Probabilistic modeling of uncertainties in earthquake-induced landslide hazard assessment

Computers amp Geosciences 28 (2002) 735ndash749

Probabilistic modeling of uncertainties in earthquake-inducedlandslide hazard assessment$

Alberto Reficea Domenico Capolongob

aDipartimento Interateneo di Fisica INFM Via Amendola 173 70126 Bari ItalybDipartimento di Geologia e Geofisica Via F Orabona 4 70125 Bari Italy

Received 12 October 2000 received in revised form 1 November 2001 accepted 8 November 2001

Abstract

Probabilistic analysis is gaining more attention in the field of landslide hazard assessment due to the possibility of

taking into account estimation uncertainties and spatial variability of geological geotechnical geomorphological and

seismological parameters In this paper an implementation of a simple approach to derive probabilistic earthquake

triggered landslide hazard maps is described The method is based on the simplified Newmark slope stability model

applied on a pixel-by-pixel basis which fully integrates into current GIS computational environments Uncertainties

and fluctuations in input parameters are considered by treating these quantities as statistical distributions Various

probability density functions can be simulated through Monte Carlo techniques on a pixel-by-pixel basis and the

simulated samples are retained through all the computing steps This allows the resulting quantities to be cast into

probabilistic hazard maps without restrictions about the symmetry or the mathematical complexity of the underlying

distributions First results on a test landslide site in Southern Italy show good performances for realistic landslide

hazard zonation The simplicity of the adopted framework allows the current approach to be easily expanded and

improved the current approach r 2002 Elsevier Science Ltd All rights reserved

Keywords Probabilistic methods Newmark model Earthquake-triggered landslides Monte Carlo simulation Asymmetric pdf

1 Introduction and motivation

In the international Decade for Natural Disaster

Reduction (1990ndash2000) a major of research effort was

initiated to develop new methodologies for landslide

hazard assessment In this context the term hazard

describes the magnitude and probability of occurrence

of landslides within a specified period of time and in a

certain area

Earthquakes are an important triggering cause for

landslides Damage from earthquake-induced landslides

and other ground failures sometimes exceeds the

damage directly related to ground shaking and fault

rupture Effects such as these have encouraged the

development of reliable techniques for anticipating slope

failures Methodologies range from modeling and

understanding of the causes of landslides to monitoring

of some probable triggering factors such as premoni-

tory small displacements to improvements in risk

management mainly through hazard zonation and

forecasting The emerging capabilities of Geographic

Information Systems the rapid increase in computa-

tional power and decrease in computer costs the

increasingly widespread use of such techniques by the

geological community at large all constitute a strong

impulse to research on these fields (Burrough 1986)

Among slope stability models Newmarkrsquos model

(Newmark 1965) is often used to derive indications

about slope instabilities due to earthquakes mostly by

virtue of its simplicity (Wilson and Keefer 1985 Jibson

$Code available on server at httpwwwiamgorg

CGEditorindexhtm

Corresponding author Tel +39+80-544-3166 fax

+39+80-544-3165

E-mail address albertoreficebainfnit (A Refice)

0098-300402$ - see front matter r 2002 Elsevier Science Ltd All rights reserved

PII S 0 0 9 8 - 3 0 0 4 ( 0 1 ) 0 0 1 0 4 - 2

1993) However to deal with some of the weaknesses

associated with the original deterministic model

probabilistic seismic slope stability techniques are being

used These are usually capable of quantifying and then

mapping a measure related to the likelihood of slope

failure of any particular terrain location Specifically by

incorporating the variability of some of the parameters

entering the model these methods give a measure of the

probabilities for shallow slope failure during future

earthquakes The general approach consists in treating

some parameters as random variables rather than fixed

values The details of how these variables are then used

to obtain the final predictive quantities differ with each

particular application or author For example in

Mankelow and Murphy (1998) it is shown that

modeling uncertainties as probability distribution func-

tions improves the forecasting capabilities of Newmarkrsquos

model The authors propagate the uncertainty through

the model equations determining the statistical para-

meters of the final probability distribution for the

Newmark displacement All distributions are modeled

as Gaussian and thus characterized by their mean and

standard deviation

Other examples of probabilistic techniques used in

landslide hazard zonation are in van Asch and Mulder

(1991) Luzi et al (1998) Chung and Fabbri (1998) and

Massari and Atkinson (1998)

Although the Gaussian hypothesis is simple to deal

with and allows a complete description of all the

statistical variability to be obtained through a relatively

small computational effort (Luzi et al 1998 Mankelow

et al 1998) it is sometimes considered too simple for

real applications However the same methodology used

for Gaussian distributions can be adapted to a number

of other statistical probability density functions (pdfs)

Nevertheless the most efficient approach to deal in a

general way with non-Gaussian distributions is Monte

Carlo simulation Due to intensive computational needs

effective applications of Monte Carlo simulation tech-

niques for risk analysis studies have only recently begun

to be used extensively (Vose 1996)

In this paper a software implementation of a

methodology is described which calculates statistical

probabilities of Newmark displacements for a given

earth surface region on a pixel-by-pixel basis The

software accepts in input geological geotechnical

geomorphological and seismological parameters in

the form of raster matrices and tables of numerical

values containing statistical parameters for the assumed

distributions of some of the input quantities These

parameters are used to perform a series of Monte

Carlo simulations in which random samples are

generated and then combined through Newmarkrsquos

model equations to obtain probabilistic distributions

of the final Newmark displacement These can then be

cast into maps displaying for example the probability

that the predicted displacement exceeds a given thresh-

old value for each map pixel

Maps of this kind are particularly important in

regions characterized by several seismic events per year

and low return periods for large magnitude events such

as the Irpinian region (Southern Italy) The active

tectonics of this area and its complex geological history

result among other things in the presence of steep and

unstable slopes that undergo active degradation Thus

extensive landsliding has occurred during earthquakes in

the past In this paper an application of probabilistic

techniques to this particular region is presented A

probabilistic earthquake-induced landslide hazard map

is built and compared with the results provided by other

methodologies

The paper is organized as follows In Section 2 some

general background regarding probabilistic applications

of Newmarkrsquos model for seismically induced landslide

hazard assessment is reviewed in Section 3 the details of

the program implementation are given then in Section

4 the Sele Valley test site is described and in Section 5

results of the described approach over this test landslide

area are presented and compared with other methods

Finally in Section 6 some conclusions are drawn

2 Landslide risk assessment through probabilistic

methods

21 Newmarkrsquos model for landslide risk assessment

Due to the problems associated with assigning

particular dynamic factors of safety and since it is

increasingly being found to be a more realistic method

of analysis the dynamic displacement model developed

by Newmark (1965) is being used instead of more

traditional pseudo-static seismic slope stability models

in many studies on earthquake-triggered landslides

(Wieczorek 1984 Jibson 1993 Mankelow and Mur-

phy 1998)

Newmarkrsquos analysis (Newmark 1965 Jibson 1993)

models the part of the slope which is under stress as a

uniform block sliding over an infinite inclined surface

With this approach the static factor of safety is

computed as (Jibson 1993)

FSstat frac14c0 thorn frac12ethg mgwTHORNz cos2 atan f0

gz sin a cos a eth1THORN

where c0 is the effective cohesion f0 the effective friction

angle g the material unit weight gw the unit weight of

water m represents the fractional depth of the water

table with respect to the total slide depth z stands for

the slope-normal thickness of the failure slab and a is

the slope angle

Newmarkrsquos analysis then calculates the displacement

of a slope as it is subjected to an earthquake Slope

A Refice D Capolongo Computers amp Geosciences 28 (2002) 735ndash749736

failure will occur and movements will be initiated when

the critical acceleration of the slope ac is exceeded The

quantity ac represents the acceleration required to

overcome the frictional resistance of the slope material

and thus initiate sliding it can be calculated as follows

ac frac14 ethFSstat 1THORN g sin a0 eth2THORN

where g is the Earthrsquos gravity acceleration and a0 is the

thrust angle of the landslide block For shallow land-

slides one can assume a0 frac14 aTo determine the Newmark displacement Dn after

Jibson et al (1997) an empirical logarithmic regression

equation can be used relating Dn the critical accelera-

tion ac and the Arias Intensity IA (a measure of the

earthquake energy)

log Dn frac14 07605 log IA 09965 log ac 0773 eth3THORN

where Dn is expressed in m IA in m s1 and ac in g units

This empirical relation has been derived from an

extensive dataset of seismic records collected in different

regions Although approximate it constitutes a useful

relation which allows information about the Newmark

displacement to be derived from seismic and geotechni-

cal records

The Arias intensity is often modeled through another

empirical logarithmic relation as a function of the

earthquake magnitude M and the site distance from

the seismogenic fault R derived in Wilson and Keefer

(1985)

log IA frac14 M 2 log R 41 eth4THORN

where IA is expressed in m s1 M is the earthquake

magnitude in the Richter scale and R is in m

The two preceding equations have been used in the

present work as a reasonable and simple computational

tool for deriving information about the Newmark

displacement given a certain geotechnical situation and

supposing a certain seismic shaking strength as is

common practice (see Mankelow and Murphy 1998)

No attempt has been made to test the validity of the

preceding relations for the geological conditions of

southern Italy This goes beyond the scope of the present

work and constitutes an interesting subject for future

research

22 Probabilistic framework

Newmarkrsquos model requires the knowledge of several

parameters some of which have to be estimated from

geotechnical field work (eg cohesion and friction

angles) others are obtained from seismic records (Arias

intensity) and some can be derived nowadays spatial

topographic data through GIS programs (slope maps)

In the situation of geotechnical data properties of soil

types are derived from laboratory tests and their spatial

variability is extrapolated on the basis of geological

maps Often such properties are difficult to determine

accurately moreover lithological distinctions are often

not reported on geological maps so that one may be led

to assume a homogenous distribution of parameters for

different lithologies of the same geological unit Finally

a poor positional accuracy is often related with the scale

of the geological map used to derive the spatial

distribution of the parameters

For these reasons the model parameters should be

thought of more as probabilistically distributed rather

than having single deterministic values (see Miles et al

2000)

The statistical uncertainties in many real-world data

can be modeled by a large variety of pdfs Although the

most used are the simple uniform or the Gaussian many

natural quantities cannot be assumed to follow these

distributions This is especially true for quantities which

have to be estimated through repeated field work often

performed in heterogeneous conditions or judged by

expertsrsquo opinions In these cases it is often preferred to

use more general distributions to model their uncer-

tainty For example the b distribution is often chosen

for its simplicity either in its original form or modified

such as in the so-called bPERT which is a mathematical

variant defined by the three parameters of minimum

most likely and maximum value (see Vose 1996 for

further details on the bPERT and its use)

3 Implementation

In this section the details of our technique are

presented The software developed consists of a series

of Matlabs functions performing specific tasks This

allows to have a very flexible framework which can be

adapted to many situations and geographic areas by

simply changing eg the statistical distributions or the

Monte Carlo simulation techniques used A scheme of

the method is illustrated in Fig 1

31 Input files

Input to the software is constituted by a set of raster

maps and tables whose file names are defined in a

parameter file Some of the maps represent information

whose accuracy is already at the pixel level such as the

slope map or the Arias intensity map Other quantities

are defined over homogeneous spatial regions or units

and are thus specified by a raster map of the unit indices

and a table in which a series of parameters is attached to

each unit index For example a lithological index map

can have a series of geotechnical parameters linked to

each lithological unit

For obvious reasons statistical variability is typically

connected to this second type of input data although in

principle any variable could be considered as a set of

A Refice D Capolongo Computers amp Geosciences 28 (2002) 735ndash749 737

probability distributions since the program can treat

each map pixel independently

Different index maps could be used for different

parameters (eg one for the cohesion another for the

friction angle etc) In these cases a simple merging of

the various index maps and consequent splitting of

homogeneous regions would yield a new index map in

which each unit would have different overall character-

istics

32 Monte Carlo simulations

Simulations are performed by Monte Carlo sampling

For each particular set of values statistically rando-

mized samples can be generated as drawn from common

distributions such as the Gaussian the simple triangu-

lar or the mentioned bPERT pdf

Each statistical sample is generated by the stratified

sampling methodology known as Latin Hypercube

Sampling (LHS) which is based on the subdivision of

the data interval into a certain number of sub-intervals

of equal probability (Vose 1996) LHS sampling allows

realistic looking distributions to be obtained from a

relatively limited number of samples Thus fewer

samples can be used without significant loss of accuracy

leading to an overall gain in computational efficiency

Moreover importance of sampling techniques such as

LHS allows low-probability tails in the simulated

distributions better to be reproduced

33 On the use of asymmetric pdfs

Fig 2 shows an example of Monte Carlo analysis

performed for one particular location of the landslide test

site in Southern Italy Histograms of the three random

samples of values simulating the cohesion c0 friction

angle f0 and water table fractional depth m with bPERT

distributions are shown on the left part of the figure The

random samples consisting of 100000 numbers each

were then combined using Eqs (1)ndash(3) with the mor-

phological (slope angle) and seismic (Arias intensity)

quantities related to the specific site to obtain the Dn

sample values whose histogram is shown on the graph on

the right of the figure This graph also shows two

continuous curves representing the theoretical distribu-

tions obtained through the application of lsquolsquostandardrsquorsquo

statistical methods which are usually applied to Gaussian

distributions Curve (a) shows the theoretical bPERT

distribution obtained by propagating the minimum most

likely and maximum values of each of the three input

parameters through the Newmark model equations

Curve (b) shows the bPERT distribution derived by

Fig 1 Schematic representation of computational methodology described in text In parameters table for simplicity number of

parameters Pk for fixed geotechnical parameter k k frac14 1yM is represented as fixed for all N lithological indices although in principle

different pdfs involving different numbers of parameters could be used for each lithology index Output dataset is shown as consisting

of whole histogram samples for output data (eg Newmark displacement) although in most examples only single value per pixelmdash

typically pdf integral above fixed thresholdmdashneeds to be represented on output map


estimating the minimum most likely and maximum

parameters from the obtained experimental distribution

through standard non-linear least-squares estimation

techniques such as a LevenbergndashMarquardt algorithm

(Press et al 1992) It can be noted that both curves show

a poor agreement with the sampled distribution obtained

by performing the calculations over each of the random

samples as expected This example shows how conven-

tional methodologies usually accepted for simulations

performed with Gaussian assumptions are not suitable

when more general types of statistical distributions are

used In these situations retaining the whole random

Fig 2 Example of Monte Carlo simulations Histograms of randomly generated samples for effective cohesion c0 friction angle f0 and

water table fractional depth m are shown on left for given location of landslide test site Resulting histogram of calculated Dn sample is

shown on right Continuous curves represent analytical distribution obtained by propagating minimum most likely and maximum

values for three input parameters through equation described in section 2 (a) and best fitting bPERT distribution obtained through

standard least-squares estimation (b) respectively


samples throughout the calculations is required in order

to avoid errors and approximations

34 Map construction

In the proposed methodology the random samples

generated for each lithological unit are retained

throughout all the map construction operations This

avoids unnecessary assumptions about their behavior

when they are used to derive features such as the critical

acceleration or the Newmark displacement Each

statistical random sample is thus combined on a pixel-

by-pixel basis with the remaining quantities such as the

slope angle and the Arias Intensity values

The whole random samples representing the various

model intermediate and final parameters such as the

factor of safety critical acceleration and the Newmark

displacement are thus retained for each pixel This as

demonstrated in the previous section is the correct way

to deal with general pdfs (non-Gaussian)

The entire three-dimensional datasets representing the

histograms of each map pixel can be stored However to

avoid excessive disk usage and since hazard assessment

results are traditionally conveyed in the form of two-

dimensional maps in most situations it is sufficient to

store only a small number of parameters for each pixel

of a given output quantity For example the most useful

output for the Newmark displacement distribution is the

probability that Dn exceeds a certain given threshold

value Such a quantity indicates the degree of landslide

hazard associated with each map site given a certain

earthquake intensity specified by the Arias Intensity

value

To derive such a probability map a certain threshold

value is determined for the Newmark displacement

then the experimental Dn distributions associated with

each pixel are numerically integrated above the thresh-

old The result gives an estimated probability of Dn

exceeding the threshold value

4 Description of a case study the Sele Valley

In this section some background information is given

about the region of the Sele Valley in southern Italy

characterized by several landslide sites and on which the

technique described in this work has been applied as a

case study

A location map of the area is shown in Fig 3 The

valley has undergone strong seismic shaking during the

past The 1980 Irpinian earthquake for example has

triggered many landslides and rockfalls on the valley

flanks The Sele Valley is the object of intensive studies

mainly due to the peculiar character of its landslide

distribution (Wasowski et al 2000)

41 Outline of the geology and geomorphology of the

upper valley of the Sele river

The outcropping lithologies can be broadly divided

into four main groups schematically shown in Fig 4

Carbonate units Limestones dolomitic limestones

and dolomites (Trias-Cretaceous) form the Picentini

mountains and the Mt OgnamdashMt Marzano ridge In

the present work carbonate terrains have been sepa-

rated from the dolomites only where their physical

characteristics and their geotechnical behaviour were

particularly different

Irpinian units Terrigenous Miocene sediments known

as Castelvetere flysch They consist mainly of sandstone

and conglomerate embedded in clayey-marly strata

which have become mixed with limestone blocks that

range in size from a few to several thousands m3 These

lithological units are referred to in the text also as flysch

or flysch formations

Sicilide units Extensive overburden of variegated

clays shales marls cherts and sandstone (Upper

Cretaceous-Paleocene) This formation is marked

mainly by clay-rich lithofacies and is characterized by

high heterogeneity and anisotropy It shows macro-

Fig 3 Location map of Italian southern Apennines area used

as test site Sele Valley is indicated by small rectangle


scopic slope deformation and mass movement in

general

Quaternary superficial deposits They consist of

colluvial and alluvial fan sediments The fan sediments

are carbonates eroded from the mountain basins and

from Quaternary gelifraction of the clastic deposits at

the mountain front In the text and the figures they are

also referred to as alluvium and colluvium

Various tectonic phases created the present-day

structure of the study area (Scandone 1973) The

Apennine tectonics that had already begun in the

Middle-Upper Miocene and continued throughout the

Plio-Pleistocene determined large-scale dislocation and

associated intensive deformations By contrast the

Pleistocene was characterized by extensional tectonics

that have mainly influenced the present-day morphology

(Ortolani 1975) The Quaternary tectonics have been

characterized by a general and significant uplift

Recently the role of strike-slip tectonics has been

emphasized (with different opinions and conclusions)

as being responsible for the recent deformation and

evolution of the southern Apennines (Cinque et al

1992)

The morphology of the study area is strongly

dependent on its structural and neotectonic

evolution Two different landscapes can be recognized

one typical of the carbonate domains the other

of the flysch formations and colluvium and alluvium

Fig 4 Lithological units used in simulation


terrain Carbonate rocks border the eastern and

western margin of the Sele valley and are delimited by

bounding faults

A slope map of the test area is shown in Fig 5 The

outcrops are characterized by steep and sometimes

subvertical slopes The flysch formations and collu-

viumalluvium terrain show low-medium angle slopes

(10ndash12 deg on average)

The hydrographic network testifies a strong structural

control only in part guided by tectonic discontinuities

and shows a dendritic pattern with a tendency to be

rectangular Mass movement is the principal geo-

morphic process active in this area

The hydrogeological setting has also undergone

extensive investigations (Cotecchia et al 1986) The

high permeability of the carbonate rocks due to

fracturing and karst phenomena allows a large accu-

mulation of water This water is confined by the flysch

acting as an impervious lsquolsquobeltrsquorsquo around the carbonate

massif A large number of springs are located at the

scarp toe of the carbonate massives In particular

springs are located at the contact between the carbonate

aquifer and the flysch formations (termed Irpinian units

in the description of Section 41)

42 Historic seismicity and 1980 earthquake main

parameters

This part of the Southern Apennines was hit by at

least 48 earthquakes of intensities up to IX in the

MercallindashCancanindashSieberg (MCS) scale between 63 AD

and 1980 In this study area earthquakes with intensity

of X MCS occurred in 1571 (Vallo di Diano) 1694

(Basilicata Settentrionale) 1702 (Benevento) 1732

Fig 5 Slope map of test area Legend units are degrees


(Irpinia) 1851 (Vulture) 1930 (Irpinia) and 1980

(CampaniandashLucania) Unfortunately information on

the triggered landslides are available only for the most

recent event The main parameters for this earthquake

are shown in Table 1 In Pantosti and Valensise (1990) it

is suggested that the 1980 earthquake must be con-

sidered as the early stage of a new tectonic regime They

show how the trend of the 1980 surface fault does not

follow any previously mapped structure and occurs at an

average elevation of 1200 m much closer to the top of

the range (1400 m) than to the Upper Sele valley floor

(300 m) The computed seismic moment is

18 1023 Nm1

Fig 6 shows the map of the Arias Intensity (IA) for

the test area as computed through Eq (4)

In Agnesi et al (1980) data pertaining to 50 landslides

that occurred after the 1980 earthquake were gathered

The area consisted of carbonate rock outcrops that were

only marginally influenced by mass movements Rock-

falls and topples were confined to the steep slopes around

the carbonate relief and to some karst cavities whose

roofs collapsed forming dolines Numerous landslides

occurred in the flysch formations Several of these were

reactivations of ancient or dormant landslides mainly of

Table 1

Source Parameters of 23 November 1980 earthquake

Location 401450Nndash161180E

Depth of focus 18 103 m

Magnitude of main shock (Richter scale) 69

Intensity at epicentre (MCS scale) X

Maximum acceleration of the EndashW

component (recorded at Sturno)

033 g

Origin time 1834

Duration gt70 s

Fig 6 Map of Arias intensity (IA) of test area calculated from 1980 Irpinian earthquake seismic data Units are in m s1


slide-flow type The morphology and the type of post-

earthquake landslides do not significantly differ from the

pre-earthquake existing landslides

Earthquake-triggered landslides are markedly predo-

minant on the western valley side both in flysch and in

carbonate rocks Such a peculiar spatial distribution is

being intensely studied since it is difficult to explain with

the simple hypothesis of similar terrain characteristics of

both valley sides which could be assumed by the

available ground data

43 Brief outline of the geotechnical features

In Cotecchia et al (1992) a study on the geotechnical

behavior of flysch units in the Sele valley is reported

The flysch formation of lsquolsquoArgille varicolorirsquorsquo part of

Sicilide Units must be considered a lsquolsquostructurally

complexrsquorsquo formation from both a geological and a

geotechnical point of view This is due to its marked

heterogeneity anisotropic nature the presence of

irregular lithological alterations together with the

widespread variously oriented discontinuities and the

structural attitude conditioned on both small and large

scale by intense tectonic and deformation history (Esu

1977) The results of the ongoing mineralogical and

geochemical studies reveal a predominance of smectite

and illite as the clay component Small and large scale

geotechnical behavior seems to be different In situ

residual strength values have been obtained by back

analysis of major and minor mass movements part of

which were reactivated after the 1980 earthquake

(Cotecchia et al 1992) Residual frictional angles

between 12 and 15 deg were calculated (Bellino and

Maugeri 1985 Cotecchia et al 1986)

5 Simulation results

In this section the results of the simulations

performed over the study region are shown To

investigate the potential of the method two kinds of

simulations were performed First a series of values was

established for the minimum most likely and maximum

parameters which characterize bPERT distributions for

the three geotechnical quantities of cohesion friction

angle and water table depth

The other parameters were assumed as fixed in these

simplified experiments although they can also be easily

modeled probabilistically in the framework of the

proposed method This choice was made to keep the

conditions simple Moreover the simulations were

performed with a focus on the variability of geotechnical

parameters more than that of other quantities

All the numbers were chosen after a critical review of

the related literature nevertheless they are often the

result of abstraction and conjecture due to the

insufficient detail with which such parameters are

described for our particular lithologic types They

should be considered here mainly as representative

values

For comparison another series of simulations was

performed by adopting Gaussian distributions for the

Table 2

Statistical parameters used for simulations with bPERT pdfs

Type c0 (kPa) f0 (deg) m g (kNm3)

Min ml Max Min ml Max Min ml Max

Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20

Alluvium and colluvium 0 3 10 15 35 40 05 08 1 15

z frac14 75m gw frac14 9807kN m3

Table 3

Statistical parameters used for simulations with Gaussian pdfs

Type c0 (kPa) f0 (degrees) m g (kNm3)

mean SD mean SD mean SD

Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20

Alluvium and colluvium 50 16 275 42 075 008 15



mentioned parameters with means and standard

deviations derived so as to best approximate the

bPERT pdfs with the obvious limitation of symmetry

around the mean The results of this last type of

simulation are in fact the same as could be obtained by

the pseudo-deterministic methodology described earlier

consisting of propagating the means and standard

deviations through the model equations to have a final

value for the Dn statistical parameters

Table 2 reports the various parameters used for the

simulation with bPERT distribution functions whereas

Table 3 shows the corresponding parameters used in the

simulations with Gaussian pdfs

A slope map was derived from digital elevation data

of the area (see Fig 5) whereas the Arias intensity IA

was modeled from seismological records (see Fig 6)

Fig 7 shows the main landslide and rockfalls triggered

by the 1980 earthquake (see Section 43)

The slope and the landslide maps are shown as draped

on a hill-shaded 3D view of the DEM used in the

simulations as well as the resulting landslide probability

hazard maps described in the following

Figs 8 and 9 show the Dn probability maps obtained

from Gaussian and bPERT simulated samples respec-

tively As can be noted both maps exhibit consistent

levels of estimated hazard on the eastern side of the

valley and a considerably lesser one on the western side

This is in contrast with the actual situation in which the

western flank of the valley is more subjected to landslide

activity as can be inferred from the higher density of

landslide areas shown by the map in Fig 7 This

behavior is probably due to the simple modelization of

the lithology and geotechnical features of the area

Nevertheless it can be seen that less grey areas are

generated on the eastern flank of the valley by using

bPERT pdfs than by using the Gaussian hypothesis for

Fig 7 Location of landslides and rockfalls triggered by 1980 earthquake on Sele Valley test site shown as light gray and white areas

respectively Seismogenetic fault of 1980 Irpinian earthquake (dashed line) is also shown


the pdfs A better agreement is therefore obtained

between the reality and the model by allowing the

statistical distribution to model uncertainties in a non-

symmetrical and thus more realistic way

Both the probabilistic approaches lead to a better

agreement with reality than a completely deterministic

model see the results shown in Fig 10 for comparison

(details can be found in Capolongo 1999)

6 Conclusions

We have presented an approach to compute prob-

abilistic hazard maps for seismically induced landslides

Based on Newmarkrsquos displacement method the proce-

dure allows some of the uncertainties usually associated

with the geological geomorphological or seismological

data involved in the model under the form of statistical

distributions to be considered

The procedure calculates and stores histogram

information about the derived quantities such

as the Newmark displacement Dn on a pixel-by pixel

basis This approach allows a considerable degree of

flexibility in modeling real-world estimates of quantities

usually difficult to model as Gaussian-distributed

Probability threshold maps can then be derived for

indicative parameters such as the Newmark displace-

ment as a representation of the spatial distribution of

the seismic-landslide hazard throughout the area under

study

Fig 8 Dn probability map obtained with methodology described in text using Gaussian pdfs for statistical modeling Filled areas

from white to black indicate increasing probability of Dn exceeding threshold value of 01m


The application of the methodology to a landslide

area in southern Italy has shown consistent improve-

ments in the capabilities to predict potentially hazardous

zones compared to other methods although many

problems are yet to be solved due to the geologic

complexity of the site Nevertheless the results are

encouraging further studies and improvements of the

presented approach

The methodology implemented as a Matlabs suite of

functions is built in a modular fashion and can be

easily expanded and enriched with more complex

features For example other models can be used rather

than Newmarkrsquos different sampling distributions can be

used to simulate different kinds of behavior or the

model can be adapted to different geographic zones

Moreover different sampling criteria could be intro-

duced or further statistical Monte Carlo tools could be

added to control other features of the simulated

quantities such as correlation between different vari-

ables or spatial autocorrelation for certain parameters

including fractal characteristics The modularity and

compactness of the approach allows an almost seamless

integration into existing GIS environments

Acknowledgements

The authors would like to thank Dr Joseph

Mankelow and Dr David Giles for the useful discus-

sions and Dr Janusz Wasowski and Dr Vincenzo Del

Gaudio of the CERIST-CNR of Bari for their kind

permission to use some of their data and for their

support They also thank the two anonymous reviewers

for the insightful comments and useful suggestions

Fig 9 Same as Fig 8 but obtained by using bPERT pdfs for statistical modeling


References

Agnesi V Carrara A Macaluso T Monteleone S

Pipitone G Sorriso-Valvo M 1980 Osservazioni pre-

liminari sui fenomeni di instabilita dei versanti indotti dal

sisma del 1980 (alta valle del sele) (preliminary observations

about versant instability phenomena induced by the 1980

earthquake (alta valle del sele)) Geologia Applicata e

Idrogeologia 17 79ndash93

Bellino S Maugeri M 1985 Confronto fra i valori di

resistenza residua ottenuti con diverse apparecchiature

anulari di taglio (comparison between residual resistance

values obtained with different annular cutting devices)

Rivista Italiana di Geotecnica 2 101ndash111

Burrough P 1986 Principles of Geographic Information

Systems for Land Resources Assessment Clarendon Press

Oxford UK 195p

Capolongo D 1999 GIS techniques for estimating earth-

quake-triggered landslide hazards PhD Dissertation

Dipartimento di Geologia e Geofisica Universita degli

studi di Bari 98p

Chung CF Fabbri AG 1998 Three Bayesian prediction

models for landslide hazard In Proceedings of The Annual

Conference of the International Association for Mathema-

tical Geology (IAMG 98) Vol I Ischia Island Naples

Italy pp 204ndash211

Cinque A Patacca E Scandone P Tozzi M 1992

Quaternary kinematic evolution of the South

Apennines relationship between surface geological features

and deep lithospheric structures Annali di Geofisica 36

249ndash260

Cotecchia V Del Prete M Tafuni N 1986 Effects of

earthquake of 23rd November 1980 on pre-existing land-

slides in the Senerchia area (southern Italy) In Proceedings

Fig 10 Dn map generated by deterministic method Fixed values were used for c0 f0 and m parameters to derive deterministic

Newmark displacement values On areas highlighted in black Dn value exceeds 01 m


of International Symposium on Engineering Geological

Problems in Seismic Areas Vol 4 Bari Italy pp 1ndash46

Cotecchia V Salvemini A Simeone V Tafuni N 1992

Comportamento geotecnico delle unita sicilide ed irpine

affioranti nelle alte valli dei fiume sele e ofanto ad elevato

rischio sismotettonico (geotechnical behaviour of sicilide

and Irpine units outcropping in the high valleys of the sele

and Ofanto rivers of high seismotectonic risk) Geologia

Applicata e Idrogeologia XXVII 1ndash47

Esu F 1977 Behaviour of slopes in structurally complex

formations In Proceedings of International Symposium on

the Geotechnics of Structurally Complex Formations Vol

2 Capri Italy pp 292ndash304

Jibson RW 1993 Predicting earthquake-induced landslide

displacements using Newmarkrsquos sliding block analysis

Transportation Research Record 1411 9ndash17

Jibson RW Harp EL Michael JA 1997 A method for

producing digital probabilistic seismic landslide hazard

maps an example from the Los Angeles California area

Open-file Report 98-113 US Geological Survey available

online at httpgeohazardscrusgsgovpubsofr98-113

ofr98-113html

Luzi L Pergalani F Terlien MTJ 1998 A probabilistic

approach to assess uncertainty of landslide vulnerability to

earthquakes using GIS techniques In Proceedings of the

Annual Conference of the International Association for

Mathematical Geology (IAMG 98) Vol I Ischia Island

Naples Italy pp 235ndash240

Mankelow JM Giles D Murphy W 1998 Probability

density function modeling for earthquake triggered land-

slide hazard assessments In Proceedings of the Annual




Mankelow JM Murphy W 1998 Using GIS in the

probabilistic assessment of earthquake triggered landslides

hazards Journal of Earthquake Engineering 2 (4) 593ndash623

Massari R Atkinson PM 1998 Using the GIbbs sampler in

mapping susceptibility to landsliding In Proceedings of the




Miles SB Keefer DK Nyerges TL 2000 A case study in

GIS-based environmental model validation using earth-

quake-induced landslide hazard In Proceedings of Fourth

International Symposium on Spatial Accuracy Assessment

in Natural Resources and Environmental Sciences Am-

sterdam pp 104ndash114

Newmark NM 1965 Effects of earthquakes on dams and

embankments Fifth Rankine Lecture pp 139ndash160

Ortolani F 1975 Assetto strutturale dei monti picentini della

valle del sele e del gruppo di monte marzanomdashmonte ogna

(appennino meridionale)(structural setup of monti picentini

sele valley and the mt marzanomdashmt ogna group (southern

Appennines)) Bollettino della societa Geologica Italiana 94

209ndash230

Pantosti D Valensise G 1990 Faulting mechanism and

complexity of the 23 november 1980 CampaniamdashLucania

earthquake inferred from surface observations Journal of

Geophysical Research 95 15319ndash15341

Press WH Flannery BP Teukolsky SA Vetterling WT

1992 Numerical Recipes The Art of Scientific Computing

2nd Edn Cambridge University Press Cambridge UK

994p

Scandone P 1973 Studi di geologia lucana Nota illustrativa

della carta dei terreni della serie calcareo-silico

marnosa Bollettino Societa Nat Napoli 81 225ndash300

(in Italian)

Van Asch TWJ Mulder HFHM 1991 Statistical

geotechnical and hydrological approaches in landslide

hazard assessment of mass movements In UNESCO-ITC

Project on Mountain Hazard Mapping in Andean Environ-

ment using Geographical Information Systems Expert

Workshop Bogota Colombia p 31

Vose D 1996 Quantitative Risk Analysis A Guide to Monte

Carlo Simulation Modeling Wiley Chichester England

328p

Wasowski J Del Gaudio V Pierri P 2000 Landslide

triggering by the 1980 Irpinian earthquake re-visited the

case of the Sele valley In Geophysical Research Abstracts

Vol 2 European Geophysical Society available on CD-

ROM

Wieczorek GF 1984 Preparing a detailed landslide-inventory

map for hazard evaluation and reduction Bulletin of the

Association of Engineering Geologists 3 337ndash342

Wilson RC Keefer DK 1985 Predicting the areal limits of

earthquakes induced landslides In Ziony J (Ed) Evalu-

ating Earthquake Hazards in the Los Angeles Metropolitan

Area US Geological Survey Professional Paper 1360 pp

317ndash345


1993) However to deal with some of the weaknesses

associated with the original deterministic model

probabilistic seismic slope stability techniques are being

used These are usually capable of quantifying and then

mapping a measure related to the likelihood of slope

failure of any particular terrain location Specifically by

incorporating the variability of some of the parameters

entering the model these methods give a measure of the

probabilities for shallow slope failure during future

earthquakes The general approach consists in treating

some parameters as random variables rather than fixed

values The details of how these variables are then used

to obtain the final predictive quantities differ with each

particular application or author For example in

Mankelow and Murphy (1998) it is shown that

modeling uncertainties as probability distribution func-

tions improves the forecasting capabilities of Newmarkrsquos

model The authors propagate the uncertainty through

the model equations determining the statistical para-

meters of the final probability distribution for the

Newmark displacement All distributions are modeled

as Gaussian and thus characterized by their mean and

standard deviation

Other examples of probabilistic techniques used in

landslide hazard zonation are in van Asch and Mulder

(1991) Luzi et al (1998) Chung and Fabbri (1998) and

Massari and Atkinson (1998)

Although the Gaussian hypothesis is simple to deal

with and allows a complete description of all the

statistical variability to be obtained through a relatively

small computational effort (Luzi et al 1998 Mankelow

et al 1998) it is sometimes considered too simple for

real applications However the same methodology used

for Gaussian distributions can be adapted to a number

of other statistical probability density functions (pdfs)

Nevertheless the most efficient approach to deal in a

general way with non-Gaussian distributions is Monte

Carlo simulation Due to intensive computational needs

effective applications of Monte Carlo simulation tech-

niques for risk analysis studies have only recently begun

to be used extensively (Vose 1996)

In this paper a software implementation of a

methodology is described which calculates statistical

probabilities of Newmark displacements for a given

earth surface region on a pixel-by-pixel basis The

software accepts in input geological geotechnical

geomorphological and seismological parameters in

the form of raster matrices and tables of numerical

values containing statistical parameters for the assumed

distributions of some of the input quantities These

parameters are used to perform a series of Monte

Carlo simulations in which random samples are

generated and then combined through Newmarkrsquos

model equations to obtain probabilistic distributions

of the final Newmark displacement These can then be

cast into maps displaying for example the probability

that the predicted displacement exceeds a given thresh-

old value for each map pixel

Maps of this kind are particularly important in

regions characterized by several seismic events per year

and low return periods for large magnitude events such

as the Irpinian region (Southern Italy) The active

tectonics of this area and its complex geological history

result among other things in the presence of steep and

unstable slopes that undergo active degradation Thus

extensive landsliding has occurred during earthquakes in

the past In this paper an application of probabilistic

techniques to this particular region is presented A

probabilistic earthquake-induced landslide hazard map

is built and compared with the results provided by other

methodologies

The paper is organized as follows In Section 2 some

general background regarding probabilistic applications

of Newmarkrsquos model for seismically induced landslide

hazard assessment is reviewed in Section 3 the details of

the program implementation are given then in Section

4 the Sele Valley test site is described and in Section 5

results of the described approach over this test landslide

area are presented and compared with other methods

Finally in Section 6 some conclusions are drawn

2 Landslide risk assessment through probabilistic

methods

21 Newmarkrsquos model for landslide risk assessment

Due to the problems associated with assigning

particular dynamic factors of safety and since it is

increasingly being found to be a more realistic method

of analysis the dynamic displacement model developed

by Newmark (1965) is being used instead of more

traditional pseudo-static seismic slope stability models

in many studies on earthquake-triggered landslides

(Wieczorek 1984 Jibson 1993 Mankelow and Mur-

phy 1998)

Newmarkrsquos analysis (Newmark 1965 Jibson 1993)

models the part of the slope which is under stress as a

uniform block sliding over an infinite inclined surface

With this approach the static factor of safety is

computed as (Jibson 1993)

FSstat frac14c0 thorn frac12ethg mgwTHORNz cos2 atan f0

gz sin a cos a eth1THORN

where c0 is the effective cohesion f0 the effective friction

angle g the material unit weight gw the unit weight of

water m represents the fractional depth of the water

table with respect to the total slide depth z stands for

the slope-normal thickness of the failure slab and a is

the slope angle

Newmarkrsquos analysis then calculates the displacement

of a slope as it is subjected to an earthquake Slope














earthquake energy)








cal records





(1985)














research






















2000)
















3 Implementation









31 Input files
























istics


































































34 Map construction




























value












case study



































general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345














earthquake energy)








cal records





(1985)














research






















2000)
















3 Implementation









31 Input files
























istics


































































34 Map construction




























value












case study



































general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345










istics


































































34 Map construction




























value












case study



































general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345






















34 Map construction




























value












case study



































general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345




34 Map construction




























value












case study



































general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345



general





















1992)










bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345




bounding faults























parameters





















18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345














18 1023 Nm1












Table 1








033 g

Origin time 1834

Duration gt70 s

























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345
























































values



Table 2




Carbonate units 100 200 600 20 42 55 05 08 1 26

Irpinian units 0 3 5 5 40 50 05 08 1 21

Sicilide units 5 39 44 10 16 23 05 08 1 20



Table 3




Carbonate units 3500 833 375 58 075 008 26

Irpinian units 25 83 275 75 075 008 21

Sicilide units 245 65 165 22 075 008 20



















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345

















































6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345










6 Conclusions


















study











presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345









presented approach
















Acknowledgements










References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345


References















Oxford UK 195p




studi di Bari 98p










249ndash260




























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345























ofr98-113html


































209ndash230








994p




(in Italian)









328p





ROM








317ndash345


Documents

Probabilistic modeling of uncertainties in earthquake-induced landslide hazard assessment