landslide characteristics and slope instability modeling using gis

7/22/2019 Landslide Characteristics and Slope Instability Modeling Using GIS

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Landslide characteristics and slope instability modeling using

GIS, Lantau Island, Hong Kong

F.C. Dai a, C.F. Lee b,*

aInstitute of Geographical Sciences and Natural Resources, Chinese Academy of Sciences, Beijing 100101, Peoples Republic of ChinabDepartment of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Peoples Republic of China

Received 22 September 2000; received in revised form 14 March 2001; accepted 20 March 2001

Abstract

Steep terrain and high a frequency of tropical rainstorms make landslide occurrence on natural terrain a common

phenomenon in Hong Kong. This paper reports on the use of a Geographical Information Systems (GIS) database, compiled

primarily from existing digital maps and aerial photographs, to describe the physical characteristics of landslides and the

statistical relations of landslide frequency with the physical parameters contributing to the initiation of landslides on Lantau

Island in Hong Kong. The horizontal travel length and the angle of reach, defined as the angle of the line connecting the head of

the landslide source to the distal margin of the displaced mass, are used to describe runout behavior of landslide mass. For all

landslides studied, the horizontal travel length of landslide mass ranges from 5 to 785 m, with a mean value of 43 m, and the

average angle of reach is 27.7

. This GIS database is then used to obtain a logistic multiple regression model for predictingslope instability. It is indicated that slope gradient, lithology, elevation, slope aspect, and land-use are statistically significant in

predicting slope instability, while slope morphology and proximity to drainage lines are not important and thus excluded from

the model. This model is then imported back into the GIS to produce a map of predicted slope instability. The results of this

study demonstrate that slope instability can be effectively modeled by using GIS technology and logistic multiple regression

analysis. D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Landslides; Runout; Logistic multiple regression; Geographical Information Systems (GIS)

1. Introduction

Landslides in mountainous terrain often occur

during or after heavy rainfall, resulting in the loss of

life and damage to the natural and/or built environ-

ment. Mapping or delineating areas susceptible to

landslides is essential for land-use activities and

management decision-making in mountainous areas.

Sites that are prone to landslides can be identified by

both analytical and empirical methods.A variety of approaches have been used in slope

instability mapping and can be classified into qual-

itative factor overlay, statistical models, and geotech-

nical process models. In the qualitative approach,

several maps representing the spatial distribution of

those physical parameters which may have influence

on the occurrence of landslides are combined into a

hazard map using subjective decision rules, based on

the experience of geoscientists involved (Anbalagan,

1992; Pachauri and Pant, 1992; Sarkar et al., 1995).

0169-555X/02/$ - see front matterD 2002 Elsevier Science B.V. All rights reserved.P I I : S 0 1 6 9 - 5 5 5 X ( 0 1 ) 0 0 0 8 7 - 3

* Corresponding author. Tel.: +852-28592645; fax: +852-

28580611.

E-mail address: [email protected] (C.F. Lee).

www.elsevier.com/locate/geomorph

Geomorphology 42 (2002) 213228


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The limitations in this approach are in the reprodu-

cibility of results and in the subjectivity in decision

rules. Statistical models involve the statistical deter-

mination of the combinations of physical parametersthat have led to past landslides. Quantitative or semi-

quantitative estimates are then made for areas cur-

rently free of landslides, but where similar conditions

exist. Both multiple regression analysis and discri-

minant analysis have been used to explore relations

between landslide occurrence and the terrain varia-

bles (e.g. Yin and Yan, 1988; Carrara et al., 1991,

1995; Brunori et al., 1996; Dhakal et al., 1999). A

major deterrent to such techniques has undoubtedly

been the logistics of collecting and calculating quan-

titative data (Rowbotham and Dudycha, 1998).

Another problem is that the probability values com-

puted from such techniques can often fall outside the

0 to 1 range of the probability values, which makes

it difficult to relate the output to a systematic pro-

bability surface. Recently, logistic regression, one of

a family of generalized linear models that are well

suited to analyzing a presence absence dependent

variable, has been used to predict slope instability

(Carrara et al., 1991; Mark and Ellen, 1995; Row-

botham and Dudycha, 1998). Geotechnical process

approaches are based on slope stability analyses, and

are applicable only when the ground conditions arefairly uniform across the study area and the landslide

types are known and relatively easy to analyze (e.g.

Terlien et al., 1995; Wu and Sidle, 1995). The

advantage of the geotechnical process models is that

they permit quantitative factors of safety to be cal-

culated, while the main problem is the high degree

of simplification that is usually necessary for the use

of such models.

An assessment of landslide hazard requires knowl-

edge of the landslide characteristics and runout behav-

ior of landslide mass. This research was undertakenwith a view to characterizing landslides on natural

terrain of Lantau Island, Hong Kong, and then devel-

oping a Geographical Information Systems (GIS)

approach to modeling slope instability. This study

area is prone to landslides when subjected to heavy

rainstorms. For example, widespread landslides

occurred in Lantau Island, following heavy rainfall

on 18 July 1992 and 5 November 1993 (Franks,

1999). There are four objectives in this research: (1)

to characterize landslides on natural terrain of Lantau

Island in Hong Kong; (2) to determine the statistical

correlations between landslide frequency and the

physical parameters contributing to the initiation of

landslides; (3) to develop a methodology for modelingslope instability using GIS; and (4) to characterize the

runout behavior of landslide mass. One assumption of

slope instability modeling is that the occurrence of

landslides in the past is indicative of the potential for

landslides to occur in the future. By identifying the


landslides, and by incorporating them in a GIS-based

logistic multiple regression model, regional slope

instability on Lantau Island was modeled.

2. Description of the study area

Lantau Island is located in the southwest part of the

territory of Hong Kong and is the largest outlying

island within the territory (Fig. 1). Primarily because

of its steep terrain, the island is virtually undeveloped

and uninhabited with the exception of small coastal

patches of flat land. Land area with slope gradients

greater than 25 accounts for 44% of the total land.

Elevation ranges from sea level to over 900 m above

sea level and changes abruptly.

The bedrock geology of the study area is domi-nated by Mesozoic volcanic rocks and the younger

Fig. 1. Location of the study area.

F.C. Dai, C.F. Lee / Geomorphology 42 (2002) 213228214


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intrusive igneous rocks (Fig. 2). The volcanic rocks,

which comprise tuffs and lavas with intercalated

sedimentary rocks, crop out in the west of the study

area. Intrusive rocks consist mainly of granites, anddykes of various compositions. Paleozoic sedimentary

strata comprising metamorphosed siltstone, sandstone

and carbonaceous siltstone occur as a small outcrop in

the northwest coastal areas of the study area. Super-

ficial deposits of the Quaternary age form large, flat-

lying areas. In hilly terrain, colluvium, including

debris-flow and other slope debris deposits, mostly

of late-Pleistocene to Holocene age, commonly man-

tle side slopes and valleys as a result of numerous

individual episodes of mass wasting and erosion

during the Quaternary period. Colluvium occurs as

relatively thin ribbon-like deposits filling drainage

courses. However, there are deposits which are con-

siderably thicker and of greater areal extent on some

hillslopes in the study area. The colluvium derived

from volcanics typically consists of subangular cob-

bles and boulders, of feldsparphyric rhyolite with

some tuff, in a matrix of mottled, reddish brown and

yellowish brown gravelly, sandy, slightly clayey silt.

Small alluvial deposits occur in hilly areas, butalluvium is generally restricted to fans developed

downslope of the colluvial deposits. Beach deposits

of sand usually form in front of alluvial deposits,

especially in coastal bays deposited under the com-

bined influence of higher sea levels and fluctuating

climatic conditions in recent times (Geotechnical

Control Office, 1988a,b). A regolith, or mantle of

weathered rock, occurs over most of the study area.

The effects of weathering vary with rock types, being

reflected in topographic relief. Intrusive rocks and the

Paleozoic sedimentary rocks are most deeply weath-

ered and eroded, forming the lower ground. The acidic

volcanic rocks are more resistant to deep weathering

and erosion. As indicated in Fig. 2, the area is

structurally affected by two sets of faults trending

NE NNE and NNW NW, respectively.

Fig. 2. Simplified geological map of the study area.

F.C. Dai, C.F. Lee / Geomorphology 42 (2002) 213228 215


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The climate is sub-tropical and monsoonal, with

mild, dry winters and hot, humid summers. Rainfall

is heavy, and occasionally intense during the rain-

storms and typhoons. Mean annual rainfall over theperiod 1961 1991 is in the range of 2000 to 2400

mm. Recent major rainstorm events occurred on 5

November 1993 (24-h rolling rainfall of 745 mm, 1

in 796 year event) and on 18 July 1992 (24-h rolling

rainfall of 454 mm, 1 in 28 year event). The hill-

slopes are drained by numerous small streams, most

of which flow only during or after heavy or pro-

longed rainfall. The hillsides are often deeply incised

as a result of erosion caused by ephemeral streams. In

general, piezometric records from previous site inves-

tigations indicate that the regional groundwater table

lies either just within the slightly to moderately

weathered bedrock or within the overlying saprolite

(Franks, 1999). The relatively high permeability of

the colluvium deposits, when compared to the under-

lying saprolite or weathered bedrock, allows for the

development of transient perched groundwater tables

at the interface during or following periods of intense

rainfall.

3. Data sources

The study area was examined using the ArcView

GIS software. The data available for this study include

topography, land-use classification, a terrain morpho-

logical map, superficial and bedrock geology, and the

locations and trails of landslides. All locational, geo-

logical, and geomorphological features provided by

the different thematic maps mentioned above were

imported into the ArcView GIS, or digitized using the

GIS software PC Arc/Info, and then transferred to

ArcView for subsequent analyses.

Contour lines and drainage lines are obtained fromthe 1:20,000 scale topographic maps with a contour

interval of 20 m. Elevation data were obtained from

the digital elevation model (DEM) with a resolution of

20 20 m derived from the 1:20,000 scale digitalcontour lines of the area. Two data layers are derived

from these elevation data, namely slope aspect and

slope gradient. Proximity to drainage line is calculated

using GIS functions.

Superficial and bedrock geological data are

obtained from 1:20,000 scale solid and superficial

geological maps developed by the Hong Kong Geo-

logical Survey of the Geotechnical Engineering

Office (GEO), previously known as the Geotechnical

Control Office (GCO). The maps covering the studyarea describe the geological groups, each comprising

geological units of broadly similar lithology. For ease

of analysis, the groups were further reclassified into

nine categories: alluvial, terrace and beach deposits

(ATB), debris flow deposits and talus (DF), sedimen-

tary rock (SR), metasedimentary rock (MSR), intru-

sive rock (IR), minor intrusive rock (MIR), ash tuff,

tuffite and tuff breccia (BCT), trachydacite, dacite

and rhyolite lava (TDR), and volcaniclastic sedimen-

tary rock (VSR), based on their stratigraphy and

genesis.

The 1:20,000-scale digital terrain classification

maps covering the study area, developed by the

GEO, were available to the authors. This dataset

contains terrain classification information that

includes erosion and stability, terrain component and

morphology, and slope gradient, which was derived

from Geotechnical Areas Studies Programme (GASP)

primarily using aerial photography interpretation

(API) technique (Brand, 1988; Geotechnical Control

Office, 1988a,b). Based on the terrain classification

information, terrain morphology which describes the

physical appearance of the slope and the general shapeof the slope profile (straight, concave or convex) is

extracted and then reclassified into 10 categories for

simplicity: hillcrest or ridge (A), straight sideslope

(B), concave sideslope (C), convex sideslope (D),

straight footslope (E), concave footslope (F), convex

footslope (G), drainage plain (H), rock outcrop (M),

and others, such as reclamation and coastal plain, (O).

All the footslope and drainage plain terrain consists of

colluvium, and all the sideslope terrain consists of

insitu geological materials (Geotechnical Control

Office, 1988a,b).The landslide database used was derived from the

Geotechnical Engineering Office work in which land-

slide locations and trails were digitized from 23

temporal sets of 1:20,000 to 1:40,000 scale stereo-

scopic aerial photographs dating from 1945 to 1994

(Evans, 1998; King, 1999). The aerial photographs

used thus cover a period of 50 years and recent

landslides as old as about 10 years were visible before

re-vegetation masked most scars. Recent landslides

(Fig. 3) were observed on aerial photographs as a



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distinctive light tone, which is generally bare of

vegetation (King, 1999). This indicates that the aerial

photographs record about a 60-year period of land-

slide activity. The location of each identified landslide

crown was recorded on the 1:5000 scale base map,

and the centerline of any landslide mass trail was

marked with a line. In the interpretation of aerial

photographs, the GEO classified the width of the

landslide scars as greater or less than 20 m wide,

and landslides with a width of greater than 20 m werereferred to as wide. This may be attributed to the

fact that landsliding with a width of greater than 20 m

is not a common occurrence. The ground slope angle

across the landslide head, calculated from the 1:5000

scale topographical maps, was noted. All these fea-

tures have been digitized by the GEO, and are

available to the authors.

A 1:50,000 scale coverage of land-use types for

the whole territory of Hong Kong, based on the

interpretation of SPOT images with verification of

field checking by Chi (Unpublished data) in 1998,

is used for the analysis. Although 35 land-use types

were mapped, these were simplified into six cate-

gories for the purposes of this study: (1) developed

land, such as cropland, roads, structures, reservoirs,

and reclamation (DL); (2) forested land (FL); (3)

shrub-forested land (SFL); (4) densely grassed land

with a shrub coverage of less than 40% (DGL); (5)

moderately grassed land with > 50% coverage

(MGL); and (6) sparsely grassed land on rockoutcrop-dominated areas (SGL). It should be noted

that land-use cover is considered to be only esti-

mates, because of increased development of coastal

flat-lying lands with time and possible temporal

change in land-use types over the past several

decades.

The above-mentioned vector datasets are then

rasterized to the DEM resolution in ArcView for

subsequent analyses. Each landslide was assumed to

be within a single 20 m pixel.

Fig. 3. Shaded relief map of the study area showing locations of landslides (black dots).



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4. Physical characteristics of landslides

Physical characteristics of landslides, including

landslide description, the physical parameters contri-buting to the initiation of landslides, and runout

behavior of landslide mass are analyzed respectively

as follows.

4.1. Landslide description

Landslide classification systems are usually based

on a combination of material and movement mecha-

nism. Using the system proposed by Cruden and

Varnes (1996), most of the landslides in the study

area are probably debris slides, debris flows, complexdebris slide-flows, or composite debris slide-flow-

falls, all of which may be either open-slope or

channelized (Evans et al., 1999). About 80% of the

2135 landslides recorded were less than 20-m in

source width. Field checking indicates that the failures

generally occurred along the colluviumbedrock con-

tact, and that the predominant failure mode is of the

translational type, involving a slipping of a thin layer

of colluvium with a planar failure surface. Most

landslides started as slides and quickly converted to

flows because of the water involved and the steepterrain below the landslide sources (Dai et al., 1999).

The vast majority of the landslides have the following

common features: a source area, defined by a surface

of rupture which comprises the main scarp and the

scarp floor, and a landslide trail downslope of the

source where landslide mass transport predominates,

though erosion and deposition may also occur, and a

deposition fan where the majority of the landslide

mass is deposited (Fig. 4). It should be noted that a

deposition fan might not be well developed for many

failures on open slopes because the landslide mass iscompletely deposited on the trail path.

The GEO carried out a systematic study of the 56

natural terrain failures in three selected areas within

the study area, and a factual and a diagnostic report on

the investigations and observations of the landslides

were given by Wong et al. (1997) and Wong et al.

(1998), respectively. Field inspections of these land-

slides have also been carried out by the authors (Dai et

al., 1999). The distributions of source length, source

width, and failure depth are shown in Fig. 5. For the

landslides examined, the source lengths vary between

6 and 40 m, with a mean value of about 15 m, and the

source widths range from 3 to 20 m, with a mean

value of about 10 m. The landslides generally have a

failure depth varying between 0.5 and 2.0 m with a

mean value of about 1.4 m. The vast majority of the

landslides examined involved the failure of a thin

surface layer of highly permeable bouldery colluvium.

In slightly over 50% of the landslides examined on

site, erosion pipe holes, usually near the interface of

the colluvium and the underlying less permeable

material, were observed in the loose colluvium

exposed at the back scarps of the landslides. It seemedthat these landslides were probably triggered by the

development of a transient water table above the

interface between the colluvium and the less perme-

able underlying material, resulting from direct surface

infiltration and subsurface seepage (Wong et al., 1998;

Dai et al., 1999). Given the heterogeneous nature of

the colluvium layer and the likely presence of prefer-

ential flow paths in the layer, subsurface seepage

flows leading to a build-up of seepage pressures

acting within selected zones in the layer might also

have contributed to triggering the landslides (Wong etal., 1998).

4.2. Physical parameters contributing to the initiation

of landslides

To examine the physical parameters contributing to

the initiation of landslides, the landslides which

occurred in the study area were correlated with those

parameters considered to have influence on their

occurrence. These physical parameters include lithol-Fig. 4. Description of typical natural terrain landslides.



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ogy and structure, slope gradient and slope morphol-

ogy, slope aspect, elevation, proximity to drainage

line, and land-use type. The digital map of landslide

distribution was overlain on the raster data layers of

physical parameters mentioned above using the GIS,

and landslide frequency, which is the number of

landslides per squared kilometer, was calculated for

each category on the physical parameter maps.

4.2.1. Lithology and geological structure

It may be reasonably expected that the properties

of the slope-forming materials, such as strength and

permeability that are involved in the failure, arerelated to the lithology, which therefore should affect

the likelihood of failure. The correlation of landslide

frequency with lithology is shown in Fig. 6a. It can be

seen that there are three geological categories with

relatively high landslide frequency, namely trachyda-

cite, dacite and rhyolite lava (TDR), sedimentary rock

(SR), and metasedimentary rock (MSR), with the

former being the highest. As mentioned previously,

the available evidence tends to suggest that surface

thin colluvium may have played an important role in

the majority of landslides. However, colluvial deposits

that are less than approximately 2 m thick are not

identified on the 1:20,000 scale geological maps

(Evans et al., 1999). Hence, landslides in thin collu-

vium are recorded as occurring within the underlying

geological group. This is not considered to be a

serious problem as the properties of the thin colluvial

layers will be very dependent on the bedrock geology

from which they are derived. Immediately downslope

from geological group boundaries, unmapped collu-

vial deposits may have been partly derived from the

upper geological group rather than from the under-

lying unit. However, the proportion of landslidesaffected by this situation will be very small (Evans

et al., 1999).

Structural information is also available from the

digital geological maps. However, visual examina-

tion of spatial distributions suggests that the corre-

lation between landslides and mapped linear

structural features at the 1:20,000-scale is not good,

and the structural information is thus excluded in this

study.

4.2.2. Slope gradient and slope morphologySlope gradient has a great influence on the sus-

ceptibility of a slope to landsliding. On a slope of

uniform, isotropic material increased slope gradient

correlates with increased likelihood of failure. How-

ever, variations in soil thickness and strength are two

factors which vary over a wide range for both failure

and non-failure sites. To quantify the relative fre-

quency of landslides on different slope gradients, it

is necessary to consider the distribution of the slope

gradient categories using the available digital eleva-

Fig. 5. Histograms showing characteristics of initial landslides: (a)source length, (b) source width, and (c) failure depth.



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tion model (DEM). Examination of landslide fre-

quency with the corresponding slope gradient catego-

ries shows an increase with slope gradient until the

maximum frequency is reached in the 3540 cate-

gory, followed by a decrease in the >40 category

(Fig. 6b).

Slope morphology can probably affect the suscept-

ibility of a slope to landslide in several ways. The

shape of a slope influences the direction of and

amount of surface runoff or subsurface drainage

reaching a site. Concentration of subsurface drainage

within a concave slope, resulting in higher pore water

Fig. 6. Correlations between landslide frequency (landslides per squared kilometer) and the physical parameters (symbols refer to text).



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pressures in the axial areas than on flanks, is one

possible mechanism responsible for triggering land-

slides (Pierson, 1980). An analysis of correlation

between landslide frequency and slope morphologyis carried out with the use of the terrain morphological

map, and the result is shown in Fig. 6c. It can be seen

that the landslide frequency is generally higher for

concave sideslopes (C), and for rock outcrop (M),

followed by straight sideslopes (B). The landslide

frequency on the sideslope terrain is much higher

than that on the footslope terrain. It can also be noted

from Fig. 6c that for both sideslopes and footslopes,

the landslide frequency is highest for concave slopes.

4.2.3. Slope aspect

The aspect of a slope can influence landslide

initiation. Moisture retention and vegetation is

reflected by slope aspect, which in turn may affect

soil strength and susceptibility to landslides. If rainfall

has a pronounced directional component by influence

of a prevailing wind, the amount of rainfall falling on

a slope may vary depending on its aspect (Wieczorek

et al., 1997). To investigate the relative relationship

between landslide frequency and slope aspect, the

DEM was used to calculate the aspect of a slope

within the study area. The distribution of aspect

among the mapped landslides is shown in Fig. 6d. Itcan be seen that on north-facing slopes the landslide

frequency is relatively low, and it increases with the

orientation angle, reaching the maximum on south-

facing slopes, and then declines.

4.2.4. Elevation

The correlation of landslide frequency with eleva-

tion is shown in Fig. 6e. At very high elevations there

are mountain summits that usually consist of weath-

ered rocks, whose shear strength is much higher. At

intermediate elevations, however, slopes tend to becovered by a thin colluvium, which is more prone to

landslides. At very low elevations, the frequency of

landslides is low because the terrain itself is gentle,

and is covered with thick colluvium or/and residual

soils, and a higher perched water table will be

required to initiate slope failure.

4.2.5. Land-use type

Extensive investigations have shown that land-use

cover or vegetation cover, especially of a woody type

with strong and large root systems, helps to improve

stability of slopes (Gray and Leiser, 1982; Greenway,

1987). Vegetation provides both hydrological and

mechanical effects that generally are beneficial tothe stability of slopes. Franks (1999) examined natural

terrain landslides in the Tung Chung area, North

Lantau Island, and concluded that a sparsely vegetated

slope is most susceptible to failure. The correlation

between land-use type and landslide frequency is

shown in Fig. 6f. It can be seen that the landslide

frequency on densely grassed land (DGL) is the

highest, followed by moderately grassed land (MGL).

4.2.6. Proximity to drainage line

An analysis has been carried out to assess the

influence of drainage lines on landslide occurrence.

For this purpose, proximity to drainage line is iden-

tified, and the results are divided into eight categories.

It can be found that as the distance from drainage line

increases, landslide frequency generally decreases

(Fig. 6g). This can be attributed to the fact that terrain

modification caused by gully erosion may influence

the initiation of landslides.

5. Slope instability modeling

5.1. Logistic multiple regression

Logistic multiple regression is a multivariate

technique which considers several physical parame-

ters that may affect probability. It accepts both binary

and scalar values as the independent variables, which

allows for the use of variables that are not continu-

ous or qualitatively derived. The advantage of logis-

t i c m u lt i pl e r eg r es s io n m od e li n g o v er o t he r

multivariate statistical techniques including multiple

regression analysis and discriminant analysis is thatthe dependent variable can have only two valuesan

event occurring or not occurring, and that predicted

values can be interpreted as probability since they

are constrained to fall in the interval between 0 and

1. In the present study, the dependent variable is a

binary variable representing the presence or absence

of landslides. The technique of logistic multiple

regression yields coefficients for each variable based

on data derived from samples taken across a study

area. These coefficients serve as weights in an



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algorithm which can be used in the GIS database to

produce a map depicting the probability of landslide

occurrence.

Quantitatively, the relationship between the occur-rence and its dependency on several variables can be

expressed as:

Prevent 1=1 eZ

where Pr(event) is the probability of an event occur-

ring. In the present situation, the Pr(event) is the

estimated probability of landslide occurrence. As Z

varies from 1 to +1, the probability varies from0 to 1 on an S-shaped curve. Z is the linear combi-

nation:

Z B0 B1X1 B2X2 . . .BnXn

where Bi (i =0, 1,. . ., n) is the coefficient estimated

from the sample data, n is the number of independent

variables (i.e. landslide-related physical parameters),

and Xi (i =1, 2,. . ., n) is the independent variable.

However, in a strict sense, it is not a probability since

the dynamic variables triggering landslides, such as

rainfall, are not accounted for. It may be more

appropriate to term it hereafter slope instability or

landslide susceptibility based on the quasi-static phys-

ical parameters. In logistic multiple regression, acoding scheme should be selected for the categorical

variables by creating a new set of variables that

correspond in some way to the original categories.

The number of new variables required to represent a

categorical variable is one less than that of the

number of categories. The coefficients of the logistic

multiple regression model are estimated using the

maximum-likelihood method. In other words, the

coefficients that make the observed results most

likely are selected. Since the relationship between

the independent variables and the probability is non-linear in the logistic multiple regression model, an

iterative algorithm is necessary for parameter estima-

tion.

Logistic multiple regression modeling is intended

to describe the likelihood of landslide occurrence on a

regional scale, and is very suitable for the assessment

of slope instability, since the observed data consist of

locations (points) or cells with a value of 0 (absence of

landslide) or 1 (presence of landslide). This method

allows a spatial distribution of probabilities or sus-

ceptibility values to be calculated within the GIS

environment.

5.2. Variables selection and sampling

All the physical parameters considered to be rele-

vant to the occurrence of landslides, as noted previ-

ously, including lithology, slope gradient, slope

aspect, slope morphology, elevation, land-use type,

and proximity to drainage line, were selected as the

initial independent variables in the present study. For

each variable, the same categorization scheme as that

used to study the relation of landslide frequency with

variable categories previously is adopted for consis-

tency.

For the purpose of the statistical analysis, sample

data representing both absence and presence of land-

slide must be provided to fit the logistic multiple

regression model. The way in which these data are

obtained will affect both the nature of the regression

relation and the nature and accuracy of the resulting

estimates (Atkinson and Massari, 1998). In this study,

the data set of landslide inventory is an indispensable

data source representative of samples of landslide

presence. All locations of the 2135 landslides studied

were thus used to extract automatically from the

existing data layers the physical parameters thatcharacterize landslide locations. To eliminate bias in

the sampling process, an equal number of points were

chosen from the not-yet-landslide area as samples

representing the absence of landslide. These locations

were obtained using a spatially uniform sampling

scheme but excluding a 40-m buffer zone for all

landslides so as to minimize the impact of the size

of landslides. Each sample point has its respective

binary value on the presence/absence of landslide, as

well as information on independent variables. These

sample data were then used to input to the logisticmultiple regression algorithm within the SPSS (SPSS,

1997), a desktop statistical software package, to

obtain the coefficients for the logistic multiple regres-

sion model.

5.3. Modeling results

A logistic multiple regression model was con-

structed initially based on the physical parameters as

defined above. Then, at each step, variables are



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evaluated for removal one by one if they do not

contribute sufficiently to the regression equation.

The variables included in the model were slope

gradient, lithology, elevation, slope aspect, and land-use cover. In the present analysis, the likelihood-ratio

test was always used for determining whether varia-

bles should be added to the model. This involves

estimating the model with each variable eliminated in

turn and looking at the change in the logarithm of

likelihood when each variable is deleted. If the

observed significance level is greater than the proba-

bility for remaining in the model (0.1 in this study),

the variable is removed from the model and the model

statistics are recalculated to see if any other variables

are eligible for removal. Both proximity to drainage

line and slope shape were not significant and were

thus eliminated from the stepwise procedure.

The coefficients for the final logistic multiple

regression are shown in Table 1. Note that all the

variables in the model are binary variables represent-

ing presences or absences of the corresponding vari-

ables. For each variable, the last category is used as

the default reference category, and the coefficient of

that category is thus overridden. Fig. 7 is a histogram

of the predicted landslide susceptibility for the train-

ing samples used in this analysis. Theoretically, if wehave a model that successfully distinguishes the two

groups based on a classification cutoff value of 0.5,

the cases for which landslide has occurred should be

to the right of 0.5, while the cases for which landslide

has not occurred should be to the left of 0.5. The more

the two groups cluster at their respective ends of the

plot, the better it is. From Fig. 7, it can be shown that

the model produced a concordance rate of 81.7% and

that 85.2% of the actual landslides were correctly

classified with the use of 0.5 as a classification cutoff

value (default in SPSS). By examining this histogram

of predicted susceptibilities, one can see what a differ-

ent classification rule should be adopted when apply-

ing the model to each cell in the study area.

To map future potential slope instability in the

study area, the logistic multiple regression model

was then transferred into the ArcView GIS, and

applied to the independent variables representing the

Table 1

Regression coefficients estimated for the model

Variable Categories Coefficient Variable Categories Coefficient

Constant term 9.755 Slope aspect Flat 0.431Slope gradient () 0 10 10.678 N 0.112

1015 4.369 NE 0.4681520 3.374 E 0.6702025 2.639 SE 0.5482530 1.153 S 0.8823035 0.863 SW 0.54735 40 0.077 W 0.303

R40 NW

Elevation (m) 0 50 11.214 Land-use type developed land 7.12150 100 11.441 forested land 0.033

100 150 11.445 shrub-forested land 0.257

150 200 11.181 densely grassed land 0.225

200 250 11.322 moderately grassed land 0.258

250 300 11.212 sparsely grassed land

300 350 10.959 Lithology alluvial, terrace and beach deposits 7.298350 400 10.816 debris flow deposits and talus 0.984400 450 10.550 sedimentary rock 0.233450 500 10.434 metasedimentary rock 0.716500 550 9.240 intrusive rock 2.076550 600 9.235 minor intrusive rock 2.413600 650 8.629 ash tuff, tuffite and tuff breccia 0.990650 700 7.653 trachydacite, dacite and rhyolite lava 0.076

>700 volcaniclastic sedimentary rock



12/16

present conditions for each cell within the study area.

For general purpose, the range of the susceptibility to

landslides is classified into 4 categories: (a) Very low

(0 0.2), (b) Low (0.2 0.35), (c) Moderate (0.35

0.5), and (d) High (>0.5). The ranges of the individual

categories were derived based on the histogram of the

estimated susceptibility to landslides shown in Fig. 7.The final product of the analysis is shown in Fig. 8.

Zones classified as being of very low susceptibility

are distributed in clusters on the coastal lowland and

on the top of high mountains that are characterized by

relatively gentle gradient, while zones of low sus-

ceptibility are sparsely distributed. In the zones of

moderate susceptibility, the combination of physical

parameters may adversely influence slope stability.

When disturbed, the slopes are prone to landslides.

The high susceptibility category exhibits a strongly

clustered pattern of spatial distribution. This categorybears a high potential for landslide occurrence, and is

characterized by relatively high elevations and steep

terrain. Most of the locations of the identified land-

slides actually fall within this category, and existing

ground conditions are very likely to create serious

landslide problems.

Generally, the slope instability map reflects the

potential for initiating a landslide on a slope, but does

not indicate how far the landslide will travel. One of

the possible solutions to this problem is that one may

use this slope instability map and runout behavior of

landslide mass that will be discussed below to roughly

estimate possible travel distance of potential land-

slides. Land use planners, developers and general

public may use this map to determine areas where

landslides may be a problem in site development.

It should be noted that the complexity of the failureprocesses means that any evaluation of stability con-

tains a considerable amount of uncertainty. The reli-

ability of the assessment results depends on a

multitude of factors ranging from the quality of the

database, the introduction of potential errors associ-

ated with data entry, manipulation, and analysis within

the GIS, to the limitations and assumptions inherent in

the statistical techniques (Rowbotham and Dudycha,

1998). In addition, temporal and spatial distribution of

rainfall, as a trigger for landslide occurrence in the

study area, is not accounted for, though the landslidedatabase used in this study including landslide inci-

dence in about 60 years may even-out the spatio-

temporal rainfall effects. It might be better to incor-

porate rainfall variables within the logistic multiple

regression analysis. In this regard, a more detailed

spatio-temporal approach to landslide hazard assess-

ment is being carried out by the authors on a much

larger scale, using a DEM with a resolution of 2 2 mand spatio-temporal landslide information derived

from multi-temporal aerial photographs by using

Fig. 7. Histogram of predicted landslide susceptibility.



13/16

aerial photogrammetric method, detailed 1:5000 scale

superficial geological maps and rainfall records.

6. Runout behavior of landslide mass

In landslide hazard assessment, the possible spatial

impact of landslides needs to be estimated. A well-

known index expressing the runout behavior of land-

slide mass is the angle of the line connecting the headof the landslide source to the distal margin of the

displaced mass. This angle has been designated as the

angle of reach (Hsu, 1978; Corominas, 1996) or the

angle of apparent friction (Wong and Ho, 1996). The

angle of reach is considered the most suitable and

practical parameter for use in assessing the mobility of

landslide mass in view of its close modeling of the

parameters for characterizing the rate of energy loss

during mass movement and its consideration of the

effect of downslope gradient (Wong and Ho, 1996).

Most studies (e.g. Hsu, 1978; Corominas, 1996;

Wong and Ho, 1996) focus on the relationship

between the angle of reach and the volume of failure.

Generally, the angle of reach decreases (or mobility

increases) with an increase in landslide volume. For

natural terrain landslides in the study area, Wong et

al. (1998) carried out a study on the relation between

the angle of reach and landslide volume based on the

assumption that the mobility of landslide mass can be

significantly affected by the mechanism of massmovement. They classified the movement of landslide

mass into three modes: (1) gravity (or sliding) mode

without a significant influence from the action of

surface water; (2) hydraulic mode that means land-

slide mass ran into stream courses and was subse-

quently subjected to significant action of surface

running water; (3) mixed mode, intermediate between

the above two modes. They concluded that the angle

of reach is highest for landslides of the sliding mode

and lowest for landslides of the hydraulic mode.

Fig. 8. Map of relative landslide susceptibility.



14/16

However, for landslide hazard assessment over a

large area, the relationship between the angle of reach

and the volume of landslide mass may not be a

practical method because it is very difficult to predictthe volume of a potential landslide and estimate the

possible mode of mass movement. A possible, more

practical approach may be used to esti mate the

variations in the angle of reach and/or travel distance

of landslide mass based on historic records.

In the present study, no attempt has been made to

obtain the relation of the angle of reach with landslide

volume because data on landslide volume are not

available. In the dataset of landslide distribution, the

elevations at the head and the distal margin of land-

slides, and the horizontal length of landslides are

noted. This permits us to carry out a statistical analysis

of the runout distance of landslide mass and the

relationship between the horizontal length and change

in elevation.

Fig. 9 shows the histogram of horizontal length of

landslides. Of all landslides studied, about 67% are

less than 40 m and about 9% are greater than 100 m in

horizontal length. For landslides with width of < 20

m, 74% are less than 40 m and 5% are greater than

100 m in horizontal length. However, for landslides

with a width of >20 m, about 41% is less than 40 m

and 27% are greater than 100 m in horizontal length.The average horizontal lengths are 35.3 and 72.6 m

for landslides with a width of < 20 m and landslides

with a width of >20 m, respectively. This indicates

that the horizontal length of landslide mass may

increase with the width of landslides, or landslide

volume.

A linear regression analysis is performed to obtain

the best relation between the horizontal length and

change in elevation of landslides. Outliers are

defined as being significantly different from points

with more than three standard deviations from themean. These significant outliers are then excluded

from the analysis and the regression is refitted so as

to obtain an equation of general applicability. Of the

2135 landslides studied, 32 outliers are determined

and then excluded. For landslides with a width of

< 20 m and landslides with a width of >20 m, 28 and

9 outliers are defined and excluded from the total

1691 and 444, respectively. This exclusion of the

outliers is considered to have little influence on the

statistical results used on regional scale, primarily

because the percentage of outliers is quite small. The

results are shown in Fig. 10. It can be seen that the

average angle of reach is 27.7 for all landslides

studied, and that a slight difference in the average

angle of reach exists between the landslides with a

width of < 20 m (29.0) and those with a width of

>20 m (26.7). This indicates that a dependency of

the angle of reach on landslide width or thus land-

slide volume may exist and that this dependency is

Fig. 9. Histogram showing the distribution of horizontal length of

landslides.



15/16

not important because the percentage of landslides

involved is quite small.

There are a lot of uncertainties not considered in

the present study. These uncertainties underlying the

model may include the type of material, mechanism of

failure, groundwater, the volume of failure, and geol-

ogy, etc. The parameters obtained are applicable to

predict the travel distance on regional scales, and

provide an effective means for the assessment of

runout distance of landslide mass when incorporated

into a map showing slope instability and the digital

elevation model (DEM) within GIS.

7. Conclusions

With Lantau Island of Hong Kong as a study area,

the pertinent landslide characteristics are described,

and the relations of landslide frequency with the


landslides are presented. The runout distance and the

angle of reach of landslides are analyzed. GIS tools

have made possible the production of innovative slope

instability maps. In particular, they have facilitated the

application of the logistic multiple regression analysis

technique. Logistic multiple regression applied to

training samples collected from existing data layers

considered to be relevant to landslide occurrence was

able to predict slope instability at a rate of about 85%

concordance. The predicted susceptibilities generated

from the model within the GIS environment were in

turn used to produce a map of relative landslide

susceptibility. The results of this study indicate that

the model is useful and suitable for the scale adopted

in this study.

Acknowledgements

Funding for this research was provided by the

Research Grants Council of Hong Kong and the Hong

Kong Jockey Club Research and Information Centre

for Landslip Prevention and Land Development, at the

University of Hong Kong. The authors wish to

express their sincere appreciation for the generous

support received from these two organizations.

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