International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 536-545, Article ID: IJCIET_10_04_055
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=04
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
Scopus Indexed
NUMERICAL ANALYSIS STUDY OF DEBRIS FLOW BY
USING HYDRO DEBRIS 2D MODEL (HD2DM)
Puji Harsanto, Jazaul Ikhsan and Nursetiawan
Department of Civil Engineering, Faculty of Engineering, Universitas Muhammadiyah
Yogyakarta, 55183 Yogyakarta, Indonesia
Mohd Remy Rozainy
School of Civil Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong
Tebal, Penang, Malaysia.
Center of Excellence Geopolymer & Green Technology, Universiti Malaysia Perlis 01000,
Perlis, Malaysia.
*Khairy Abdul Wahab
School of Civil Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong
Tebal, Penang, Malaysia.
*Corresponding author
ABSTRACT
This study presents a computational method smoothed particle hydrodynamics
(SPH) to model debris flows containing mixed grain consist of two types (10mm and
2.5mm) particles. The two-dimensional numerical simulations are validated by
comparing based on the experimental study of hydraulic physical model. This study was
performed using particle tracking equations which is lagrangian equation. Numerical
calculations were carried out at the waterways (flume inlet channel) which at two
places (erodible bed (upstream) and near the bottom of flume channel (downstream)).
The ratio of numerical model particle and actual particle mass is 1:1, but the physical
shape of the particles are not similar. The numerical simulation frequency distribution
results of the velocity shows fairly good agreement with the experimental results.
Keywords: debris flow, Hydro debris 2D model, Lagrangian
Cite this Article: Puji Harsanto, Jazaul Ikhsan, Nursetiawan, Mohd Remy Rozainy and
Khairy Abdul Wahab, Numerical Analysis Study of Debris Flow by Using Hydro
Debris 2d Model (Hd2dm). International Journal of Civil Engineering and Technology,
10(04), 2019, pp. 536-545
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1. INTRODUCTION
In the recent decade, several debris flow events occurred and caused hundreds of deaths,
missing or injury and damaged many facilities. In addition to causing significant morphological
changes along riverbeds and mountain slopes, these flows are frequently reported to bring
about extensive property damage and loss of life [1], [2], [3], [4]. To prevent and mitigate
disaster effectively, it is necessary to understand the initiation mechanism of debris flow. In
previous study, there seems scare to define the debris flow initiation from engineering
mechanism point of view. It is necessary to discuss further into causes, dominant factors and
mechanism of debris flow.
Many researchers have their ways to give the definition of the debris flow. Even though the
definitions may not the same from one researcher to others and it completely depend on the
various characteristics. Debris flows are flows of mixture of soil, rocks and water. These flows
are commonly initiated by landslides, bank failure or hills lope failures related to high rainfall
and/or large runoff [5]. Debris flows include many events such as debris slides, debris torrents,
debris floods, mudflows, mudslides, mudspates, hyperconcentrated flow and lahar [6].
Interaction of solid and fluid forces not only distinguishes debris flow physically but also gives
them unique destructive power. Because of their high velocities in the order of several meters
per second, they are the most dangerous type of mass movements and cause significant
economic loses as well as casualties [7]. Debris flow mainly dealt with laboratory simulations
[8], [9], modeling trigger and movement mechanisms [10], [11], deposits [12] and case studies
of extreme events that caused damage or casualties [13].
2. THE LAGRANGIAN MODEL
Models of sediment transport in turbulent flow are determined with another aspect. The model
of van Rijn can be classified as a deterministic model and Eulerian. There is another aspect of
the modeling of sediment transport, the model probabilistic and, sometimes, Lagrangian. The
fundamentals of this model were made by using the [8] parameters pick up rate and step length.
More sophisticated model was developed by [7] that explains about the mechanism step length
using a probabilistic function. This model was known as an Eulerian model. The model of
Nakagawa and Tsujimoto is very sensitive especially in term of changing the input and
favorable in explaining the phenomenon. The mechanisms of the sediment pulling up and
transport of saltation and rolling had been searched. Gotoh clarified the mechanism of transport
based on the model of Nakagawa and Tsujimoto. Lagrangian model was used in this study with
following reasons:
1. Allows the simulation of motion of each particle of the sediment.
2. Unifies the phenomenon of sediment transport.
The first reason was used because the existences of coarse sediment near the downstream
area. The Lagrangian model has its advantage when the diameter of the material is large. The
second reason was it easily explained about transition of the sediment transport phenomenon.
When a particle of sediment is pulled up and picked up by runoff, it will be transported by the
macro turbulence. The equation of motion of the particle in the flow, according to Newton's
second law can be written as:
M as  FD  FL  Fg
(1)
where
M : virtual mass of sediment particle
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a s : sediment particle acceleration
FD : drag force hydrodynamic
FL : ascending hydrodynamic forces
Fg : force of gravity
Assumed that the particle is a sphere, the quantities above are:
M  (

 C M ) A3 d 3

(2)

 C M ) g A3 d 3

(3)
F g  (
1
Du f
FD   C D A2 d 2 u x u x   (1  C M ) A3 d 3
2
Dt
where
(4)
u r  u p  u f : relative velocity of the particle
According to the work of [25], the hydrodynamic forces in turbulent flow and upward:
 du 
F L   L v1 / 2 d 2  
 dn 
 
(5)
where
n : Vector perpendicular to the vector u r
 L : Ancestry coefficient, varying according to the number
3. NUMERICAL SIMULATION OF HD2DM
3.1. Basic Equations of the Liquid Phase Portion
Basic equations of liquid phase in the particle tracking model in two-fluid model used in this
study is the continuous equation of motion of the liquid phase and two-dimensional latticeaveraged unsteady.
Continuity equation for water


fL 
f L u j  0
t
x j
(6)
(7)
Reynolds term
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Puji Harsanto, Jazaul Ikhsan, Nursetiawan, Mohd Remy Rozainy and Khairy Abdul Wahab
1   u  u j 
2
Rij  2KS ij , S ij   i 
, K  C S   2S ij S ij
2  x j xi 


1/ 2
(8)
  (x  y  z ) / 3
2
2
2
2
(9)
Leonards term

(10)
(11)
In which fL,fg,fs are volumetric ratio of liquid (water), gas (air) and solid (sediment)
phases, respectively, i,j,k=1,2,3, ui velocity component of water in direction, : water density,
p: water pressure, g : gravity force (when i=3) , Rij, Cij, Lij are Reynolds, Cross , Leonards
terms, respectively, determined by [6] Cs： [7] coefficient, : is water viscosity, grid spacing
for each direction V: Cell volume, Spi is negative production term for flow field by particle
movement, mpk specific mass of particle K, upik：i direction velocity component of particle
k. The lagrangian sediment transport equation, which treats both bed load and suspended load
as follows [8].
Negative production term of particle movements happen when there are changes of the
momentum transfer into the liquid during collision or particle movement process. Internal force
of liquid will become lesser therefore the inertial force of particle will be increase. Changes in
momentum in solid phases calculated by Lagrangian particle model will be transferred into
momentum changes in the liquid phase through negative production term determined in
Equation (11). Similarly the loss of the energy when collision occurs also transferred into liquid
phase through this negative production term. Fig. 1 and 2 show the effect of negative
production term during collision and particle movements respectively. The details expression
of Equation 6 can be seen from equations 12 to 15.
Figure. 1: Effect of negative production term during particles collision.
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Figure. 2: Effect of negative production term during particles movements.
12
13
14
15
where:
M  Amount of sediment movement
V  Cell volume
m pk  Mass of particle k
u pk  Velocity component of particle k
Particle equation
In the present study was performed using particle tracking equations which is lagrangian
equation. Basic equations are as follows:
(16)
(17)

In which CD: drag coefficient, u p : velocity vector of sediment particle (for each diameter),
: water phase velocity vector A2 = /4 , A3= /6 , d : diameter of the sediment CM: virtual mass
coefficient (=0.2, 0.35 and 0.5), s :density of sediment particle, water density. : shading
coefficient determined only when sediment is in the bed and shaded by other sediment, friction
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coefficient only works when sediment is at the bottom. This term was determined according to
[29] for the simulation of successive saltation movement as followed Gotoh method. The
lagrangian air bubble transport equation is introduced similarly as:
(18)
where is virtual mass, given as 0.5, is water density, is a air bubble diameter, : friction
coefficient of air bubble, as given as equation 13. The Adam-Bashforth method was used for
time integration.
 = c +  tan 
(19)
Where is the resolved normal stress, the internal angle of friction, and c the cohesion The
quasi-static form of generally takes values between 20° and 45°, while its dynamic counterpart
is about 3-4° smaller under rapid shear (but slow enough that rubbing- type friction between
the particles occurs). The Mohr-Coulomb criteria only describe the conditions for yield; a
corresponding (non-associated) flow rule for the ongoing motion beyond plastic yield must, if
needed, be separately formulated. Most descriptions restrict themselves to simple gravity
driven shear, see, e.g., [3], a full account is given by [1].
The air entrainment process was treated as follows: The entrainment from the water surface
was treated by distributing air bubble marker particles in the sub-cells of the surface cells with
no water marker cell. These distributed air bubble marker particles are transported according
to the surface air drag coefficient which is assumed to 1.0. The air entrainment by the air bubble
capitation is simulated by distributing the air bubble marker particles in the inner air cells. The
air bubble pairing and dividing cannot be simulated in this study.
4. BOUNDARY CONDITION
Numerical calculations were carried out at the waterways (flume inlet channel) which at two
places (erodible bed (upstream) and near the bottom of flume channel (downstream)). The
length of the channel is 5m. Mixed grain consist of two types (10mm and 2.5mm) are installed
at the upstream portion of the rectangular flume (1.5m from the water tank outlet).
The ratio of numerical model particle and actual particle mass is 1:1, but the physical shape
of the particles are not similar. For the numerical simulation purpose, the shape was assumed
round and smooth. The ratios of the particle dominated conditions (2.5mm and 10mm) are as
follows. These two conditions are examined as preliminary study to inspect the ability of
HD2DM.
a) The ratio of particles, 2.5mm: 10mm (9:1)
b) The ratio of particles, 2.5mm: 10mm (4:1)
In addition, bed slope is set at 25° slope angle in which gravitational acceleration allocation
is considered in each direction.
5. CALIBRATION OF HD2DM BASED ON EXPERIMENTAL DATA
(CM=0.5)
5.1. Erodible bed (upstream)
This section presents the comparison of the velocity between experimental and numerical
results. Three cases have been chosen for the comparison purposes. All these three cases
correspond to three different times which represented by initial (1s), intermediate (3s) and last
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(5s) case. Figure 3 shows the particle velocity distribution and means average values for both
experimental and numerical results. The experimental and numerical velocities shown a wider
range of value from the smallest of 0.048cm/ms to the highest 0.18cm/ms. The numerical mean
velocity result is slightly higher than the experimental mean value. The values of each case are
0.115cm/ms and 0.096cm/ms respectively. The numerical results predicted about 16.5% higher
in mean velocity than experimental result. Same trend of mean velocity can be observed in last
case (big particle) as well. As a result, we can declare that this is the lowest value in terms of
numerical model prediction compared to experimental value. Mean velocity for experimental
is recorded as 0.161cm/ms which is 0.012cm/ms slower compared to the numerical result. It
means that, the numerical result predicted about 6.9% higher in mean velocity than
experimental result. The different of mean velocity of numerical and experimental value is
lower compared to the initial case (big particle). The best prediction of numerical model
compared with experimental mean velocity result can be seen in intermediate case (small
particle). The mean average value is 5.7%. The highest velocities in experimental and
numerical are 0.19cm/ms and 0.21cm/ms while the lowest velocities are 0.09cm/ms and
0.10cm/ms respectively. Figure 3 shows the velocity distribution in intermediate case (small
particle) for experimental and numerical. The second best of numerical model prediction
compared with experimental mean velocity can be seen in last case (small particle). The mean
average value is 14.1%. Fig. 4 shows the particle routing segregation from 2.22s to 2.4s. Each
image was captured at every 0.02s.
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Figure. 3: Comparison of frequency distribution of particles velocity at different cases near the
erodible bed (upstream) with CM=0.5
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Numerical Analysis Study of Debris Flow by Using Hydro Debris 2d Model (Hd2dm)
Figure. 4: Numerical simulation result of the particle routing segregation for case CM=0.5
(2.5mm: 10mm=4:1) from 2.22s to 2.4s, captured at every 0.02s.
6. CONCLUSION
This paper presents a two-dimensional Lagrangian computer model to simulate debris flow.
The motion of the debris flow is simulated using the Hydro Debris 2D Model approach. The
simulation results was verified by comparing with existing experimental results for the mean
average velocity. The transportation processes of debris and air bubble were simulated in
Lagrangian form by introducing air bubble and debris markers. The numerical simulation
frequency distribution results of the velocity shows fairly good agreement with the
experimental results.
ACKNOWLEDGMENTS
This research was carried out with financial support from the Visiting Fellow Research Grant
UMY, Indonesia (Grant No. 164/SK-UMY/VIII/2018) and the Fundamental Research Grant
Scheme (FRGS) under Ministry of Higher Education of Malaysia (Grant No. 7611800357). A
very special thanks goes to the School of Civil Engineering, Universiti Sains Malaysia and
Department of Civil Engineering, Engineering Faculty, Universitas Muhammadiyah
Yogyakarta for the support on conducting this research. Also thanks to Mr. Mr. Taib Yacob,
Mr. Halmi Ghazalli, Mr. Dziauddin Zainol Abidin and Mr. Nabil Semailfor their assistance on
performing the experiments.
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