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GIS-Based Probabilistic Mapping of Landslide Hazard Using a ThreeDimensional Deterministic Model
Article in Natural Hazards · October 2004
DOI: 10.1023/B:NHAZ.0000037036.01850.0d
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Natural Hazards 33: 265–282, 2004.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
265
GIS-Based Probabilistic Mapping of Landslide
Hazard Using a Three-Dimensional Deterministic
Model
MOWEN XIE1,2 , TETSURO ESAKI1 and GUOYUN ZHOU1
1 Institute of Environmental Systems, Kyushu University, Hakozaki 6-10-1, Higashi Ku, Fukuoka,
Japan; 2 College of Resource Engineering, The University of Science and Technology Beijing,
Xueyuan Lu 30, Haidian District, Beijing, 10083, China
(Received: 7 February 2003; accepted: 4 November 2003)
Abstract. Based on a new Geographic Information Systems (GIS) grid-based three-dimensional
(3-D) deterministic model and taking the slope unit as the mapping unit, this study maps landslide
hazard using the 3-D safety factor index and failure probability. Assuming the initial slip to be the
lower part of an ellipsoid, the 3-D critical slip surface in the 3-D slope stability analysis is located by
minimizing the 3-D safety factor using the Monte Carlo random simulation. The failure probability
of the landslide is calculated using an approximate method in which the distributions of c, φ and the
3-D safety factor are assumed to be in normal distribution. The method has been applied to a case
study on three-dimensionally and probabilistically mapping landslide hazard.
Key words: Geographic Information Systems (GIS), three-dimensional slope stability, failure
probability, Monte Carlo simulation, slope unit, landslide hazard
1. Introduction
Landslide hazard maps are widely used in resource development planning, in land
use and development planning, and in planning linear projects such as roads, railways, pipelines and transmission lines. Landslide hazard is the probability of the
occurrence of a potentially damaging landslide within a certain period within a
given area (Varnes, 1984).
The probability of a landslide event is the likelihood that a mass movement
(or slope failure) will occur. It can be expressed in relative (qualitative) terms or
probabilistic (quantitative) terms. Probability can refer to the probability of occurrence within a certain period, or to the probability caused by the uncertainty of
geomechanical parameters or geotechnical models, or the frequency, intensity and
duration of triggering agents (Chowdhury and Flentje, 2002). In this paper, the
hazard map aims to predict where slope failures are most likely to occur. This kind
of hazard map is more accurately defined as a landslide susceptibility map (Brabb,
1984). Landslide events, according to movement type, are commonly classified
Author for correspondence. E-mail: xie@ies.kyushu-u.ac.jp
266
MOWEN XIE ET AL.
into five main groups (National Academy of Science, 1978): falls, topples, slides,
spreads and flows; according to material type, are divided into two classes: rock
and engineering soil. In this paper, landslide means a slide of engineering soil.
Geographic Information Systems (GIS), as a computer-based system for data
capture, input, manipulation, transformation, visualization, combination, query,
analysis, modeling and output, with its excellent spatial data processing capacity,
has attracted great attention in natural disaster assessment (Carrara et al., 1999).
For the past 20 years, GIS has been widely used in landslide hazard assessment
(Brabb, 1984, 1995; Carrara et al., 1991; Carrara, 1995; Aleotti and Chowdhury,
1999; Dai and Lee, 2001). GIS has strong functions for spatially distributed data
processing and analysis. Using GIS can also ease the problem of slope stability
analysis if a GIS-based geotechnical analysis model is used.
With GIS, the methods for mapping landslide hazard can be briefly classified
into three groups: qualitative methodologies, statistical methodologies and geotechnical model-based methodologies. Generally, qualitative approaches are based
entirely on the judgment of those conducting the susceptibility or hazard assessment (Van Westen et al., 1999). The input data are usually derived from assessment
during field visits, possibly supported by aerial photo interpretation. Because of the
lack of a concrete physical concept with slope failure, qualitative approaches are
seldom used as a guide for large-scale areas. The statistical approach is an indirect
method in which either a predictive function or index is derived from a combination of weighted factors. The relative contribution of each factor is obtained by
means of statistical analyses (bivariate and multivariate). Using GIS makes these
overlayering operations much easier and largely explains the increasing popularity
of the statistical approach, which closely parallels the ever-increasing application
of GIS techniques. Deterministic, or physically based, models are based on the
physical laws of conservation of mass, energy and momentum. The parameters
used in these models can be determined in the field or in the laboratory. Most
deterministic models employed in civil engineering and the engineering geology
are site-specific and do not consider the spatial distribution of the input parameters. Models that consider the spatial distribution of input parameters are called
deterministic distributed models. Deterministic distributed models require maps
that give the spatial distribution of the input data. GIS is a tool for collecting,
storing, retrieving, transforming, manipulating and displaying spatially distributed
data, and therefore it is frequently used in distributed deterministic modeling (De
Roo, 1993).
The geotechnical model, which is deterministic or probabilistic, has been
widely employed in civil engineering and engineering geology for slope stability
analysis. A deterministic approach was traditionally considered sufficient for both
homogenous and non-homogenous slopes. The index of stability is a well-known
safety factor, based on an appropriate geotechnical model and on the physical
mechanical parameters. Calculating the safety factor requires geometrical data,
data on the shear strength parameters and information on pore water pressure.
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
267
Unfortunately, there has been an increasing tendency to adopt an “infinite slope”
model, which is well known as a “one-dimensional model” that represents the
potential failure of long natural slopes along the slip surface parallel to the ground
surface (Aleotti and Chowdhury, 1999; Van Westen and Terlien, 1996; Van Westen
et al., 1997; Van Westen, 1998; Xie et al., 2001; Zhou et al., 2003). This model
may be valid for shallow slope failure.
Two-dimensional (2-D) deterministic analysis models for slope stability analysis are widely used in civil engineering design and evaluation. Various 2-D
methods have been developed and have employed for practice use. Of all these 2-D
models, Janbu’s 2-D model (Janbu et al., 1956; Janbu, 1973), Bishop’s method
(Bishop, 1955) and Sarma’s method (Sarma, 1973), which are based on slice
analysis, are widely adopted in various professional standards for slope stability
analysis. Since an area consists of many “slopes” in the 2-D concept, the use of 2D models to obtain the spatial distribution of safety factors is almost impossible as
“each slope” has to be analyzed separately, and “each slope” means “each random
profile”, which should be analyzed for the 2-D safety factor.
All slope failures have a three-dimensional (3-D) geometry, which varies in
space even along a short distance. Therefore, it is reasonable to use a 3-D model
to analyze slope stability. Since the mid 1970s, increasing attention has been
directed toward the developing and applying 3-D slope stability models. Several
3-D methods of analysis have been proposed in geotechnical literature (Hovland,
1977; Gens et al., 1988; Chen and Chameau, 1983; Hungr, 1987, 1994; Lam and
Fredlund, 1993; Leshchinsky and Huang, 1992). Most of these methods have used
a column-based approach. These methods either neglect inter-column forces or
make assumptions for the 3-D safety factor calculation. Because the entire sloperelated data can be changed to grid-based data in GIS, these column-based 3-D
models could be used for the 3-D stability calculation using the GIS grid-based
data. Because of the difficulty of complex algorithms, iteration procedures and the
third dimension in conventional, two-dimensional GIS, 3-D deterministic model
applications have not yet been initialized in the literature.
Combining GIS grid-based data with a column-based 3-D slope stabilityanalysis model (Hovland, 1977), this study uses a new GIS grid-based 3-D
deterministic model for calculating the safety factor. To detect 3-D critical slip,
the search is performed by minimizing the 3-D safety factor using the Monte Carlo
random simulation method. The basic slip surface is assumed to be the lower part
of an ellipsoid slip, and the critical slip will be changed according to different
strengths of strata and conditions of the discontinuous surface. The object of this
change is to minimize the 3-D safety factor.
In fact, the 3-D landslide stability calculation results in only an average 3-D
safety factor. The problem is that any variability (introduced by error and uncertainty) in the input parameters is not accounted for in this result of the 3-D safety
factor. Thus, there has been an increase in the development and use of the probability technique (Joseph and Willian, 1998). Soil composition and properties vary
268
MOWEN XIE ET AL.
from one location to another, even within homogeneous layers. This variability is
caused by factors such as variation in mineralogical composition, conditions during
deposition, stress history, and physical and mechanical decomposition processes
(El-Ramly et al., 2002).
This study takes effective cohesion and effective friction angle φ of the soil
properties as the major source of uncertainty, and assuming variables of c, φ, and
the 3-D factor of safety to be in the normal distribution, the 3-D probability of
the landslide is calculated by an approximate method that uses a probability in the
range of µ ± 3σ ; the 99.75% of precision in this range is sufficient for landslide
hazard assessment.
The other important problem for the landslide hazard map is the mapping unit
(the nature and extent of the study object), but this topic has not received adequate attention in the literature. Many researchers assume the pixel (or grid) to
be the study object (Anbalagan, 1992; Carrara, 1983, 1995; Dai and Lee, 2001;
Van Westen and Terlien, 1996; Xie et al., 2001) because grid-based objects can
be easily obtained and managed. Grid-based objects are regularly distributed in
space, so computer processing and manipulation is fast and algorithmically simple.
However, the grid cell does not bear any relation to the mechanism of slope failure
or even to geological, geomorphologic and other environmental boundaries, so the
results obtained by this approach are relatively unacceptable in physical terms.
Landslide is intrinsically related to the geological and geomorphologic aspects
of the study area when no activity is recorded in the mass movement. Therefore,
this study takes the slope unit as the mapping unit. The slope unit, that is, the
portion of land surface with a set of ground conditions that differ from the adjacent units, has an explicit topographical (break line, stream, aspect and slope)
and geological form. Slope units are divided by geomorphological, geological and
hydraulic conditions. The appropriate size of a slope unit should depend on the
average size of the landslide bodies and the type of landslide in the study area.
Since it is virtually impossible to draw consistent dividing lines on topographic
maps covering large regions, an automatic computer procedure is required. This
study uses a GIS-based hydrologic analysis and modeling tool to automatically
divide the slope unit.
2. A GIS-Based Probabilistic Deterministic Model
Using the functions of GIS spatial analysis, all input data (such as elevation, inclination, slope, groundwater, strata, slip surface and mechanical parameters) for the
3-D safety factor calculation are available with respect to each grid pixel, while
all slope-related data are grid-based (Figure 1). By inputting these data into a
deterministic model of slope stability, a safety factor value can be calculated.
Based on Hovland’s (1977) model, a GIS-based 3-D model in which pore
groundwater pressure is considered based on effective stress analysis, and in which
all input data can be easily presented in a grid-based form, is used to calculate
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
269
Figure 1. GIS data managing for slope-stability analysis. (a) Is a three-dimensional schematic figure of a landslide. In GIS, the reality of a landslide is abstracted to GIS layers for
each topographic and geological theme. (b) Shows the GIS vector layers relating to a landslide, each layer of which represents each theme: ground surface, strata, weak discontinuities,
groundwater and slip surface, respectively. This study, to use a column-based 3-D model for
slope-stability analysis, converts each layer of theme into a grid layer (c) by using the GIS
spatial analysis function. At the same time, a point layer is used to integrate grid layers (d)
and (e); in this point dataset, the point shape represents the central point of each grid, and a
feature table is used to relate to all grid layers.
the safety factor. Because of the amount of slope-related data, managing all these
grid-based datasets is ineffective, so this study uses a point dataset to store all these
grid datasets (Figure 1). In this point dataset, a feature table is used to relate all the
slope-related data. The point shape is set as the central point of each grid column,
and the other fields are respectively set to relate all slope-related data (for example:
ground surface elevation, strata interface, fault, groundwater and slip surface).
Using this point database, 3-D slope safety factor SF3D can be calculated by
Equations (1)–(4), which are deduced from Hovland’s (1977) model (Figure 2),
(cA + [(Zj i − zj i )γ cos θ − uj i ] tan(φ)) cos θAvr
(1)
SF3D = J I J
I (zj i − zj i )γ sin θAvr cos(θAvr )
the apparent dip of X and Y axis can be derived:
tan θyz = tan θ cos(Asp), tan θxz = tan θ sin(Asp)
(2)
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MOWEN XIE ET AL.
Figure 2. Schematic figure of a deduced GIS grid-based 3-D model. (a) Is the 3-D schematic
figure of a landslide body. By even-dividing the study area into columns that correspond to the
GIS grid cell, for each column, using 3-D column (b) to model the strata structure. Based on
the spatial relationship of 3-D column (c) and (d), the equation for calculating the 3-D safety
factor can be deduced (Equations (1)–(4)).
the area of slip surface of one grid column is


(1 − sin2 θxz sin2 θyz )

A = cellsize2 
cos θxz cos θyz
(3)
and the apparent dip of the main direction of the inclination of the landslide area
can be calculated by the following equation:
tan θAvr = tan θ| cos(Asp − AvrAsp)|
(4)
where, for each grid, Zj i , zj i = the ground surface elevation and the slip surface;
uj i = the pore water pressure on the slip surface; γ = the unit weight; θ = the dip
271
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
Figure 3. Minimum and maximum 3-D safety factor calculation. Assuming two parameters,
effective cohesion c and effective friction angle φ, are in normal distribution. The minimum
and maximum values of the 3-D safety factor are calculated using the range of these two
parameters (the other parameters relating to slope safety factor are set as constants).
of the grid column slip surface; θxz = the apparent dip of X-axis; θyz = the apparent
dip of Y-axis; θAvr = the apparent dip of the main direction of the inclination of the
slip surface; Asp = the dip direction of the slip surface of the grid column; AspAvr
= the average dip direction of the slip surface; and cellsize = the grid size.
Here, the probability of a landslide failure is calculated using an approximate
method. Two main variables c and φ are considered in the calculation of probability, and variables c, φ and probability function P = f (c, φ) are assumed to be
in normal distribution. From the characteristic of the normal distribution, in the
range of µ ± 3σ (µ is the mean and σ is the standard deviation), the probability
is 99.75%, so the range of µ ± 3σ can be taken approximately as the highest and
lowest limits of the variable. Then the range of parameters c, φ and probability can
approximately equal µ ± 3σ .
In fact, if parameters c, φ are taken as random variables in the probability calculation, a range of value such as [Min, Max] is always suggested by the engineer,
and standard deviation σ can be evaluated by the range of [µ − 3σ, µ + 3σ ]. With
reference to Figure 3, the mean of SF3D is calculated by Equation (1), and the
minimum (µ − 3σ ) and the maximum (µ + 3σ ) of SF3D can be calculated by the
process shown in Figure 3. Finally, with reference to Figure 4, the probability of
landslide failure can be calculated by Equation (5):
P (SF3D ≤ 1) =
1
−∞
√
1
2π σ
e(
x−µ
σ
1
) 2 dx ∼
=
1
−3σ
√
1
2π σ
e(
x−µ
σ
1
) 2 dx
(5)
272
MOWEN XIE ET AL.
Figure 4. Failure probability calculation. Based on the characteristics of normal distribution,
probability in the range of µ ± 3σ is 99.75%. If range of the 3-D safety factor is limited to this
range, the failure probability of landslide can be calculated by Equation (5).
3. Slope Unit Identification
For the 3-D landslide hazard map of a certain mountain area, the critical sliding
surface is identified and the minimum 3-D safety factor calculated based on each
mapping unit (slope unit). A slope unit, here, is defined as one slope part, or the
left/right part of a watershed. Topologically, slope units can be divided by the
watershed divide and drainage line.
This study employs a GIS-based hydrologic analysis and modeling tool, Arc
Hydro (David, 2002), to draw dividing lines for forming slope units automatically.
Arc Hydro is an ArcGIS-based (ESRI’s GIS software: ArcGIS) system geared to
support water resources applications. It provides a consistent method for watershed
and stream network delineation using digital elevation models (DEMs) of landsurface terrain.
The watershed feature class is a subclass of the drainage area, which contains
a landscape subdivision into human-selected drainage areas, which may drain to a
point on a river network, to a river segment or to a water body. It can be automatically delineated using a set of rules applied to a terrain model. The definition
of watershed requires a human intervention process, where the analyst selects
and edits the watershed subdivision of the landscape unit to obtain the desired
arrangement.
By using Arc Hydro tool, the watershed (the size of which can be determined by
the user) can be obtained from digital elevation model (DEM) data. Topologically,
the outline of the watershed polygon is the watershed divide (ridge line). To detect
the drainage line (valley line), the reverse DEM data is used. By DEM grid analysis,
high DEM values can be turned into low values, and low DEM values can be turned
into high values, so the original drainage line can be turned into a watershed divide.
Thus, by using this reverse DEM data, the drainage line can also be obtained by
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
273
Figure 5. Slope unit derived using a GIS-based hydrological and modeling tool. No. 1 watershed is the result of using DEM for watershed analysis, No. 2 and No. 3 watersheds can also
be obtained using reverse DEM (a). One watershed polygon can then be divided to two slope
units (a) and (b).
watershed analysis. As shown in Figure 5, the No. 1 watershed can be obtained
using the DEM data, and No. 2 and No. 3 watersheds can be determined using the
reverse DEM data. It can be seen that No.1 watershed is divided into left and right
parts, these two parts representing two slope units.
By combining the watershed by DEM and watershed by reverse DEM, the slope
unit can be obtained. Figure 6 is a flow chart to determine the slope unit from DEM.
Using a hydro model, firstly filling the DEM data, secondly by obtaining the flow
direction by this filled DEM, then by calculating the accumulation, the watershed
can eventually be calculated by setting the minimum number of cells that flow
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MOWEN XIE ET AL.
Figure 6. Flow chart for obtaining slope unit from DEM. Using DEM and reverse DEM
for watershed analysis, using the GIS-based hydrological analysis and modeling tool can
automatically derive the slope unit.
to the calculating point (cell). It is certain that with the increase in the minimum
number of cells, a larger watershed can be obtained.
Figure 7 shows the difference between the grid-based mapping unit and the
slope unit-based mapping unit of a example; it can be seen that, unlike the
grid-based mapping unit, each slope unit-based mapping unit corresponds to the
right/left part of each slope.
4. Computational Implementation
The whole study area (or the slope failure range) can be evenly divided into small
rectangular meshes that are the same as GIS-based grids. For numerical calculation
of this grid-based 3-D slope stability analysis, all of the above calculation procedures are programmed by Microsoft’s Visual Basic (using GIS components). This
program, called 3DSlopeGIS, employs Visual Basic 6.0 and ESRI’s MapObjects
2.1. MapObjects as a GIS component is used for implementing GIS data management and spatial analysis, so no data export or import between GIS and the 3-D
model is needed to perform the slope stability analysis. The process for calculating
the minimum 3-D safety factor and for hazard mapping is illustrated in Figure 8.
In this process, the function of the data module is to obtain all slope-related geological, geomorphologic and hydraulic data and geomechanical parameters; the
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
275
Figure 7. Difference between the grid-based mapping unit and the slope unit-based mapping
unit. (a) Is the grid-based mapping unit; each even-dividing mapping unit has no relation to
topographical characteristics. (b) Shows the slope unit-based mapping unit; each slope unit
corresponds to the left/right part of each slope.
Monte Carlo module is used for randomly selecting each trial slip surface using
the Monte Carlo simulation; the 3-D safety factor is calculated in the 3-D stability
module; finally, the critical slip surface and its corresponding 3-D safety factor
can be obtained by numberous trial calculations. Using this 3-D safety factor as a
mean value, the failure probability of the landslide can be calculated by considering
two random variables: effective cohesion and effective friction angle . Additionally
in Figure 8, it can be seen that all modules are related to a GIS spatial analysis
function that is implemented by a GIS component; by implementing a GIS component in this 3DSlopeGIS system, the 3-D safety factor problem can be effectively
computed. By using the slope-related GIS data, all of the related data and results
can at the same time be visualized in the 3DSlopeGIS system.
5. A Case Study
Based on a GIS-based 3-D slope stability-analysis model and the Monte Carlo simulation, the critical slip surface and the minimum 3-D safety factor can be obtained
for each slope unit, and the landslide hazard can then be mapped. Harabun town
in the northern part of the Sasebo district, where a representative slide landslide
occurred in July 1997, has been selected for landslide hazard mapping. The case
study area (Figure 9) for the landslide hazard mapping is about 3.4 km2 in an area
located in the northern part of Kyushu, the southwestern part of Japan.
In this area, the most frequent type of landslide is the Hokusho-type landslide
(a type of slide failure), which is shown in Figure 10. The Hokusho-type landslide,
names second landslide, is a slope failure of collapsed sediment sliding along the
interface between the tertiary strata and the collapsed sediment. The Kitamatsuura
basalt overlies the tertiary strata. Since columnar jointing is prominent in the Kit-
276
MOWEN XIE ET AL.
Figure 8. Computational processes of 3DSlopeGIS. The Data module obtains all slope-related
geological, geomorphologic and hydraulic data and geomechanical parameters; the Monte
Carlo module randomly selects each trial slip surface using the Monte Carlo simulation; the
3-D safety factor is calculated in the 3-D stability module; finally, the critical slip surface and
its corresponding 3-D safety factor can be obtained by numerous trial calculations.
amatsuura basalt, the basalt collapses frequently with rock fall and rock debris
spreading over the hillside of the tertiary strata during rainfall. This type of landslide is usually termed the first Hokusho landslide which is no longer a active one.
The collapsed sediment of the first landslide forms colluviums over the tertiary
strata. The landslide, of the slide slope failure type, which occurred in the upper
weathered colluvium layer (collapsed sediment), is called the second landslide. In
the case of the second landslide, the sliding surface is usually along the base of
the weathered collapsed colluviums, or along the top of the tertiary strata. The
colluvium layer (collapsed sediment) is about 5–30 m thick. Landslide hazard in
this paper concerns the second landslide that is now the main potential hazard in
this urban residential area.
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
277
Figure 9. A case study area in Japan. The left part shows the relative position of the study
area, and the right part shows the study area with the distribution of buildings.
Figure 10. Hokusho-type landslide model. This study concerns the second landslide type,
which is now the main type of landslide hazard in the study area.
Table I. Physical and geomechanical parameters for
the case study. To calculate the probability of landslide, the range of the two main parameters (effective
cohesion c and effective friction angle φ) is listed in
this table.
Layer
c (kN/m2 )
φ (◦ )
γ (kN/m3 )
Upper layer
Bedrock
Slip
5–15
100
5–15
5–15
34
5–15
16.4
22.6
–
278
MOWEN XIE ET AL.
Figure 11. The landslide probability (%) and the potential landslide boundary. The distribution of the potential landslide bodies with a 3-D safety factor smaller than 1 are shown in
this figure. The numbers in the slope units indicate the landslide probability. The slope units
without numbers have no possibility of landslide failure.
The interface between the tertiary strata and the colluviums inclines gently and
consists predominately of weathered materials and clay, forming a slide surface
in the case of the second landslide. To map landslide, it is essential to determine
the spatial distribution of the slide surface. According to field investigations, due
to rainfall and long-term erosion, a complicated stream network has formed in
this area; outcrops of the tertiary strata are frequently found at the bottom of the
channel. In other words, the bed position of the colluviums is nearly equal to the
streambed elevation along the stream network. Then, by interpolating the stream
network, the slide surface or the bed position of colluviums can be identified. By
overlaying the stream network with the DEM data, the elevation in each pixel of
the stream network can be obtained. Finally, the slide surface can be determined
using the Kriging interpolation method. The preciseness of the interpolation results
is verified by comparing them with eight items of boring data, and the difference is
acceptable. The digital elevation data is newly produced with the scale of 1/500 that
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
279
Figure 12. The boundary distribution of all potential landslides with a 3-D safety factor smaller than 1. By overlayering with the distribution of buildings, the risk of landslide can be
evaluated.
is suitable for detailed study of the landslide, and the DEM used in this research is
in grid form with a 2 m pixel size. The map of the distribution of buildings in the
scale of 1/2500 is scanned and read in GIS as a polygon dataset. The groundwater
is assumed to be 30% of the possible landslide depth, which are groundwater
conditions in the rainy season. By collecting past in-situ test and laboratory test
results for the slide surface clay, the range of properties for the clay and bedrock
are decided as shown in Table I.
The appropriate size of the slope unit should depend on the average size of the
landslide bodies in the study area; referring to past landslide records, the average
width, 80 , of the landslide is selected as the appropriate size to identify the slope
unit.
Figure 11 shows the landslide probability of each slope unit (the slope units
without numbers have no possibility of landslide failure). The potential landslide
boundary, with a 3-D safety factor smaller than 1, shows the distribution of critical
landslide bodies.
As a 3-D potential landslide hazard map, Figure 12 shows the boundary distribution of all the critical landslides in which their 3-D safety factor is smaller than
1. From Figure 12, it is clear that there are eight main positions with high landslide
susceptibility. These results are an effective reference for landslide prevention.
Figure 13 shows the results of certain slope units, identified critical landslide
280
MOWEN XIE ET AL.
Figure 13. The identified potential landslide boundary of certain slope units. Using the
plane distribution and the section of potential landslide bodies, the potential landslide can
be predicted and managed three-dimensionally.
boundaries and landslide bodies. Using these results, in addition to the 3-D safety
factor and the failure probability, possible landslide boundaries and bodies can be
three- dimensionally quantitatively assured.
6. Conclusions
A new Geographic Information Systems (GIS) grid-based 3-D deterministic model
has been used for mapping landslide hazard using the index of the 3-D safety factor
of slope. Unlike most research that has taken the rectangular pixel as the mapping
unit, in this study, the slope unit, which has a fixed relationship with the landslide,
has been used for the mapping unit. Using a hydrologic analysis and modeling tool
for the watershed analysis, an automatic process has been developed for identifying the slope unit. Assuming the initial slip to be the lower part of an ellipsoid,
the 3-D critical slip surface in the 3-D slope stability analysis is performed by
minimizing the 3-D safety factor using the Monte Carlo random simulation in
which three parameters, a, b, c, and the central point of an ellipsoid are taken
3-D PROBABILISTIC MAPPING OF LANDSLIDE HAZARD
281
as random variables. The failure probability of the landslide is calculated using an
approximate method in which effective cohesion c, effective friction angle and 3-D
safety factor are assumed to be in normal distribution. A computational program
called 3DSlopeGIS, in which a GIS component is used to fulfill the GIS spatial
analysis function and effective data management, has been developed to implement
all the calculations of the 3-D slope problem. In using the spatial analysis functions,
the data management and the visualization of GIS for processing the complicated
slope-related data, the 3-D slope problem is easier to study.
Confined by the proposed 3D model, this paper adapts the developed approach
to map the hazard of slide slope failure in the engineering soil strata. In the case
study of this paper, only one type of landslide hazard, with a typical width of
80 m was mapped. However, by changing the size of the slope unit, other landslide
hazards of different potential sizes could also be mapped.
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