When the safety factor of natural or artificial slopes reaches critical value of 1.0, the increment of triggering factors, i.e. precipitation, rise of groundwater level, earthquake, and slope interference may prompt slope failure. Considering the impacts and damages possibly caused by rapid landslides, it is important to predict its runout distance, velocity, moving volume, and coverage area. A numerical model was developed to calculate the rapid landslide motion and applied to 26 cases of landslides and 6 cases of debris flows, with volume ranging from less than 100 m3 up to 3.5 9 109 m3. This quasi-three-dimensional model used the Navier–Stokes equation as the governing equation of motion and Coulomb’s resistance rule along the sliding surface to compute runout distance and coverage area corresponding with the real rheological conditions in the field. Due to the influence of dynamic conditions and excess pore water pressure, the internal friction of the sliding mass and the sliding surface are much smaller than the internal friction obtained by static soil tests. The moving volume affects the dynamic coefficient of friction and the velocity, whereas a small volume landslide occurs at a higher value of dynamic coefficient of friction and yields lower velocity. In addition, a landslide with a gentler slope occurs at a lower value of dynamic coefficient of friction, where in the case of the debris flow, it tends to have an even lower dynamic friction compared to landslide. This numerical model can be used to simulate the motion of rapid landslides with potentially long run-out in order to support hazard and risk assessment of landslides.

1. ORIGINAL PAPER
A Numerical Model for the Analysis of Rapid Landslide
Motion
Teuku Faisal Fathani . Djoko Legono . Dwikorita Karnawati
Received: 27 June 2016 / Accepted: 22 April 2017
Ó Springer International Publishing Switzerland 2017
Abstract When the safety factor of natural or artifi-
cial slopes reaches critical value of 1.0, the increment of
triggering factors, i.e. precipitation, rise of groundwater
level, earthquake, and slope interference may prompt
slope failure. Considering the impacts and damages
possibly caused by rapid landslides, it is important to
predict its runout distance, velocity, moving volume,
and coverage area. A numerical model was developed
to calculate the rapid landslide motion and applied to 26
cases of landslides and 6 cases of debris flows, with
volume ranging from less than 100 m3
up to
3.5 9 109
m3
. This quasi-three-dimensional model
used the Navier–Stokes equation as the governing
equationofmotionand Coulomb’sresistancerulealong
the sliding surface to compute runout distance and
coverage area corresponding with the real rheological
conditions in the field. Due to the influence of dynamic
conditions and excess pore water pressure, the internal
friction of the sliding mass and the sliding surface are
much smaller than the internal friction obtained by
static soiltests. Themovingvolume affectsthedynamic
coefficient of friction and the velocity, whereas a small
volume landslide occurs at a higher value of dynamic
coefficient of friction and yields lower velocity. In
addition, a landslide with a gentler slope occurs at a
lower value of dynamic coefficient of friction, where in
the case ofthe debrisflow,ittendstohave aneven lower
dynamic friction compared to landslide. This numerical
model can be used to simulate the motion of rapid
landslides with potentially long run-out in order to
support hazard and risk assessment of landslides.
Keywords Landslide movement Á Run-out distance Á
Simulation model Á Dynamic coefficient of friction Á
Landslide volume
1 Introduction
Landslide is a natural phenomenon of soil or rock mass
movement in a slope due to rainfall, earthquake, or
slope interference among other causes. Disaster mit-
igation is very important to anticipate possible infras-
tructure damage and casualties. One type of deadly
mass movement is a rapid landslide that takes place in
a very short period of time with potentially long run-
out distance and massive destructive power. Rapid
landslides in general, occur in medium to steep slopes
triggered by intense rainfalls on a previously saturated
soil. The mechanism of this movement should be
investigated thoroughly to be able to predict the
T. F. Fathani (&) Á D. Legono
Department of Civil and Environmental Engineering,
Faculty of Engineering, Universitas Gadjah Mada,
Yogyakarta 55281, Indonesia
e-mail: tfathani@ugm.ac.id
D. Karnawati
Department of Geological Engineering, Faculty of
Engineering, Universitas Gadjah Mada,
Yogyakarta 55281, Indonesia
123
Geotech Geol Eng
DOI 10.1007/s10706-017-0241-9

2. direction of movement, run-out distance, velocity,
moving volume, and coverage area (Rickenmann
1999; Crosta et al. 2003). The hazard and risk
assessments of landslides are very important to be
used as a consideration in determining a regional
development plan (Quan Luna et al. 2013).
The numerical models based on continuum
mechanics have been developed to simulate rapid
movement of landslides (debris flows, flowslides,
debris/rock avalanches, and mudflows) with various
assumptions and approaches. Several models assume
that the landslide mass behaves as a liquid mixture of
interacting fluids and solids, which are classified as the
depth-integrated models. The models were primarily
developed to simulate flowslides or debris flows; and
at the later stage were used in modeling all types of
fast-moving landslides. By considering the low depth
to length ratio and a very small vertical velocity, this
model uses a depth integration approximation. The
equations reduce from 3D to 2D, as all variables
depend only on x and y, while the z-dependence
components are discarded in the integration process.
The method allows the inclusion of information on the
basal pore pressure (Iverson and Denlinger 2001;
Pastor et al. 2009), levees deposition and entrainment
(Mangeney et al. 2007a, b; Johnson et al. 2012;
Iverson 2012) and the extension to two-phase models
(Pitman and Le 2005; Pelanti et al. 2008; Pudasaini
2012). These depth integrated models have been
widely used to simulate rock avalanches, mudflows,
laharic flows, debris flow, flow-like landslides, and
snow avalanches (McDougall and Hungr 2004; Hungr
2009; Sosio et al. 2012; Pastor et al. 2014; Wang et al.
2016).
In the past decades, the continuum models coupled
with non-linear partial differential equations solved by
discretization in both time and spatial grids have been
developed. Nakamura et al. (1989, 2002) proposed a
numerical model of rapid landslides using the Navier–
Stokes equations as the governing equation of motion.
As the shear resistance along the sliding surface, this
model uses Coulomb’s resistance rule, Newton’s
viscous resistance rule or Manning’s resistance rule.
It has been applied to rapid landslides and debris flow
cases, and it was found that the dynamic friction angle
is much smaller than those obtained from static soil
tests due to the influence of dynamic conditions and
excess pore water pressure (Fathani et al. 2001;
Fathani 2006). Hungr (2009) developed a numerical
modelling of flow-like landslides based on S–H
equations that allows the application of different
rheologies. Furthermore, Sassa et al. (2010) studied
the phenomenon of soil strength reduction due to
excess pore pressure in landslides to develop a
simulation model considering material softening and
loss of strength. This model is able to simulate
movement triggered by pore pressure generation and
seismic acceleration, and has been implemented to
analyze the mechanisms of rapid and long run-out
earthquake-induced landslides by using a ring-shear
apparatus (Dang et al. 2016). Miyamoto (2010)
proposed a two dimensional model with the friction
of the sliding surface based on the constitutive
equation of shear stress on hyper concentrated sedi-
ment–water mixture proposed by Egashira et al.
(1997). Recently, Pastor et al. (2014) proposed a
meshless method of Smoothed Particle Hydrodynam-
ics (SPH) depth-integrated model to simulate flow-
slide problems accounting for the pore water pressure
dissipation, which caused the landslide mass to come
to rest. This model includes the rheological models
describing basal friction of Bingham, frictional,
Voellmy and cohesive-frictional viscous models.
The numerical model described in this paper focuses
on rapid landslides in medium to steep slopes that are
faster than 0.5 mm/s (Cruden and Varnes 1996). This
research attempts to analyze the motion of rapid
landslide by using a quasi three-dimensional model
developed by Nakamura et al. (1989, 2002), assuming
that the sliding mass is an incompressible Newtonian
viscous fluid and using the Navier–Stokes equations as
the governing equation. In order to validate this
numerical model to estimate the run-out distance,
scale, and velocity of landslide, the analysis was done
by examining 26 cases of landslides and 6 cases of
debris flows. Further, the relationship among important
parameters, i.e. the dynamic coefficient of friction,
landslide volume, moving velocity, and the inclination
of source area were observed and examined.
2 Numerical Model of Landslides Movement
This numerical model adopts a quasi three-dimensional
method to simulate the plane flow by computing sliding
mass thickness distribution in iteration as a function of
time. Governing equations use the Navier–Stokes
equations with the assumption that the sliding mass is
Geotech Geol Eng
123

3. an incompressible Newtonian viscous fluid. This
numerical model was developed by Nakamura et al.
(1989, 2002) and refined by Fathani et al. (2001, 2006).
Seismic forces can also be included in the calculation.
The resistance rule along the sliding surface is
computed with one of the following methods: Cou-
lomb’s resistance rule approach, Newton’s viscous
resistance rule, or Manning’s resistance rule.
2.1 Fundamental Equations
The equation of motion of the non-compressive
viscous fluid using Navier–Stokes equations can be
expressed as follows (Nakamura et al. 1989, 2002):
q
Du
Dt
¼ À
op
ox
þ lr2
u þ Fx ð1Þ
q
Dv
Dt
¼ À
op
oy
þ lr2
v þ Fy ð2Þ
q
Dw
Dt
¼ À
op
oz
þ lr2
w þ Fz ð3Þ
where V~(u, v, w) = velocity vector; q = density; p =
pressure; l = coefficient of viscosity; r2
= Lapla-
cian; and F~ ¼ Fx; Fy; Fz
À Á
¼ volume force vector.
The equation of continuity of the non-compressive
fluid is as follows:
divðqv~Þ ¼ q
ou
ox
þ
ov
oy
þ
ow
oz
!
¼ 0 ð4Þ
Considering the low depth to length ratio and a very
small vertical velocity, then the velocity to vertical
direction (w) can be discarded. It is assumed that u and
v are uniform in a vertical direction and the inertial
force of fluid particle is considerably small, compared
to the acceleration due to gravity in the equation of
equilibrium in a vertical direction (Nakamura et al.
1989, 2002). Considering the acceleration from grav-
ity (gz) and horizontal acceleration by earthquake (gx
and gy), Eqs. 1–3 can be written as follows:
q
ou
ot
þ
ou
ox
þ
ou
oy
!
¼ À
op
ox
þ lr2
2u þ
orzx
oz
þ qgx ð5Þ
q
ov
ot
þ
ov
ox
þ
ov
oy
!
¼ À
op
oy
þ lr2
2v þ
orzy
oz
þ qgy ð6Þ
À
op
oz
À qgz ¼ 0 ð7Þ
The volume transport discharge (flux) is defined by
the following formula:
Q~ ¼ M~i þ N~j ð8Þ
where M ¼
Rh
u dz; N ¼
Rh
v dz; and i~; j~ are respec-
tively the unit vectors in the x and y directions.
By integrating Eqs. 5–6 in the z direction, and
substituting this into the equations for the two-
dimensional field, the following equations can be
obtained:
oM
ot
þ u
oM
ox
þ v
oM
oy
¼ Àgzh
oH
ox
þ gxh þ mr2
2M À
s0
zx
q
ð9Þ
oN
ot
þ u
oN
ox
þ v
oN
oy
¼ Àgzh
oH
oy
þ gyh þ mr2
2N À
s0
zy
q
ð10Þ
where H = height from the reference plane to the top
surface of sliding mass; h = height from the sliding
surface to the top surface of sliding mass; and szx,
szy = the components of shear-resisting force at the
sliding surface in the x and y directions.
Conditions for continuity for the non-compressive
flow considering recharge a(x, y, z, t) are given by the
following formula:
div V~ ¼ aðx; y; z; tÞ ð11Þ
If Eq. 11 is integrated in the z direction and the
recharge is considered to be given only at the ground
surface, then the following equation is obtained:
oh
ot
¼ ÀV:Q þ a; ða ¼ aðx; y; z ¼ h; tÞÞ ð12Þ
where, r ¼ i o
ox þ j o
oy þ k o
oz : gradient
Equations 9–11 become three formulas containing
five unknown quantities, h, M, N, s0
zx and s0
zy. In this
research, Coulomb’s criterion is used as the resistance
rule along the sliding surface, as suggested by
Nakamura et al. (1989, 2002) and Fathani et al.
(2001). The cohesion and internal friction angle of the
sliding surface are c and / respectively, and
hc ¼ c= q:gzð Þ, then Eqs. 9–10 and 12 can be
expressed as follows:
Geotech Geol Eng
123

4. oM
ot
þ
oðuMÞ
ox
þ
oðvMÞ
oy
¼ Àgzh
oH
ox
þ gxh þ mr2
2M
À gzðhc
þ h tan /Þ
u
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2 þ v2 þ w2
p
ð13Þ
oN
ot
þ
oðuNÞ
ox
þ
oðvNÞ
oy
¼ Àgzh
oH
oy
þ gyh þ mr2
2N
À gzðhc
þ h tan /Þ
v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2 þ v2 þ w2
p
ð14Þ
oh
ot
¼ À
oM
ox
þ
oN
oy
!
ð15Þ
2.2 Discretization Scheme
Nakamura et al. (1989, 2002) developed the dis-
cretization of the governing equations Eqs. 13–14 and
the equation of continuity Eq. 15, by using differential
calculus. For this purpose, (x, y) space was grid-
divided, then dependent variables M and N were
defined at the center of a grid’s side, and h was defined
at the center of the grids. Grid interval of x, y, t were
respectively determined as Dx, Dy and Dt. For the
differentiation, subscripts i, j showing the position on
(x, y) plane were attached to the right bottom of each
variable, and the subscript n showing time step was
attached to the right shoulder of the variable. In the
differentiation of Eqs. 13–14, the windward differ-
ence calculus was applied to the convection term for
stabilizing the calculations.
At first, by discretization of the equation of motion
Eq. 13 in x direction, Eq. 16 is obtained. Each term is
explained below.
Mnþ3
i;jþ1=2 À Mnþ1
i;jþ1=2
2Dt
þ MX þ MY
¼ MGZ þ MGX þ MNU þ MF ð16Þ
For convection items MX and MY of the equation,
when Mi,j?1/2
n?1
C 0,
MX ¼ u1
Mnþ1
i;jþ1=2 À Mnþ1
iÀ1;jþ1=2
Dx
ð17Þ
when Mi,j?1/2
n?1
0,
MX ¼ u2
Mnþ1
iþ1;jþ1=2 À Mnþ1
i;jþ1=2
Dx
ð18Þ
when v C 0,
MY ¼ v
Mnþ1
i;jþ1=2 À Mnþ1
i;jþ1=2
Dy
ð19Þ
when v 0,
MY ¼ v
Mnþ1
i;jþ3=2 À Mnþ1
i;jþ1=2
Dy
ð20Þ
where,
u1 ¼
Mnþ1
1;jþ1=2 þ Mnþ1
iÀ1;jþ1=2
2hnþ2
iÀ1=2;jþ1=2
;
u2 ¼
Mnþ1
1þ1;jþ1=2 þ Mnþ1
i;jþ1=2
2hnþ2
iþ1=2;jþ1=2
v ¼
1
4 Nnþ1
iÀ1=2;j þ Nnþ1
iÀ1=2;j þ Nnþ1
iþ1=2;jþ1 þ Nnþ1
iÀ1=2;jþ1
1
2 hnþ2
iþ1=2;jþ1=2 þ hnþ2
iÀ1=2;jþ1=2
For the pressure term:
MGZ ¼ Àgz
h sign
oH
ox
oH
ox
À tan /m
!
ð21Þ
where,
h ¼
hnþ2
iþ1=2;jþ1=2 þ hnþ2
iÀ1=2;jþ1=2
2
oH
ox
¼
Hnþ2
iþ1=2;jþ1=2 À Hnþ2
iÀ1=2;jþ1=2
Dx
Hnþ2
iþ1=2;jþ1=2 ¼ hnþ2
iþ1=2;jþ1=2 þ zBiþ1=2;jþ1=2
Hnþ2
iÀ1=2;jþ1=2 ¼ hnþ2
iÀ1=2;jþ1=2 þ zBiÀ1=2;jþ1=2
zBiþ1=2;jþ1=2 ¼
zBi;j þ zBiþ1;j þ zBiþ1;jþ1 þ zBi;jþ1
4
zBiÀ1=2;jþ1=2 ¼
zBiÀ1;j þ zBi;j þ zBi;jþ1 þ zBiÀ1;jþ1
4
sign xð Þ ¼ 1 when x ! 0 and À1 when x0:
x½ Šþ¼ x when x ! 0 and 0 when x0:
Geotech Geol Eng
123

5. For the horizontal seismic intensity term:
MGX ¼ gx
hnþ2
iþ1=2;jþ1=2 þ hnþ2
iÀ1=2;jþ1=2
2
ð22Þ
For the viscosity term:
MNU ¼
v
2
Mnþ1
iÀ1=2;jþ1=2 þ Mnþ1
iþ1;jþ1=2 À 2Mnþ1
i;jþ1=2
Dxð Þ2
þ
Mnþ1
i;jÀ1=2 þ Mnþ1
i;jþ3=2 À 2Mnþ1
i;jþ1=2
Dyð Þ2
#
ð23Þ
For the friction term:
MF ¼ Àgzðhc þ h tan /sÞ Â
Mnþ3
i;jþ1=2 þ Mnþ1
i;jþ1=2
2h
Â
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2 þ v2 þ w2
p
ð24Þ
where,
h ¼
1
2
ðhiÀ1=2;jþ1=2 þ hiþ1=2;jþ1=2Þ
u ¼
Mnþ1
i;jþ1=2
h
v ¼
1
4h
ðNiÀ1=2;j þ Nnþ2
iþ1=2;j þ Nnþ2
iþ1=2;jþ1 þ Nnþ2
iÀ1=2;jþ1Þ
w ¼ Àðu tan a þ v tan bÞ
tan a ¼
ðzBiÀ1;j þ zBiÀ1;jþ1Þ À ðzBiþ1;j þ zBiþ1;jþ1Þ
4Dx
;
tan b ¼
zBi;j À zBi;jþ1
Dy
In the same manner, the equation of motion Eq. 14
in y direction was made discrete and the Eq. 25 was
obtained.
Nnþ3
iþ1=2;j À Nnþ1
iþ1=2;j
2Dt
þ NX þ NY
¼ NGZ þ NGY þ NNU þ NF ð25Þ
For respective terms, the same notations as for the
direction of x, were adopted. Also, by discretization of
the equation of continuity Eq. 15, the Eq. 26 was
obtained.
hnþ2
iþ1=2;jþ1=2 þ hn
iþ1=2;jþ1=2
2Dt
þ
Mnþ1
iþ1;jþ1=2 À Mnþ1
i;jþ1=2
Dx
þ
Nnþ1
iþ1=2;jþ1 À Nnþ1
iþ1=2;j
Dy
¼ 0
ð26Þ
2.3 Boundary Conditions
The equation of motion was solved by the assumption
that no debris inflow from the surrounding area of
landslides will occur. At the boundary between the
deposition area of debris and natural ground, the flux is
zero in the normal direction of the boundary. Then,
whether the boundary grid is further provided around
the debris deposition area and these relational expres-
sions are applied, then the discretization equations can
be utilized for the calculation of the boundary.
The calculation continues even if the debris flows
out of the boundary grid. That is, runoff and inflow
volumes between the cells deposited with debris and
the cells not deposited are determined. In this case,
Nakamura et al. (1989, 2002) proposed the assumption
for the discharge equation between cells, as shown in
the following equation:
oQ
ot
¼ ÀCgzhsign
oH
ox
!
oH
ox
À tan/m
!
þ g0
h À
s
q
ð27Þ
where Q = the flux between cells and coincides with
M in the x direction and with N in the y direction;
C = the runoff coefficient between cells; and
g0
= horizontal acceleration in the x or y direction.
Introducing m as the sum of pressure term,
horizontal acceleration term and resistance term, and
their discretization equations by differential calculus
are respectively given by Eqs. 21, 22 and 24. By
substituting m in the right expression of Eq. 27 and
performing discretization, Eq. 28 is obtained.
Qnþ3
À Qnþ1
2Dt
¼ m ð28Þ
In addition, the flux was zero, so for the previous
time (n ? 1), Qn?3
= 2 mDt. Inflow to the empty
cells having no debris can be found as explained
above, and the thickness of deposited debris in empty
cell can be calculated from the following equation of
continuity:
Geotech Geol Eng
123

6. h ¼ 2Dt
M1 À M2
Dx
þ
N1 À N2
Dy
!
ð29Þ
where M1, M2, = inflow and runoff in x-direction and
N1 and N2 = inflow and runoff in y-direction
respectively.
3 Application of the Model to Landslides
and Debris Flows
A comprehensive field investigation is required to
define an accurate input dataset for this numerical
model. The input data required for the numerical
model are geometrical conditions of the landslide
slope, i.e. the ground surface and the sliding surface,
the bulk density of sliding mass (c), the dynamic
coefficient of viscosity (m), the cohesion (c), the angle
of internal friction of sliding mass (/m) and sliding
surface (/s), and input seismic waves (three compo-
nents of sine wave, horizontal, and vertical). The
physical properties of the sliding mass and sliding
surface can be changed depending on the location
within the analysis region. The output data are
dynamic and geometrical parameters which can be
obtained with numerical analysis of maps (GIS).
These landslide maps can be determined by rheology
issued from the interpretation of satellite imagery,
combined with LiDAR and geodetic measurements in
the site.
Roessner et al. (2005) developed a satellite remote
sensing and GIS-based system for quantitatively
oriented and spatially differentiated landslide hazard
assessment. Recently, Bossi et al. (2015) used LiDAR
digital terrain models (DTMs) to set up the initial
condition for the application of the dynamic model of
complex landslides. In this research, the topographic
maps coupled with the geodetic measurements in the
site were used to model the landslides. A sliding
surface is determined in order to plot the base
geometry and volume of source area of the landslides.
Physical properties of the sliding mass are determined
from field and laboratory tests. Overall data affect the
results of simulation, particularly the dynamic coef-
ficient of friction of sliding mass and sliding surface,
which will very significantly determine the run-out
distance.
Several case studies were calculated and examined
in order to validate this numerical model. In the
simulations of 26 landslides and 6 debris flows, the
iteration was properly conducted by combining the
physical properties of sliding surface and sliding mass
in attempting to find a rheology that produces the best
agreement in terms of run-out distance and debris
covered area. For the first trial of this back analysis, the
dynamic friction angle of sliding mass (/m) and
sliding surface (/s) refer to the site investigation and
approximate correlations between static friction angle
(/c) and dynamic friction angle proposed by Lang and
Nakamura (1998), as shown in the following equation:
tan /s þ tan /m ¼ 0:41 tan /c þ 0:10 ð30Þ
In order to show the performance and accuracy of
this numerical model, three landslides are selected,
namely the Mt. Galunggung landslide caused by a
volcanic eruption, the Sum Wan Road landslide
caused by rainfall, and the Tsaoling landslide caused
by an earthquake.
3.1 Landslide in Mount Galunggung
The Galunggung Amphitheatre is a horseshoe-shaped
volcanic valley, 2–5 km wide and 8 km long, which
opens to the east southeast (ESE). The collapse caldera
floor lies 1300 m below the highest point of the
amphitheatre rim (?2168). The height of the caldera
wall decreased from over 1000 m in the eruption
center to 10 m in the ESE. The gigantic landslide
debris of Mt. Galunggung traveled down-slope toward
the ESE covering the Tasikmalaya plain (?351 m)
over 4200 ± 150 years (Bronto 2001). More than
one-third of the SE part of the volcano slid onto the
Tasikmalaya plain to form a fan-shaped hummocky
topography (as shown in Fig. 1) and is known as the
Ten Thousand Hills of Tasikmalaya. The geological
profile of the Galunggung Volcano along the cross-
section A–A0
(WNW to ESE) is shown in Fig. 2. The
sizes and heights of the Galunggung hummocks vary
from one part of the deposit to another. The largest
concentration of hummocks is in the central zone of
the fan-shaped topography that is located 14–15 km
away from the crater (Fig. 1). The largest hummocks
are up to 50 m high, 500 m across, and conical in
shape. An isolated depression forming a lake, named
Situ Gede, is also present with a diameter of about
500 m. Assuming that Mt. Galunggung was a sym-
metrical cone with a small summit crater before the
landslide occurred, the volume of missing material
Geotech Geol Eng
123

7. from the amphitheatre is approximately 3.5 km3
. The
volume of this landslide is larger than that of the 1980
Mt. St. Helens’ debris avalanche that was only
2.8 km3
(Voight et al. 1983; Ward and Day 2006).
The Galunggung volcanic debris deposit forms
hummocks consisting of large, fractured blocks from
the volcano, tens to hundreds of meters in maximum
dimensions. Although this form is already tilted and
deformed into varying degrees, the primary stratigra-
phy is still recognizable. Moreover, extreme fragmen-
tation and mixing with sediments can be seen
incorporated along the path of travel. This mixture is
usually found in the marginal and distal parts of the
debris avalanche deposit (Bronto 2006). Some vol-
canic debris avalanches are also found inside the
Galunggung Amphitheatre where they form several
hills.
Based on the previous research by Lang and
Nakamura (1998) and Fathani et al. (2001) and
concerning the relation between static and dynamic
coefficient of friction of sliding mass and sliding
surface, this research analyzes landslide movement
where the friction angle of sliding surface (/s) is equal
to the friction angle of sliding mass (/m). When the
value of /s = /m = 3.8° was used as input, the
resulted debris run-out distance and debris covered
Fig. 1 Topographical map of Mt. Galunggung, where more than one-third of the SE part of the volcano slid to form a fan-shaped
hummocky topography
Fig. 2 Geological profile of Mt. Galunggung along cross-section A–A0
(modified from Bronto 2006)
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123

8. area (shown in Fig. 3) are nearly similar with the
actual conditions of these phenomena after the occur-
rence of the landslide (as shown in Fig. 1). The results
show that the maximum length of debris from the toe
of the source area is 9 or 16.5 km from the crater;
maximum width of debris is 13.5 km; and the debris-
covered area is 60 km2
. Figure 3 describes the change
in topography of the landslide in Mt. Galunggung that
stopped 350 s after the beginning of failure. The
maximum velocity of the sliding mass was estimated
at 70.6 m/s, which occurred at 4.75 km from the
source area of landslide.
3.2 Shum Wan Road Landslide
On August 13, 1995, a landslide took place at the
hillside above Shum Wan Road, Hong Kong. It caused
the collapse of a 30 m long section of Nam Long Shan
Road that included a passing bay supported by a fill
embankment. Knill (1996) reported that the landslide
debris crossed Shum Wan Road and damaged three
shipyards and a factory near the seafront. Prior to the
landslide, the hillside was densely vegetated and had
an overall gradient of about 27°. The geology at the
landslide area comprised a thin mantle of colluvium
overlying partially weathered fine-ash to coarse-ash
crystal tuff.
The landslide resulted in a 70 m high scar, with a
width varying from about 50 m just below Nam Long
Shan Road to about 90 m above Shum Wan Road.
Figure 4 shows the map of the landslide based on
topographic survey, geological mapping and field
observations, modified from Knill (1996). The upper
part of the landslide surface was concave in shape and
was up to about 12 m in depth below the pre-failure
ground surface, as shown in section A–A0
through the
landslide (Fig. 5). The landslide released about
2.6 9 104
m3
of soil and rock, and about
1.2 9 104
m3
of which remained on the landslide
surface. The remaining debris was deposited on Shum
Wan Road and the reclaimed land to the west,
spreading over an area of about 0.5 ha.
The failure was caused principally by the presence
of weak layers in the ground, ingress of water during
prolonged heavy rainfall, a minor failure of the fill
embankment below a passing bay on Nam Long Shan
Road, and discharge of flowing water along Nam Long
Shan Road on the hillside because of partial blockage
of its drainage system. Based on the actual condition
of debris deposition observed immediately after the
occurrence of the landslide (Fig. 4), it is found that the
calculation results (shown in Fig. 6) when /s and /m
equal to 12.1° give a good agreement with the actual
ground topography after the landslide occurrence.
Figure 7 shows the cross section of the motion of the
Shum Wan Road Landslide. The landslide debris
stopped moving after 300 s and the maximum velocity
of debris movement was 8.3 m/s.
3.3 Tsaoling Landslide
The Chi-chi Earthquake occurred on September 21,
1999 in the central part of Taiwan with the magnitude
of 7.6 R, where the peak ground acceleration greater
than 1 g was recorded. The earthquake induced a
variety of mass movements including large-scale
landslides. Across the Central Mountain Range of
Taiwan, at least 7000 landslides hit an area of several
thousand square kilometers. There were 16 individual
landslide area exceeding 10 ha, one of which is the
Tsaoling Landslide. This landslide is located in the
headwaters of the Qingshui-shi River which is a
tributary of the Zhuoshui-shi River. The total volume
of the source area is about 1.25 9 108
m3
and the
affected area is 698 ha with the distance between the
crown of landslide and the toe of the debris deposition
at about 4 km. The length of the sliding area is 1.5 km;
the width is 2 km; and the average thickness of
landslide debris is about 140 m. This area experienced
landslides in 1862 due to an earthquake (unknown
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
12000
0s
(km)
50s100s150s
200s350s
(km)
Fig. 3 Change in topography of the landslide in Galunggung
Volcano vs time
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123

9. volume); in 1941 due to the Chiayi Earthquake
([108
m3
); in 1942 due to a heavy rainfall
([1.5 9 108
m3
); and in 1979 due to a heavy rainfall
([1.5 9 108
m3
). The Qingshui-shi River was
dammed up by the 1941 landslide and a lake was
formed upstream. It became larger due to the blockage
of the 1999 landslide (Fathani 2006).
The Tsaoling landslide is a typical dip-slope rock
slide that moved along bedding surfaces (Yang et al.
2014). There is a main scarp of horseshoe type at the
Fig. 4 The map of the Sum Wan Road Landslide (modified from Knill 1996)
Fig. 5 Geological profile on Section A–A0
from East to West (modified from Knill 1996)
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123

10. center of the top part. It was accompanied by two
shallow landslides on its right and left side at a slightly
higher position. The main block extends to the
southwest from the main scarp and there are two steps
of the secondary scarp. The upper one represents a
cross section of layered strata and the other does not
present obvious lamination. Such structure is a typical
formation of the sliding along the bedding plane of a
gentler angle. The denudation area and the transport
area were not easily distinguished, since many land-
slides had occurred repeatedly here. The depositional
area was beyond the original channel of the Qingshui-
shi River. Figure 8 shows the geological profile of the
Tsaoling Landslide. The sliding was inferred to be
caused by the intercalation of permeable sandstone
and impermeable siltstone, which store perched
Y (m)
X (m)
0
1
2
3
4
5
6
7
8
9
10
Debris
thickness (m)
Source area
0 50 100 150
50
100
150
200
250
Y (m)
X (m)
Factory
Fig. 6 Calculation result of the final deposition of the Shum Wan Road Landslide
-10
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260
Y (m)
Z(m)
Source area
Nam Long Shan Road
5s
10s
20s
50s
100s
300s after failure
Shum Wan Road
Rock cliff
Concave scar
Planar scar
Slip surface
Fig. 7 Cross-section of the motion of the Shum Wan Road Landslide
Geotech Geol Eng
123

11. groundwater that lubricated the interface. There, water
was found to seep out of the interface between
sandstone and siltstone and flow on the planar surface
of the latter. The depositional area of the main block is
composed of an obvious heap of the sliding mass on
the southern side of the original channel of the
Qingshui-shi River.
Fathani (2006) applied this numerical model to
simulate the runout zone of the Tsaoling Landslide.
The input data are: the bulk density is 20 kN/m3
; the
dynamic coefficient of viscosity is 0.01 m2
/s; and the
cohesion is 1 kN/m2
. Trial calculations were con-
ducted to find the values of the dynamic coefficient of
friction angle of sliding surface (/s) and sliding mass
(/m) which reproduces the calculated landslide depo-
sition similar to the actual debris deposit as shown in
Fig. 9. Using back analysis, it is found that /s = /m is
5.5° reproduces the deposition area similar to the actual
debris deposit in the Tsaoling landslide. The landslide
debris stopped moving after 140 s with the maximum
velocity of 55 m/s. Figure 9 shows the calculation
results of debris movement of the Tsaoling Landslide.
Based on the actual condition shown in Fig. 9, it has
been clarified that /s and /m equal to 5.5° gives the
calculation result a close resemblance to the actual
ground topography after the landslide movement.
4 Analysis and Discussion
The landslide simulation program was applied to 26
cases of landslides and 6 cases of debris flows. The
correlations among dynamic coefficient of friction,
landslide volume, the inclination of the source area,
and moving velocity were then analyzed. Table 1
shows the landslide features and the results of
calculation, where V is landslide volume, L is the
maximum run-out distance, H is the maximum drop
height of landslide debris, /s is the friction angle of
sliding surface, /m is the friction angle of sliding mass,
Fig. 8 Geological profile of Tsaoling Landslide. a Before failure, b After failure
Geotech Geol Eng
123

12. h is the inclination of source area, and vmax is the
maximum velocity. The equivalent coefficient of
friction has been defined as the maximum drop height
divided by the maximum horizontal run-out distance.
The relation between the dynamic coefficient of
friction and the gradient of source area is shown in
Fig. 10. For gentler slopes, the dynamic coefficient of
friction is smaller than the one in the steep slopes. This
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
Time = 1 sec.
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
Time = 10 sec.
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
Time = 20 sec.
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
Time = 40 sec.
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
Time = 60 sec.
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00 Time = 80 sec.
Time = 140
500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 4500.00
500.00
1000.00
1500.00
2000.00
2500.00
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Debris
thickness
(m)
213500.00 214500.00 215500.00 216500.00 217500.00
7500.00
8000.00
8500.00
9000.00
9500.00
0000.00
Actual deposition
Fig. 9 Calculation results of the motion of Tsaoling Landslide and its comparison with the actual deposition
Geotech Geol Eng
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13. is justified as steeper slopes have higher soil strength
compared to gentler slopes. The debris flow cases
generally generate lower dynamic coefficient of
friction compared with landslides in slopes with the
same inclination. The correlation between the
dynamic coefficient of friction and the inclination of
the source area in all debris flows belongs to a lower
than second order polynomial trend line (Fig. 10).
This low dynamic coefficient of friction causes debris
flow to move farther with high velocity.
Figure 11 shows the relation between dynamic
coefficient of friction and landslide volume. Even
though the small number of data are scattered, it
indicates that in the case of a landslide of small
volume, the pore water pressure along the sliding
surface is easily released; therefore a landslide of
Table 1 Landslide features and the results of calculation
Landslide V (m3
) L (m) H/L h (°) Calculation result Remarks
/s = /m (°) Vmax (m/s)
Galunggung (Indonesia) 3.5 9 109
16,500 0.10 14.8 3.8 70.6 Andesite
St. Helens (USA) 2.6 9 109
26,830 0.07 5.7 3.3 58.2 Andesite, Basalt
Bandai (Japan) 7.0 9 108
11,300 0.15 10.0 2.7 37.3 Andesite
Mayuyama (Japan) 3.0 9 108
6762 0.11 16.0 4.0 43.4 Andesite
Tsaoling (Taiwan) 1.4 9 108
4420 0.17 19.0 5.5 55.0 Sandstone, Shale
Chiufenerhshan (Taiwan) 3.0 9 107
2180 0.21 24.8 7.0 25.0 Sandstone, Shale
Kalitlaga (Indonesia) 2.2 9 105
240 0.49 32.0 10.3 12.6 Tuff, Sandstone
Tambaksari (Indonesia) 1.2 9 105
310 0.52 37.0 12.0 14.9 Silty clay, Sandstone
Bishamon (Japan) 1.0 9 105
360 0.23 22.4 6.5 10.1 Weathered Granite
Cililin (Indonesia) 6.3 9 104
200 0.49 48.0 16.0 16.6 Silty clay, Tuff (debris flow)
SumWan (Hong Kong) 2.6 9 104
220 0.34 27.0 12.1 8.3 Crystal tuff
Cintamanik (Indonesia) 1.3 9 104
190 0.62 49.0 20.0 12.2 Sandy clay, Sandstone
Cimeong (Indonesia) 1.0 9 104
140 0.48 52.0 22.0 13.8 Sandstone, Claystone (debris flow)
Gerdu (Indonesia) 5.2 9 103
105 0.42 59.0 30.0 11.2 Sandy clay, Tuffaceous breccia
Yasukawa (Japan) 4.6 9 103
480 0.20 24.3 2.0 15.3 Weathered granite (debris flow)
Cijati (Indonesia) 4.1 9 103
132 0.91 58.0 24.0 17.2 Clayed sand, Andesite (debris flow)
Yahatagawa (Japan) 2.6 9 103
231 0.40 33.5 9.0 11.6 Weathered granite (debris flow)
Plompong (Indonesia) 1.7 9 103
67.5 0.70 48.0 16.0 10.7 Clayed sand, Sandstone
Saeki Myojoen (Japan) 653 82.5 0.42 38.9 12.0 6.3 Weathered granite
Yahata (Japan) 640 58.8 0.46 36.2 15.0 6.3 Weathered granite
Shimokawachi (Japan) 572 49.8 0.57 40.3 18.0 9.3 Weathered granite
Imurodoi (Japan) 529 45.8 0.61 41.5 20.0 8.8 Weathered granite
Nagari Batu Merah (Indonesia) 504 23.5 0.74 58.0 27.0 14.0 Clayed sand, Weathered limestone
(debris flow)
Sakoya (Japan) 377 61.2 0.82 43.4 25.0 10.3 Weathered granite
Kegoya (Japan) 196 44.1 0.45 33.5 13.0 5.7 Weathered granite
Tohata (Japan) 195 134.9 0.46 42.6 8.0 11.9 Weathered granite
Yashiro (Japan) 162 22.1 0.59 40.4 20.0 4.0 Weathered granite
Hori (Japan) 113 21.0 0.57 50.8 28.0 5.7 Weathered granite
Wonolelo (Indonesia) 110 27.0 0.63 60.0 27.5 8.9 Clayed sand, Tuffaceous breccia
Shimizu (Japan) 42 11.2 0.98 65.4 41.0 6.8 Weathered granite
Murose (Japan) 41 64.1 0.39 37.9 6.0 7.5 Weathered granite
Kitashioya (Japan) 22 12.4 0.52 43.1 14.0 6.2 Weathered granite
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14. small volume occurs at a higher value of dynamic
coefficient of friction. As shown in Fig. 12, a small
volume landslide occurs at a lower value of maximum
velocity, whereas a large volume landslide yields a
higher value of maximum velocity. This difference is
obvious since the dynamic coefficient of friction of a
large volume landslide is lower than the one of a small
volume landslide, and it affects the maximum velocity
directly. Debris flow cases in general have higher
velocity than landslides of the same sliding volume.
The relationship among these parameters then can
be used to predict the movement of a potentially
unstable slope. In a potentially moving slope, the
gradient of the source area is measurable. Afterwards,
by using Fig. 10, this value can be used to predict
friction angle of sliding surface (/s) and the friction
angle of sliding mass (/m). These input parameters can
be very difficult to determine because its values are
significantly lower than the internal friction obtained
by soil tests and highly affected by its type of soil,
water content, and dynamic coefficient of viscosity.
From Table 1, the value of dynamic coefficient of
friction (/s = /m) can also be predicted from equiv-
alent coefficient of friction (H/L) value. Moreover,
dynamic coefficient of friction value (/s = /m) can be
used to predict the possible highest volume of
landslide and velocity.
The destructive power of a fast landslide depends
on velocity (Hungr 2007) and therefore predicting the
velocity becomes an important issue in designing the
countermeasures. Further, these results of analyses can
be used in assessing the hazard and risk of landslides,
selecting type of countermeasures, and conducting
evacuation activities in dangerous areas during times
of impending landslides.
5 Conclusions
The movement of rapid landslides and debris flows can
be calculated by using this proposed numerical model.
Based on calculation results from rapid landslides and
debris flows, it can be seen that this numerical model is
able to produce accurate calculations on deposited
sliding mass close to the actual rheological conditions
measured after the landslide occurrence. This calcula-
tion should be supported by comprehensive field
investigation to determine accurate input data. Among
input data used in this model, the dynamic coefficient
Fig. 10 Relation between the dynamic coefficient of friction
and the gradient of source area
100
102
104
106
108
1010
Fig. 11 Relation between dynamic coefficient of friction and
landslide volume
100
102
104
106
108
1010
Fig. 12 Relation between the maximum velocity and landslide
volume
Geotech Geol Eng
123

15. of friction of sliding mass and sliding surface very
significantly govern the results of calculation. The
friction angle of sliding surface and sliding mass are
much smaller than those obtained from static soil tests.
This difference is due to the influence of dynamic
conditions and excess pore water pressure. The value
of friction angle of sliding surface and sliding mass
may be predicted from the measurement of the gradient
of source area or correlations in Fig. 10.
The volume of sliding mass affects the dynamic
coefficient of friction and the velocity. A landslide
with a small volume occurs at a higher value of
dynamic coefficient of friction and yields a lower
velocity value. In addition, a landslide with a gentler
slope occurs at a lower value of dynamic coefficient of
friction. The appropriate and reliable calculating
method explained in this paper may require verifica-
tion through model experiments, determination of
appropriate physical properties of the sliding surface
and sliding mass, and eventually should be verified
through soil tests.
These results are beneficial in predicting the impact of
landslide movement in terms of run-out distance,
velocity and the scale of moving mass. Moreover, this
model is very important to study the post-failure
behavior of rapid landslides for hazard and risk assess-
ment. The result of this research method should be
utilized by related stakeholders in order to develop their
disaster-based regional and spatial planning in the future.
Acknowledgements We would like to show our gratitude to
Prof. Hiroyuki Nakamura for his leadership and supervision in
the development of the simulation model. We also thank Mr.
Refi Noer Fauzan and Ms. Monika Aprianti Popang for their
technical assistance.
References
Bossi G, Cavalli M, Crema S, Frigerio S, Quan Luna B, Man-
tovani M, Marcato G, Schenato L, Pasuto A (2015) Multi-
temporal LiDAR-DTMs as a tool for modelling a complex
landslide: a case study in the Rotolon catchment (eastern
Italian Alps). Nat Hazards Earth Syst Sci 15:715–722
Bronto S (2001) Volcanic debris avalanches in Indonesia. In:
Proceedings of the 3rd Asian symposium on engineering
geology and environment, Yogyakarta, Indonesia 3–6
September 2001, pp 449–462
Bronto S (2006) Fasies gunung api dan aplikasinya. J Geol
Indones 1(2):59–71 (in Indonesian)
Crosta GB, Imposimato S, Roddeman DG (2003) Numerical
modelling of large landslides stability and runout. Nat
Hazards Earth Syst Sci 3:523–538
Cruden DM, Varnes DJ (1996) Landslide types and processes. In:
Landslides, investigation and mitigation. Special Report
247, Transportation Research Board, Washington, pp 36–75
Dang K, Sassa K, Fukuoka H, Sakai N, Sato Y, Takara K, Quang
LH, Loi DH, Tien PV, Ha ND (2016) Mechanism of two
rapid and long-runout landslides in the 16 April 2016
Kumamoto earthquake using a ring-shear apparatus and
computer simulation (LS-RAPID). Landslides. doi:10.
1007/s10346-016-0748-9
Egashira S, Miyamoto K, Itoh T (1997) Constitutive equations
of debris flow and their applicability. Debris-Flow Hazards
Mitigation, Water Resources Engineering Division/ASCE,
pp 340–349
Fathani TF (2006) The analysis of earthquake-induced landslides
with a three-dimensional numerical model. In: Proceedings of
Geotechnics symposium, Yogyakarta, Indonesia, pp 159–165
Fathani TF, Suryolelono KB, Suhendro B, Legono D (2001)
Numerical analysis on the reach and velocity of landslide
movements. J Forum Tek 25(3):354–363
Hungr O (2007) Dynamics of rapid landslides. In: Sassa K,
Fukuoka H, Wang F, Wang G (eds) Journal of progress in
landslide science. Springer, Berlin, pp 47–57
Hungr O (2009) Numerical modelling of the motion of rapid,
flow-like landslides for hazard assessment. KSCE J Civ
Eng 13(4):281–287
Iverson RM (2012) Elementary theory of bed-sediment
entrainment by debris flows and avalanches. J Geophys Res
117:F03006. doi:10.1029/2011JF002189
Iverson RM, Denlinger RP (2001) Flow of variably fluidized
granular masses across three dimensional terrain. 1. Cou-
lomb mixture theory. J Geophys Res 106(B1):537–552
Johnson CG, Kokelaar BP, Iverson RM, Logan M, LaHusen RG,
Gray JMNT (2012) Grainsize segregation and levee for-
mation in geophysical mass flows. J Geophys Res 117:23.
doi:10.1029/2011JF002185
Knill J (1996) Report on the Shum Wan Road Landslide of 13
August 1995. Landslide investigation by the Geotechnical
Engineering Office, Civil Engineering and Development
Department. Hong Kong. http://www.cedd.gov.hk/eng/
publications/geo/geo_swr.html. Accessed March 2016
Lang YH, Nakamura H (1998) Characteristics of slip surface of
loess landslides and their hazard area prediction. J Jpn
Landslide Soc 35(1):9–18
Mangeney A, Bouchut F, Thomas N, Vilotte JP, Bristeau MO
(2007a) Numerical modeling of self-channeling granular
flows and of their levee-channel deposits. J Geophys Res
112:F02017. doi:10.1029/2006JF000469
Mangeney A, Tsimring LS, Volfson D, Aranson IS, Bouchut F
(2007b) Avalanche mobility induced by the presence of an
erodible bed and associated entrainment. Geophys Res Lett
34:L22401
McDougall S, Hungr O (2004) A model for the analysis of rapid
landslide motion across three-dimensional terrain. Can
Geotech J 41:1084–1097
Miyamoto K (2010) Numerical simulation of landslide move-
ment and Unzen-Mayuyama disaster in 1792, Japan.
J Disaster Res 5(3):280–287
Nakamura H, Tsunaki R, Ishihama S (1989) Simulation model
for debris movement of landslides. In: Proceedings of the
Japan–China symposium on landslides and debris flows,
Niigata - Tokyo, pp 81–86
Geotech Geol Eng
123

16. Nakamura H, Fathani TF, Karna AK (2002) Analysis of land-
slide debris and its hazard area prediction. In: Proceedings
of the international symposium on landslide mitigation and
protection of cultural and natural heritage, Kyoto, Japan,
pp 173–189
Pastor M, Haddad B, Sorbino G, Cuomo S, Drempetic V (2009)
A depth-integrated coupled SPH model for flow-like
landslides and related phenomena. Int J Numer Anal
Methods Geomech 33:143–172
Pastor M, Blanc T, Haddad B, Petrone S, Sanchez M, Drempetic
V, Issler D, Crosta G, Cascini L, Sorbino G, Coumo S
(2014) Application of a SPH depth-integrated model to
landslide run-out analysis. Landslides 11(5):793–812
Pelanti M, Bouchut F, Mangeney A (2008) A Roe-type
scheme for two-phase shallow granular flows over variable
topography. ESAIM Math Model Numer Anal
42(05):851–885
Pitman EB, Le L (2005) A two-fluid model for avalanche and
debris flows. Philos Trans A Math Phys Eng Sci
363:1573–1601
Pudasaini SP (2012) A general two-phase debris flow model.
J Geophys Res 117:F03010. doi:10.1029/2011JF002186
Quan Luna B, Cepeda J, Stumpf A, van Westen CJ, Remaitre A,
Malet J-P, van Asch TWJ (2013) Analysis and uncertainty
quantification of dynamic run-out model parameters for
landslides. In: Margottini C et al (eds) Landslide science
and practice, vol 3. Springer, Berlin, pp 315–318
Rickenmann D (1999) Empirical relationships for debris flows.
Nat Hazards 19:47–77
Roessner S, Wetzel H-U, Kaufmann H (2005) Sarnagoev A
(2005) Potential of Satellite Remote Sensing and GIS for
Landslide Hazard Assessment in Southern Kyrgyzstan
(Central Asia). Nat Hazards 35:395–416
Sassa K, Nagai O, Solidum R, Yamazaki Y, Ohta H (2010) An
integrated model simulating the initiation and motion of
earthquake and rain induced rapid landslides and its
application to the 2006 Leyte landslide. Landslides
7(3):219–236
Sosio R, Crosta GB, Hungr O (2012) Numerical modeling of
debris avalanche propagation from collapse of volcanic
edifices. Landslides 9:315–334
Voight B, Janda RJ, Glicken H, Douglass PM (1983) Nature and
mechanics of the Mount St. Helens rockslide-avalanche of
18 May 1980. Geotechnique 33:243–273
Wang W, Chen G, Han Z, Zhou S, Zhang H, Jing P (2016) 3D
numerical simulation of debris-flow motion using SPH
method incorporating non-Newtonian fluid behavior. Nat
Hazards 81(3):1981–1998
Ward SN, Day S (2006) Particulate kinematic simulations of
debris avalanches: interpretation of deposits and landslide
seismic signals of Mount Saint Helens, 1980 May 18.
Geophys J Int 167(2):991–1004
Yang C-M, Yu W-L, Dong J-J, Kuo C-Y, Shimamoto T, Lee
C-T, Togo T, Miyamoto Y (2014) Initiation, movement,
and run-out of the giant Tsaoling landslide—What can we
learn from a simple rigid block model and a velocity–dis-
placement dependent friction law? Eng Geol 182:158–181
Geotech Geol Eng
123