
became the source term and the erosion rate become
the sink term of the bed surface elevation dynamics.
D( CV) = ilC.
Dt
ax
(16)
127
V
=(0 0 0 lu
CV
~
I
h
2
ltV)
(19)
cose)
(20)
The 4th International Workshop on Multimodal Sediment Disaster (4 th -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
to the depth, for very small depth control volume,
the relative error of depth (from truncation error or
round-off error) my cause very large velocity values
and unrealistic coordinate position. Therefore, the
momentum equation (Eq. 17) is modified as follows
u
i/[C, + (1- C. )Sh]+ rl
ilC.
R=
(21 )
o
gVsm -Irh
-
Du.
oh Th u DV
-=gsmB-gcosB-----Dt
ox hPT V Dt
. f)
Pr
The time derivative term is discretized in form of
first order forward difference and the space
derivative term and the source term are discretized
using the Galerkin Method as follows.
The Galekin fommlation is as follows.
The time derivative term in the right hand side
terms of Eq. (25) can be replaced by right hand side
term ofEq. (13). The Eq. (19), (20) and (21) follow
the above modification and become,
U
=6f[f N aNi
)
f NNdD(6U)
.I
i
aD dDF" + f NNidDR;'
.I
I
n
n
j
I
FT
n
T
=(x
N j N;dn
J
K
~[!
Nj
~
(23)
(27)
(28)
o
U DV
asmf}----- -
.
dol
b
hPr
= (OUM)
er~max
(24)
For 10 case the above formulation is identical to
the Forward Time Central Space (FTCS) Finite
Difference Scheme.
ox
Cr~l1ax
V Of
.
The 4th-International Workshop on
MULTIMODAL SEDIMENT DISASTER
"Disaster Mitigation through
Partnership-Based Knowledge Sharing"
September 8-9,2013
Civil and Environmental Erlgineering Department, Faculty of Engineering,
Universitas Gadjah Mada, Indonesia
Editors
Djoko legono
Teuku Faisal Fathani
Rachmad Jayadi
Jazaullkhsan
Puji Harsanto
Muhammad Sulaiman
Civil al'ld fl'lvirol'lmental
Rese.,ch Cel'lter for Fluvial ill'ld Coastal Disaster,
El'llIll'leeril'l8 Departmel'lt,
DI$ilster Prevel'ltlol'l Research Institute,
F.culty of Enail'leerin&,
Kyoto Ul'liversity
Ul'llversit.s Gadjah Mada
.
•
UniVt!rsity ofTsukuba
~ J
MSD
NetWork
Proudly co-organize
The 4th International Workshop on Multimodal Sediment Disaster {4th-IWMSDJ
Disaster Mitigation Through Partnership-Based Knowledge Shoring
Published by
Department of Civil and Environmental Engineering
Faculty of Engineering, Universitas Gadjah Mada
Jalan Grafika No.2, Yogyakarta 55281, INDONESIA
Tel: +62·274-545675
Fax: +62·274·545676
Website: http://msd2013.cee-ugm .com/
E-mail: msd2013@cee-ugm.com
ISBN : 978-602-95687.8·3
The teKts of the papers in thiS volume were set individually by the authors or under their supervision.
Only minor correaions to the text may have been carried out by the publisher. By submitting the
paper in the The 4t1'1lnternational Workshop on Multimodal Sedtment Disaster (4th-IWMSD)-Disaster
Mitigation Through Partnership-Based Knowledge Sharing. the authors agree that they are fully
responsible to obtain all the written permission to reproduce figures, tables and text from
copyrighted material. The authors are also fully responsible to give sufficient credit included in the
figures, legends or tables. The organizer of the workshop, reviewers of the papers, editors ilnd the
publisher of the proceedings are not respons ible for any copyright Infringements ilnd the damage
they may cause.
LIST OF PAPERS
PREFACE
LIST OF PAPERS
1.
Predicting the Bed Material Load of Non-uniform Sediment using Selected Transport
Formulas ............................................................................................................................. .
Wan Hanna Melini WAN MOHTAR, JUNAIDI and Muhammad MUKHLISIN
2.
Morphological Changes of Riverbed Induced by Channel's Cross Section and
Discharge Variation ............................................................................................................. 7
Endro P. W AHONO, Djoko LEGONO, ISTIARTO, Bambang YULISTIY ANTO and Gcrrit J.
KLAASSEN
3.
A Practical Idea for Disaster Prevention in the Areas around Active Volcanoes such as
Mt. Merapi, Y ogyakarta, Indonesia - A Preliminary Research ......................................... 13
Masayuki WATANABE
4.
Hydrological Characteristic and Simulation of the Jakarta 2013 Flood, Indonesia
19
Ratih Indri HAPSARI, Satoru OISHI, Sri WAHYUNI, Dian SISINGGIH and Reni SULISTYOWATI
5.
Debris Force on Rectangular Column due to Tsunami ...................................................... 25
Maulina INDRIYANI, Radianta TRIATMADJA, KUSWANDI
6.
Simulation of Sediment Runoff Following Landslides ..................................................... 31
Masaharu FUJITA, Chen-Yu CHEN, Daizo TSUTSUMI and Kazuki YAMANOI
7.
Slope Management Survey using SMART Method at Precint 20 Putrajaya Malaysia ..... 37
Muhammad MUKHLISIN, Nur Syahira ZAINAL and Wan Hanna Melini Wan MOKHTAR
8.
The Investigation of Sediment Accumulation and Its Distribution over Sentani Lake,
Jayapura ............................................................................................................................. 45
YusufBUNGKANG and SOEMARNO
9.
Study on Surge Triggered by Debris flow Plunging into River ........................................ 51
Hideaki MIZUNO and Takaaki ANKAI
10. Prediction of Lahar Triggered by Snowmelt using Numerical Simulations Involving
Snowmelt and Drainage Processes ..................................................................................... 57
Shusuke MIY A T A, Daizo TSUTSUMI, Keiki MURASHIGE and Masaharu FUJITA
11. Lift up Force on Concrete Blocks due to Tsunami ............................................................ 65
Nurul AZIZAH, Radianta TRIATMADJA, KUSW ANDI
12. EFDC Three Dimensional Model Assumption for Sediment Deposition in Wonogiri
Reservoir ............................................................................................................................ 71
Dyah Ari WULANDARI, Djoko LEGONO and Suseno DARSONO
13. Community-based Approach on Flood Disaster Risk Reduction ....................................... 77
Agus SUHARY ANTO
14. Time-prediction Method of Upset of Landslides based on the Stress-dilatancy Relation
for Early Warning against Shallow Landslides .................................................................. 83
Katsuo SASAHARA
15. Community Based Disaster Risk Reduction: lember Debris Flow Experiences ............... 91
M. Farid MA'RUF and Evita S. HANI
16. Community Awareness and Attitudes to Urban Floods: Findings from Questionnaire
Survey of Flooding and Non-Flooding Areas in East lava, Indonesia .............................. 97
Dian SISINGGIH, Ichiko INAGAKI, Sri WAHYUNI and Ratih Indri HAPSARI
17. Influence of the Correction Factors in Simulating Debris Flows .................................... 103
Yih-Chin TAl and Chia-Chi SHEN
18. Bridges Condition in the Rivers of Boyong-Code, Kuning and Gendol in the Post 2010
Merapi Eruption.......... ............ ......... ........... ............................... ................................. ...... 109
Iman SATY ARNO, Andreas TRIWIYONO, Ali AKBAR, Mega A. WIDIASTUTI and Ulil M.
MUSAKKIR
19. Influence of Past Landslides and Resulting Sedimentation in a Sediment Disaster at
Hsiaolin Village, Taiwan, during Typhoon Morakot, 2009 ....... ............ .......................... 117
Norifumi HOTT A, Tomoharu KUBO, Fumitoshi IMAIZUMI, Kuniaki MIYAMOTO, Shin-Ping LEE,
Yuan-Jung TSAI and Chjeng-Lun SHIEH
20. Progress on Numerical Model Development of ID Debris Flow using Lagrangian
Galerkin Method ............................................................................................................... 125
Adam Pamudji RAHARDJO and Beni Zakaria AR RIDLO
21. Effect of Debris Flows Post the 2010 Eruption of Mount Merapi on Environment and
Socio-Economic Condition In Progo River and Its Tributaries ....................................... 133
Jazaul IKHSAN, Puji HARSANTO and Muhammad SULAlMAN
22. Experimental Study of Pore Water Pressure in Multi-layer Soil Structure ..................... 141
Fumitoshi IMAIZUMI, Kuniaki MIYAMOTO and Yuta MATSUMURA
23. Debris Flow and Flash Flood at Putih River after the 2010 Eruption of Mt. Merapi,
Indonesia ....... .................. ..... ................ .... ... ... ........... .................... .......... ......................... 147
Yutaka GONDA, Djoko LEGONO, Bambang SUKA TJA and Untung Budi SANTOSA
24. An Evaluation of River Bank Erosion in Volcanic Rivers Post Eruption 2010 of Mount
Merapi .............................................................................................................................. 153
Puji HARSANTO, Jazaul IKHSAN and Hiroshi TAKEBA Y ASH I
25. Tools of Prediction of Lahar Occurrence after Volcanic Eruption .................................. 161
Kouji MORITA, Nagazumi TAKEZA WA, Tadanori ISHIZUKA, Takao Y AMAKOSHI, Hiroshi KISA,
Toshiki Y ANAGIMACHI and Yukinori NOWA
The 4th International Workshop on Multimodal Sediment Disaster (4th_IWMSD)
Disaster Mitigation Through Partnership-Based Knowledge Sharing
Progress on Numerical Model Development of ID Debris
Flow using Lagrangian Galerkin Method
I
Adam Pamudji RAHARDJO ,and Beni Zakaria AR RIDLO
I
1 Civil and Environmental Engineering Dept., Universitas Gadjah Mada (J1. Grafika 2, Yogyakarta, 55281, Indonesia)
E-mail: adam@tsipil.ugm.ac.id;adam.pamudji.r@gmail.com
The Lagrangian Finite Element Galerkin Method is implemented for modeling ID debris flow model. This
approach is expected will provide better simulation result for the fast moving abrupt front modeling than
that of the most of Eulerian based numerical methods that face difficulties in handling phase elTor of higher
frequency components. Semi two-phase flow equations for debris flow model are adopted. There are two
conservation of mass equations that are for the mixture and for the solid phase. However, there is only one
equation for momentum conservation. The Galerkin formulation is applied for the matrix-vector form
equations. Issues on numerical stability and boundary treatment are discussed. The CUlTent progress shows
promising results for the expected improvement of the debris flow model performance.
Key words: debris flow model, Lagrangian, finite element Galerkin method
1. INTRODUCTION
2. DEBRIS FLOW MODEL
In order to supp0l1 development of warning systems
and hazard maps for debris flow, a numerical model
of debris flow is developed. The model would be lD
and 2D models or an integrated one. Since the
nature of debris flow is strongly convection,
especially the front of the debris flow, the Eulerian
approach that is popular in surface flow modeling
has some drawback and difficulties.
Eulerian approach is preferred in modeling
studies of flow in a fixed region such as flow around
structures within the channels or flow in a certain
river reach, or flow around a moving vessel with
constant speed. For the case of debris flow or flash
flood in river reaches, Eulerian approach has been
used, however, it has been facing difficulties
concerning with numerical stability in modeling
water surface discontinuity and drying wetting.
There is a challenge in using the Lagrangian
approach in solving the stability and wetting drying
problems and having better simulation results.
This paper presents the early stage progress of the
development of the ID debris flow model.
Numerical schemes have been developed and the
evaluation of the performance of the schemes will
be presented.
The debris flow model implemented is semi-two
phase model. The equation of mass conservation is
for the mixture of water and solid particles and the
conservation of solid particles in form of
concentration. It assumed that the debris flow is of
the turbulent muddy type. In Eulerian coordinate
system the debris flow equations of [Takahashi,
2007] are as follows.
The equation of conservation of the mixture
ah + a(uh) =i[C.+(l-C,)sh]+r
at ax
The equation of conservation
particles
of the
a(Ch) a(Cuh)
iC.
at
ax
(1)
solid
--+
(2)
The equation of conservation of flow momentum
and forces is only for the mixture. The fonn
equation form is combined from [Takahashi, 2007]
and [Shrestha et al., 2008] as follows,
2
auh
au
h.
ah [,
- + - - = ghsmB- ghcosB- --'
at ax
ax Pr
wi th h is depth of the mixture flow,
125
1I
(3)
is the depth
The 4th International Workshop on Multimodal Sediment Disaster (4 th -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
averaged velocity, t is time coordinate, x is space
coordinate, f) is bed slope angle, g is the
gravitational acceleration, i is erosion or deposition
rate, C is solid volume to volume concentration, C.
is the maximum solid concentration of the bed, Sb is
degree of saturation in the bed sediment. As for the
other symbols, P is density of water, Pr is the
mixture density and r is lateral water discharge. The
symbol Th accounts for the bed shear stress that
depends on the constitutive relation related to the
debris flow type as in Eq.(6), (8) and (10).
The are several source terms in the right hand
side of Eq.(3), namely the projection of gravitational
force (first term), the hydrostatic pressure gradient
(second term) and the friction force from bed (third
term). The friction forces from the deposition and
erosion processes, from the lateral inflow and also
drag force from the air is neglected.
The erosion and deposition rate follows these
conditions [Takahashi, et al., 1992] in [Shrestha, et
al.,2008].
For C < Ch , erosion takes place and
Ch-C
i=6
e
uh
C. -Cb d
(4)
Ch is the equilibrium concentration that its value
depends on the bed slope and internal friction angle
as follows.
F or stony type debris flow (C > 0.4 C. or tan f) >
0.138):
C _
b -
T
tanB
(a/ p - 1Xtan ¢ - tan B)
=p , tan-h+ P
hI
'f'
8
(5)
r
(al p) (dlll)2Ulul
[(C. /C)'(3 -1 h
(6)
where,
PI' = f(CXCJ- p)CghcosB
C-C3
f( C) =
•
C. - C3 '
0;
C::;C3
C is the limitative concentration which Ps
(static pressure) affects.
For immature debris flow (0.01 < C < 0.4c. or
0.03 < tan f)~
0.138):
tan B
Cb = 6 7[
. (CJ/ p - 1Xtan ¢ -
T=
b
tan e)
]2
(7)
1!L(d )2 ulul
ll1
0.49
h
(8)
For bed load transport flow (C
0.03 or hid? 30):
~
0.01 or tan
T'''][I-a;t'J
Ch = (I+Stane)(I_ag
(CJ/ p -1)
T.
T.
()~
(9)
(10)
For C> CI" deposition takes place and
•
l=UJ~-
where,
nM
s:'
Cb -C uh
C. d
( 11)
is Manning bed roughness coefficient,
Pill is apparent density of the institial fluid, (J'is the
specific density of the bed material, () is the bed
slope angle, ¢ is the internal friction angle of the bed
material, be is the erosion coefficient (=0.0007) and
6d is the deposition coefficient (=0.01).
[Nakatani, et aI., 2011] in developing the 1D-2D
debris flow, Kanako v 2.0 software implements the
above debris flow erosion and deposition model.
The Eulerian Finite Difference Method is used for
the discretization.
3. LAGRANGIAN APPROACH
The drawback of Eulerian approach in modeling
flow phenomena for certain cases especially
convection dominated problem with moving abrupt
change has been being concerned by many
researchers. In the Finite Element Methods there are
some efforts to encounter such drawback. In the
early period, there were proposed methods such as
the Petrov-Galerkin (up-wind method) [Brooks and
Hughes, 1982], the Taylor-Galerkin (second order in
time) [Donea, 1984] and the Characteristic-Galerkin
[Zienkiewics and Taylor, 1991] methods. Recently,
there are other methods proposed such as the multi
scale approach that use the bubble function enriched
elements to encounter the high order polynomial
present in the element containing abrupt change
[Nasehi and Parvazinia, 2011]. Those efforts have
delivered satisfied result for some cases such as
steady state problems and stand still abrupt change
("shock") problems. However, for moving abrupt
change cases and cases with strong source tenns,
instability or too diffused results are still
experienced.
There are other effort in increasing accuracy and
minimizing wiggles around the stand still "shock"
by adaptive mesh refinement strategy [Lohner,
1987] or by moving mesh strategy [Miller, 1981].
Lagrangian
approach
has
been
studied
126
th
The 4th International Workshop on Multimodal Sediment Disaster (4 -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
intensively for modeling flow of 20 vertical and 3D
problems [Shakibaeinia and Jin, 2009, Padova, et
al., 2013, Fu and Jin, 2013,]. The one for ID and
20 horizontal (depth averaged) surface flow model
is hardly to find.
In the Lagrangian approach, the equations
represent the condition of a certain particle that are
moving. The particle position coordinate is also a
dependent variable.
where: V is volume of the control volume, h is the
depth of the control volume and I is the length of the
control volume.
\
\ \,
'.
\.
'~
Figure 2. Forces acting on the moving control volume.
The rate of momentum change is equal to the
resultant of all forces acting on the moving control
volume (see Fig. 2). Therefore, the equation of
momentum conservation of the mixture is
Dl
1=10 +-dt
Dt
x
D(u V) = g V sin e _ g V cos ah _ IT b
Figure 1. Sketch of a moving control volume of 10 debris flow.
A moving control volume as shown in Fig. 1 has
initial position at Xo. After an elapse time of dt, the
position became X. Since by definition the velocity
of the moving control volume is the rate of position
coordinate change, therefore, there is a total
differential equation for the control volume position
coordinate rate of change as follows.
DX
--=U
Dt
(12)
where,
-D· = -a· + -a·
Dt
ax
at
is the total differential operator.
There are two things to be described related to
the mass balance of the moving control volume. The
first is that the mass balance of the moving control
volume depends on the erosion or deposition rate
and the lateral inflow or outflow. The second is that
the control volume defonns so that the depth and the
length are changing while the control volume is
moving. Therefore the mass balance equations are
DV = if[ C. +(l-C. )s/ J+r1
)
Dt
Dt
The governing equations can be packed into a vector
form equation as follows.
DU =aF +R
Dt ax
ax
uT=(X
FT
(15)
ax
( 18)
where,
(13)
Dl =1 all = a(lu)
Dt
(17)
4. NUMERICAL DISCRETIZATION
(14)
V=h·l
PT
The first tenn of the right hand side terms of
Eq.17 comes from F3 in Fig. 2. The second tenn
comes from FJ and F] together and the last tenn
comes from F 4 . The convection term in Eulerian
equation (Eq.3) is replaced by the equation of the
position coordinate rate of change (Eq.12).
At this development stage, the bed change
process has not been included, since the
concentration is still set to constant. The bed change
equation is based on the mass conservation principle
of the bed surface. Therefore, the deposition rate
became the source term and the erosion rate become
the sink term of the bed surface elevation dynamics.
D( CV) = ilC.
Dt
ax
(16)
127
V
=(0 0 0 lu
CV
~
I
h
2
ltV)
(19)
cose)
(20)
The 4th International Workshop on Multimodal Sediment Disaster (4 th -IWMSD)
Disaster Mitigation Through Partnership-Based Know/edge Sharing
to the depth, for very small depth control volume,
the relative error of depth (from truncation error or
round-off error) my cause very large velocity values
and unrealistic coordinate position. Therefore, the
momentum equation (Eq. 17) is modified as follows
u
i/[C, + (1- C. )Sh]+ rl
ilC.
R=
(21 )
o
gVsm -Irh
-
Du.
oh Th u DV
-=gsmB-gcosB-----Dt
ox hPT V Dt
. f)
Pr
The time derivative term is discretized in form of
first order forward difference and the space
derivative term and the source term are discretized
using the Galerkin Method as follows.
The Galekin fommlation is as follows.
The time derivative term in the right hand side
terms of Eq. (25) can be replaced by right hand side
term ofEq. (13). The Eq. (19), (20) and (21) follow
the above modification and become,
U
=6f[f N aNi
)
f NNdD(6U)
.I
i
aD dDF" + f NNidDR;'
.I
I
n
n
j
I
FT
n
T
=(x
N j N;dn
J
K
~[!
Nj
~
(23)
(27)
(28)
o
U DV
asmf}----- -
.
dol
b
hPr
= (OUM)
er~max
(24)
For 10 case the above formulation is identical to
the Forward Time Central Space (FTCS) Finite
Difference Scheme.
ox
Cr~l1ax
V Of
.