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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
1023
DOI: 10.4408/IJEGE.2011-03.B-111
THREE-DIMENSIONAL CRITICAL SLIP SURFACE IDENTIFICATION AND
SLOPE STABILITY ASSESSMENT OF 11
#
LAVA LOBE
OF UNZEN VOLCANO, JAPAN
m
owen
XIE
(*)
, x
ianGyu
LIU
(*)
, t
etsuRou
ESAKI
(**)
, z
enGfu
WANG
(*)
& J
ieHui
HUANG
(*)
(*)
School of Civil and Environmental Engineering, The University of Science and Technology Beijing, Xueyuan Lu 30,
Haidian District, Beijing, 100083, China
(**)
Research Institute for East Asia Environments,744 Motooka Nishi-ku Fukuoka ,819-0395, Japan
tion of pyroclastic flows. However, it has been now,
once more, been declared to be in a state of relative
dormancy (y
anaGi
et alii, 1994). In these 20 years, the
slope failures of lava lobes have been experienced and
44 persons have been killed. Based on the latest re-
search, the latest formed 11
#
lava lobe now represents
a potential slope failure mass. This paper concentrates
on the stability of the 11
#
lava lobe and its possible
critical sliding mass.
Presently, the majority of slope stability analyses
are performed using a two-dimensional (2D) limit
equilibrium method within the domain of geotechni-
cal engineering while the safety factor is commonly
assessed using a 2D representation of the slope: for
example, an “equivalent” plane-strain problem is pos-
tulated and analyzed. The results of the 2D analysis
are usually conservative, and although more expen-
sive, the three-dimensional (3D) analysis tends to
increase the safety factor. The failure surface is pre-
sumed to be infinitely wide in the 2D model, negating
the 3D effects caused by the infinite width of the slide
mass. Summarized studies concerning 3D slope sta-
bility led d
unCan
(1996) to conclude that the 3D safe-
ty factor exceeds that of 2D equivalent, provided that
the 2D safety factor is calculated for the most critical
2D section. It will be shown herein that the percentage
difference between the 2D and 3D analyses may be as
large as 30% (the difference is between around 3%-
30% with an average is 13.9%; G
ens
et alii, 1988),
and thus a 3D analysis is the preferred means of con-
ABSTRACT
Althoug Unzen volcano has been declared to be
in a state of relative dormancy, basing on the latcst
researchthe latest formed 11
#
lava lobe now represents
a potential slope failure mass. This paper concentrates
on the stability of the 11
#
lava lobe and its possible
critical sliding mass. Based on the proposed Geo-
graphic Information Systems (GIS) three-dimensional
(3D) slope stability analysis models, a 3D locating ap-
proach has been used to identify the 3D critical sliding
mass and to analyse the 3D stability of 11
#
lava dome.
At the same time, the new 3D approach has shown
the effectiveness in selecting the range of the Monte
Carlo random variables and in locating the critical slip
surface in different parts of the lava dome. The results
are very valuable for judging the stability of the lava
lobe and for planing the monitoring points.
K
ey
words
: three-dimensional (3D) slope stability, limit equi-
librium equation, Unzen volcano, lava lobe, Geographic In-
formation Systems (GIS)
INTRODUCTION
Unzen volcano, located in Nagasaki prefecture
of Japan, abruptly started to erupt after 198 years of
dormancy in November 1990 (y
anaGi
et alii, 1994).
Following around 8 major incidents up to 1995, it dis-
played varying aspects of volcanic activities, ranging
from early phreatic eruption through to the successive
extrusion and growth of lava domes and the forma-
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M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
slide is abstracted to GIS layers for each topographic
and geological theme, each layer of which represents
each theme: ground surface, strata, weak discontinui-
ties, groundwater and slip surface, respectively. By in-
putting these data into a deterministic model of slope
stability, a safety factor value is calculated.
In this study, combining the GIS grid-based data
with four proposed column-based 3D slope stability
analysis models, their GIS grid-based 3D deterministic
models is deduced to calculate safety factor:
1) the first one is based on H
ovland
’s model (1977);
2) the second one is based on the algorithm of the
3D stability analysis method proposed by H
unGR
(1987): it is a 3D extension of b
isHoP
(1954) 2D
model, it allows to consider conside the differ-
enttypes of slip surface ,and has been widely ad-
dressed in geotechnical literatures (H
unGR
, 1987;
H
unGR
et alii, 1989).
3) the third one is also based on the work of H
unGR
et
alii (1989): this model is an extension of Janbu’s
simplified 2D method, deduced from the horizon-
tal forces equilibrium equation along the slip di-
rection.
4) The fourth model is based on the assumption of
H
ovland
’s model (1977). The basic algorithm
is based on a former research (x
ie
et alii, 2003a;
2003b) in which the external load and the seismic
load are considered.
The first and the fourth methods assume that the
vertical sides of each pixel column are frictionless
and can be used for any shape slip surface. The sec-
ond method is based on two assumptions:
1. the vertical shear force acting on both the longi-
tudinal and lateral vertical faces of each grid-col-
umn can be neglected in the equilibrium equation
2. the vertical force equilibrium equation of each grid-
ducting slope stability analyses.
Since the mid-1970s, the development and appli-
cation of 3D stability models (d
unCan
, 1996) has at-
tracted growing interest. However, although several 3D
methods of analysis have been proposed in geomechan-
ical literature (x
ie
et alii, 2003a; C
Hen
et alii, 2003), a
practical 3D slope stability analysis method and related
computer programs are still urgently required.
In this study, as a new contribution and a follow
up to former research (x
ie
et alii, 2003a; 2003b; 2004a;
2004b), the Geographic Information Systems (GIS)
grid-based data is analyzed with four proposed col-
umn-based 3D slope stability analysis models (x
ie
et
alii, 2003b; H
unGR
et alii, 1989) and the correspond-
ent new GIS grid-based 3D deterministic models will
be applied in order to calculate the safety factors. At
the same time, a new developed GIS-based program,
3DSlopeGIS, will be used to evaluate the 3D stabil-
ity of the 11
#
complicated lava lobe of Unzen volcano
(y
anaGi
et alii, 1994). This practical application of
the 3D slope stability assessment will illustrate the ef-
fectiveness of 3DSlopeGIS in selecting the range of
the Monte Carlo random variables and in locating the
critical slip surface of the lava dome.
GIS GRID-BASED 3D MODELS AND CRI-
TICAL SLIP SURFACE LOCATING
Using the functions of the GIS spatial analysis, all
input data (such as elevation, inclination, slope, ground-
water, strata, slip surface and mechanical parameters)
for the safety factor calculation are available with re-
spect to each grid pixel, while all slope-related data are
grid-based. Figure 1 shows a real slope mass and its
abstracting GIS layers. In GIS, the reality of a land-
Fig. 1 - A slope failure mass and its abstracted GIS layers
Fig. 2 - A slope failure mass and forces acting on a single
grid-column
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THREE-DIMENSIONAL CRITICAL SLIP SURFACE IDENTIFICATION AND SLOPE STABILITY ASSESSMENT OF 11# LAVA LOBE OF
UNZEN VOLCANO, JAPAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
1025
Using the grid database of surface (x
ie
et alii,
2003a; 2003b), strata, groundwater, fault and slip sur-
face, a GIS grid-based equation, all the resistant and
sliding forces refer to the possible sliding direction,
but not necessary to the Y-axis direction that is used in
H
ovland
’s model (1977).
where, SF
3D
= the 3D slope safety factor; w = the
weight of one column; A = the area of the slip surface;
c'
= the effective cohesion; Φ' = the effective friction
angle; θ = the dip (the normal angle of slip surface);
and J , I = the numbers of row and column of the grid
in the range of slope failure (in this study, a polygon
feature will be used to confine the boundary of the
slide mass); U is the pore pressure acting on the slip
surface of each column; P is the vertical force acting
on each column (the distributed force of upper load);
k is the horizontal earthquake acceleration factor; E is
the resultant of all horizontal components of applied
point loads, the reinforcement force is considered in
this force.
For each methods indicated before,the most criti-
cal situations have been investigated,by means of
minimization of the 3D safety factor using the Monte
Carlo random simulation method for detecting the
3D critical slip. The initial slip surface is assumed
as the lower part of an ellipsoid slip, then each ran-
domly produced slip surface is changed according to
the different stratum strengths and conditions of weak
discontinuities. Finally, the critical slip surface is ob-
tained and consequently a relative minimization of the
column and the summary moment equilibrium
equation of the entire assemblage of grid-column
are sufficient conditions to determine all of the un-
known forces.
Then, this method can only be used for rotation
surface. The third one can be deduced from the hori-
zontal forces equilibrium equation and then can be
used for any shape slip surface.
Refer to the first method- Using the pixels in the
range of sliding mass, the 3D safety factor is deduced
by force and/or moment equilibrium of each pixel-
column (Fig. 2). The equation of H
ovland
’s (1977)
model is deduced to GIS grid form as following (x
ie
et alii, 2003a):
Refer to the secon method- With reference to Fig.
2, considering the equilibrium equation of the vertical
force of one grid-column, the following equation can
be obtained:
Then, the equation for calculating the 3D safety
factor is deduced as the Bishop 3D extending model
(H
unGR
, 1987):
Because the SF
3D
is implicit in equation(3), the
safety factor SF
3D
is calculated using equations(2) and
(3) by an iterative procedure. Refer to the third meth-
od, a 3D equivalent of the Janbu simplified method
without a correction factor can be deduced from the
horizontal forces equilibrium equation along the slip
direction (H
unGR
et alii, 1989):
The safety factor SF
3D
is calculated using equa-
tions (2) and (4) by an iterative procedure
(1)
(2)
(3)
(4)
(5)
Fig. 3 - Assumed slip surface and calculation parametrs
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M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
variables for Monte Carlo simulatingin the range of
[0,1]
The random variable of a uniform distribution
within the range of [0,1] is obtained by the method of
multiplicative congruity:.
where a = a constant of positive integer; m = the mod-
ule; r
i
= the random variable of the uniform distribu-
tion within the range of [0,1]; by setting an initial val-
ue of y
0
, each random variable r
i
can be obtained. The
random variable within the range of is then calculated
by Equation (8),
where x
i
= the random variable within the range of
[a,b].
3D SLOPE STABILITY ASSESSMENT OF
11# LAVA LOBE OF UNZEN VOLCANO
BASIC INFORMATION AND GIS DATA PRO-
CEEDING
Unzen volcano is located in Nagasaki prefecture of Ja-
3D safety factor is achieved (x
ie
et alii, 2004b).
The critical slip surface is obtained by means of
a trial searching and 3D safety factor calculation, in
which, the five parameters, of size and posture of the
ellipsoid, are selected as random variables for Monte
Carlo simulating: three axial parameters “ a,b,c ”, the
central point “C” and the inclination angle “θ ” of the
ellipsoid. If a randomly produced slip surface based on
the lower part of an ellipsoid is lower than a weak dis-
continuous surface or the confines of the hard stratum,
the weak discontinuity or the confine surface of the
hard stratum will be given priority for being selected
as one part of the assumed slip surface. Figure 3 shows
an assumed slip surface is composed of one part of the
ellipsoid and one part of the weak discontinuity.
The geometrical parameters, a,b,c of the ellip-
soid, are randomly selected in a certain range that is
set as in Equation (1):
The central point
“C” of the ellipsoid is first set to
be the centroid of the search limit or a researcher-se-
lected point, and then in each trial searching, random
walking will change the central point.
The inclination direction of the ellipsoid is set to
be the same as the direction of the slope, and the incli-
nation angle θ of the ellipsoid is basically set accord-
ing to the slope angle. If a slope has complicated topo-
graphic characteristics, the inclination parameter of an
ellipsoid is set to the main inclination of the slope as
shown in Fig. 4.
The five parameters, three axial parameters
a,b,c”, the central point “C” and the inclination an-
gle “θ ” of the ellipsoid, are selected as the random
(6)
Fig. 4 - The inclination of ellipsoid and slope
(7)
(8)
Fig.5 - The Unzen volcano and its location
Fig. 6 - 11# lava lobe of the Unzen volcano (east view-
point)
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THREE-DIMENSIONAL CRITICAL SLIP SURFACE IDENTIFICATION AND SLOPE STABILITY ASSESSMENT OF 11# LAVA LOBE OF
UNZEN VOLCANO, JAPAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
1027
2004b), and here the method will be applied to this
practice problem in order to detect the critical slip sur-
face and the sliding bodies respectively.
For the critical slip identification, a test for the
suitable Monte Carlo random calculating time is per-
formed; with a trial calculation frequency of up to
1000 times. The resultant minimum 3D safety factors
of each trial calculation are illustrated in Fig. 8. For
this case, considering the time consumed and effec-
tiveness, the minimum safety factor can be obtained
following around 300 trial calculations. In the follow-
ing random variables studies, the calculating time for
the Monte Carlo simulation is set at 300 times.
In a former study (x
ie
et alii, 2004b), for explain-
ing the relationship of the ratio of a / b (the width and
length of the ellipsoid) and the critical 3D safety fac-
tor, different a / b ratios are selected to locate the criti-
cal slip and calculate the 3D safety factor. When the
ratio of a / b is smaller than 0.8, the 3D safety factor
will increase sharply corresponding to the decreased
a / b ratio. Conversely, if the ratio of a / b exceeds
pan (Fig. 5a). In this study, we select the latest formed
11# lava lobe as study object (Fig. 5b) for evaluating
the stability of the 11
#
lava lobe and for locating the
critical slip surface. Fig. 6 shows a photo of the 11
#
lava lobe of volcano lava.
The topographic data are calculated using aerial
photography, and comparing the difference in such pho-
tos before and after each eruption allows each lava lobe
to be detected, and at the same time, the topographical
data for each occasion to be determined. The 11
#
lava
lobe was formed between Apr. 1993 and Apr.1994, and
its shape can be revealed from comparison between two
aerial photos taken in Feb.1993 and Sept.1994 respec-
tively, revealing the 3D shape of the 11
#
lava lobe. The
DEM data on each occasion, meanwhile, is deduced
from the aerial photo by means of the following steps:
1) Selecting datum: using local triangle net and level
points;
2) Triangle measure: air triangle surveying;
3) Grid measure: in the range of 1200 m × 1700 m, the
X, Y, and Z values of each grid are obtained (the
grid size is 20 m and the DEM precision elevation
is in centimeter. please indicate the DEM precision
in elevation);
4) Digital photos georeference: georeferencing the air
photos and corresponding to the actual site;
5) Coordinate conversion: changing to a common co-
ordinate system;
6) Forming TIN and converting into grid data: con-
verting the TIN dataset to a grid raster dataset.
The ground surfaces of each eruption are then ab-
stracted as a GIS grid dataset. The adjacent interface
is considered as the possible sliding surface, then the
interface of two lava lobes in Feb.1993 and Sept.1994,
as a weak layer, is considered as a possible slip surface
and the geomechanical parameters of the lava layer
and interface are listed in Table 1.
SUITABLE RANDOM VARIABLE SELEC-
TION IN MONTE CARLO SIMULATION
The basic Monte Carlo simulation method has
been detailed in a former research paper (x
ie
et alii,
Tab. 1 - The geomechanical parameters
Fig. 8 - Resultant minimum safety factor and random
Monte Carlo calculating times
Fig. 9 - Relationship between the minimum safety factor
and the a / b ratio
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M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
0.8, the 3D safety factor will decrease slowly with an
increase in the a / b ration until finally, the 3D safety
factor will approach the 2D safety factor (with the in-
crease in the ratio of a / b , the problem of 3D safety
factor calculation approaches the plain-strain assump-
tion that is used to calculate the 2D safety factor).
In this application study, the relationship of a / b
and the minimum safety factor has been studied based
on two conditions (Fig. 9). is maintained in the same
range, with the increasing values of a / b , the mini-
mum safety factor will increase. However, in the case
of the same b, with increasing values of a / b , the
minimum safety factor will decrease, since the ran-
dom selected sliding mass will approach a 2D case
(x
ie
et alii, 2004b). This study reveals that the a / b
ratio of around 0.5-0.6 will be a suitable ratio for ef-
fectively locating the critical slip surface.
When calculating the 3D safety factor, the force
and moment equations for each column are based on the
value of AvrAsp the average dip direction is assumed as
the sliding direction). To confirm this assumption, the
different range of AvrAsp were studied in this applica-
tion study. For one case of AvrAsp = 90, the ranges of
dip direction (aspects) were selected as 89~91, 80~100
and 70~110 respectively, and their minimum safety
factors 1.415,1.437 and 1.490 respectively. At the same
time, three cases provided a broadly similar critical slip
surface and with the same critical direction (about 90
degrees). This comparative study can confirm the as-
sumptions of “AvrAsp = sliding direction”.
A suitable range for the dip (slope angle) has also
been studied. For one case of AvrSlope=33.5, the
ranges are set to be 25~40, 25~33.5 and 33.5~40 re-
spectively, with resulting minimum safety factors of
1.412, 1.455 and 1.406 respectively. At the same time,
using AvrSlope±10%, ±20%, ±30%, ±40%, the corre-
sponding results are 1.412, 1.407, 1.409, and 1.407 re-
spectively. This result indicates that more than ±20%
range set cannot result a lower safety factor. Then, we
set the range of AvrSlope±20% for effectively locating
the critical slip surface.
In the Monte Carlo simulation, each central point
of the ellipsoid was randomly selected around the start
point. As shown in Fig.10, the randomly selected cen-
tral points are around a start point. At the same time,
we found that the different start points result different
minimum safety factors which are depending on the
geological structure and the topographic conditions.
This means that prior to the calculation, the geological
engineering and topographic conditions had to be care-
fully studied to determine a suitable start point.
The resultant minimum safety factor and calcula-
tion time have also been compared using different 3D
models. For certain case study, the differences are illus-
trated in Table 2. It can be seen that there is no apparent
difference in the calculation time because of the same
data management for different models, while the itera-
tive proceeding for the Bishop and Janbu 3D extension
Fig. 10 - The start point and random central points in the
Monte Carlo simulation
Fig. 10 - The start point and random central points in the
Monte Carlo simulation
T
ab. 2 - Calculating time and minimum safety factors for
different models
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THREE-DIMENSIONAL CRITICAL SLIP SURFACE IDENTIFICATION AND SLOPE STABILITY ASSESSMENT OF 11# LAVA LOBE OF
UNZEN VOLCANO, JAPAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
1029
ble (y
anaGi
et alii, 1994). Therefore, in this study, the
relative potential of a minor slope failure in the front toe
section was studied too, Fig.13,14 and 15 represent the
section and the 3D view of the critical sliding masses in
range B,C, and D respectively. The resultant minimum
safety factors are 1.508, 1.531 and 1.509 in the north
(D), mid (B) and south (C) sections of the toe respec-
tively. Considering the possible vertical cracks cutting
through the 11
#
lava lobe, the minimum safety factors
would be 1.012, 1.221 and 1.210 respectively. At the
same time, the same earthquake with the horizontal co-
efficient of k =0.05 will result the 3D minimum safety
factors of 1.322, 1.351 and 1.300 respectively.
Finally, the following conclusions can be obtained
from the stability study of the 11
#
lava lobe of Unzen
volcano:
1) The study shows the 11
#
lava lobe is now in a sta-
ble condition based on the proposed geomechanical
parameters(discuss this point not considering the
influence of earthquake);
2) A trial study is necessary to set a suitable range of
models takes a little more time. On the other hand, be-
cause it neglects the interactive forces of the column,
Hovland’s model results in the lowest safety factor.
OVERALL AND PARTIAL STABILITY OF
11
#
LAVA LOBE OF UNZEN VOLCANO
For evaluating the 3D stability of 11# lava lobe
comprehensively, 4 scenarios are selected to identify
the 3D critical sliding masses. In Fig.11,sliding volum
A is used to assess the possible slope failure of the 11
#
lava lobe as a whole. At the same time,B, C and D are
set to analyzing the critical sliding masses of the front
toe of the 11
#
lava lobe. Theses 4 sliding volume sce-
narios assures that the different sityationsbe considered
in the 11
#
lava lobe.
Taking the 11
#
lava lobe as a whole, varying cases
with a range of different random variables have been
calculated. The section of resultant critical sliding
mass is illustrated in Fig.12a (with a 3D view shown in
Fig.12b), and the minimum safety factors are revealed
as 1.322, 1.388 and 1.346 using Hovland’s, Bishop and
Janbu 3D extension models respectively; considering
the possible influence of earthquake with the horizon-
tal coefficient of k =0.05, the 3D safety factors will be
1.162, 1.235 and 1.159 respectively.
The former study of the sliding patterns concluded
that the front toe of the 11
#
lava lobe is relatively unsta-
Fig. 12 The section and 3D view of a critical sliding mass
in range A
Fig. 11 - The searching ranges for locating critical sliding
masses
Fig. 15 - The section and 3D view of a critical sliding mass
in range D
Fig. 14 - The section and 3D view of a critical sliding mass
in range C
Fig. 13 - The section and 3D view of a critical sliding mass
in range B
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M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
fectively selecting the range of the Monte Carlo ran-
dom variables, and in licating the critical slip surface.
These results will be a valuable reference for taking
measures against the slope failure hazard and for set-
ting the monitoring equipments.
Benefiting from the convenient functions of data
management and the GIS spatial analysis, the new da-
tabase approach will present a new challenge for the
geotechnical researchers using traditional numerical
methods for 3D slope stability assessment.
ACKNOWLEDGMENTS
The authors are most grateful for the funding sup-
port for this research provided by JSPS and Sabo Tech-
nical Center, Japan.
random variables to effectively identify the critical
slip surface;
3) If the possible vertical cracks are considered, the
front toe of the 11
#
lava lobe will be considered in a
dangerous condition;
4) Moreover, if any slope failure in the front toe takes
place, the whole stability of 11
#
lava lobe will be
affected too.
CONCLUSIONS
Combining the GIS grid-based data with four
proposed column-based 3D slope stability analysis
models, the slope stability of Unzen volcano lava lobe
has been evaluated and the results have illustrated
the convenience in the data management, in the ef-
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