# IJEGE-11_BS-Xie-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*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**

once more, been declared to be in a state of relative

dormancy (y

*et alii*, 1994). In these 20 years, the

44 persons have been killed. Based on the latest re-

search, the latest formed 11

on the stability of the 11

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

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

*et alii*, 1988),

**ABSTRACT**

researchthe latest formed 11

on the stability of the 11

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

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)

formation Systems (GIS)

**INTRODUCTION**

dormancy in November 1990 (y

*et alii*, 1994).

played varying aspects of volcanic activities, ranging

from early phreatic eruption through to the successive

extrusion and growth of lava domes and the forma-

*M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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.

analysis models, their GIS grid-based 3D deterministic

models is deduced to calculate safety factor:

1) the first one is based on H

enttypes of slip surface ,and has been widely ad-

dressed in geotechnical literatures (H

*et alii*, 1989).

*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.

*et alii*, 2003a;

load are considered.

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-

umn can be neglected in the equilibrium equation

methods of analysis have been proposed in geomechan-

ical literature (x

*et alii*, 2003a; C

*et alii*, 2003), a

computer programs are still urgently required.

*et alii*, 2003a; 2003b; 2004a;

grid-based data is analyzed with four proposed col-

umn-based 3D slope stability analysis models (x

*et*

*alii*, 2003b; H

*et alii*, 1989) and the correspond-

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

*et alii*, 1994). This practical application of

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**

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*

**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*

*et alii*,

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

*SF*

*3D*

*w*= the

*A*= the area of the slip surface;

*= the effective cohesion;*

c'

c'

*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.

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

equation of the entire assemblage of grid-column

are sufficient conditions to determine all of the un-

known forces.

zontal forces equilibrium equation and then can be

used for any shape slip surface.

by force and/or moment equilibrium of each pixel-

column (Fig. 2). The equation of H

*et alii*, 2003a):

force of one grid-column, the following equation can

be obtained:

(H

*SF*

*3D*

*SF*

*3D*

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

*et alii*, 1989):

*SF*

*3D*

*Fig. 3 - Assumed slip surface and calculation parametrs*

*M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

[0,1]

multiplicative congruity:.

*a*= a constant of positive integer;

*m*= the mod-

ule;

*r*

ue of

*y*

*r*

*i*

by Equation (8),

*x*

**3D SLOPE STABILITY ASSESSMENT OF**

**11# LAVA LOBE OF UNZEN VOLCANO**

*BASIC INFORMATION AND GIS DATA PRO-*

CEEDING

CEEDING

*et alii*, 2004b).

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.

*a,b,c*of the ellip-

set as in Equation (1):

*“C”*of the ellipsoid is first set to

lected point, and then in each trial searching, random

walking will change the central point.

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.

*a,b,c*”, the central point

*“C”*and the inclination an-

gle

*“θ*” of the ellipsoid, are selected as the random

*Fig. 4 - The inclination of ellipsoid and slope*

*Fig.5 - The Unzen volcano and its location*

*Fig. 6 - 11# lava lobe of the Unzen volcano (east view-*

*point)*

**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*

practice problem in order to detect the critical slip sur-

face and the sliding bodies respectively.

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.

*et alii*, 2004b), for explain-

*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

11# lava lobe as study object (Fig. 5b) for evaluating

the stability of the 11

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

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

from the aerial photo by means of the following steps:

1) Selecting datum: using local triangle net and level

3) Grid measure: in the range of 1200 m × 1700 m, the

grid size is 20 m and the DEM precision elevation

is in centimeter. please indicate the DEM precision

in elevation);

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**

*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*

*M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

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).

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

*et alii*, 2004b). This study reveals that the

*a / b*

fectively locating the critical slip surface.

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”.

*AvrSlope=33.5*, the

ranges are set to be 25~40, 25~33.5 and 33.5~40 re-

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.

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.

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*

**THREE-DIMENSIONAL CRITICAL SLIP SURFACE IDENTIFICATION AND SLOPE STABILITY ASSESSMENT OF 11# LAVA LOBE OF**

**UNZEN VOLCANO, JAPAN**

*et alii*, 1994). Therefore, in this study, the

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

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.

1) The study shows the 11

parameters(discuss this point not considering the

influence of earthquake);

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**

the 3D critical sliding masses. In Fig.11,sliding volum

A is used to assess the possible slope failure of the 11

set to analyzing the critical sliding masses of the front

toe of the 11

in the 11

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.

*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*

*M. XIE, X. LIU, T. ESAkI, Z. wANG & J. HUANG*

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.

tabase approach will present a new challenge for the

geotechnical researchers using traditional numerical

methods for 3D slope stability assessment.

**ACKNOWLEDGMENTS**

nical Center, Japan.

slip surface;

**CONCLUSIONS**

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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