13
Rock falls induced by earthquakes: a statistical approach S. Marzorati a , L. Luzi a , M. De Amicis b, * a Istituto Nazionale di Geofisica e Vulcanologia, via Bassini 15, 20133 Milano, Italy b Dipartimento di Scienze dell’Ambiente e del Territorio, Universita ` degli Studi di Milano-Bicocca, Piazza della Scienza 1, 20126 Milano, Italy Accepted 1 May 2002 Abstract During September and October 1997 a seismic sequence of moderate magnitude struck the Umbria and Marche regions, central Italy. As a consequence of the main shocks several rock falls were triggered along the flanks of the Valnerina valley, an important canyon formed by the erosion of the Nera river on limestone formations. This landslide data set was used to explore the correlation existing among rock falls and several causal factors, like slope angle, geology and strong ground motion parameters. All the data have been digitised and georeferenced with the aid of a Geographic Information System in the form of digital thematic layers. The landslide inventory has been overlaid to the maps of causal factors, and the result arranged in order to create a data structure suitable to perform a multivariate statistics. A multiple regression allowed to formulate a predictive rule that can be used to produce a rock fall susceptibility map in case of an earthquake, in regions with similar geologic and geomorphologic characteristics. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Rock fall; Earthquake; Geographic Information System; Umbria; Marche 1. Introduction The study of landslides induced by an earthquake plays an important role in the determination of seismic risk, as earthquakes can induce considerable damage to infrastruc- tures and cause life loss and injuries. Generally landslide hazard determination is approached by two main strategies: the detailed examination of single landslide cases, or the study of the distribution of mass movements over wide areas. The first approach to the problem investigates the physical behaviour of the phenomena and requires a detailed knowl- edge of limited areas, achieved by accurate surveys and in field measurements. The second one, on the contrary, requires large georeferenced data sets, to characterise the different distri- bution of environmental factors related to the landslide occurrences, and makes use of statistical analysis. Fundamental studies in landslide hazard induced by earthquakes have been conducted by Keefer [15,16], who analysed the distribution of types and magnitude of mass movements in active tectonic regions. He subdivided them according to type, material involved and velocity, after examining a set of 40 historical earthquakes. A general summary of the results achieved is shown in Table 1. Rock falls are not only the most abundant among landslide types, but also the ones that mostly endanger human lives. In fact about 90% of the movements classified as rock avalanches has caused the highest number of casualties, because of their extreme rapidity. Keefer and Wilson [24] have also been pioneers in evaluating dynamic slope stability over large areas, by applying the theory proposed by Newmark [20] to the territory of Los Angeles California. The model based on Newmark’s theory [20] still represents the simplest and at the same time most reliable among the ones proposed in literature. It models the landslide as a block sliding on an inclined surface, that represents the slope, and has a resistance to the movement expressed by an inertial force corresponding to the critical acceleration coefficient kc £ g where g is the acceleration due to gravity. The critical acceleration is the minimum ground acceleration required to initiate movement. The acceleration history is crucial to establish the amount of displacement, which is obtained by solving the equation of motion. Fig. 1 exemplifies the basis of the analysis. The acceleration is overlaid on the horizontal line represents the critical acceleration when the ground motion exceeds the critical threshold movement starts, when the ground motion does not exceed the critical acceleration, the slope remains stable. Many refinements of this technique have been proposed, 0267-7261/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S0267-7261(02)00036-2 Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 www.elsevier.com/locate/soildyn * Corresponding author. Fax: þ 39-2-6448-2895. E-mail address: [email protected] (M. De Amicis).

Rock falls induced by earthquakes: a statistical approach

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Page 1: Rock falls induced by earthquakes: a statistical approach

Rock falls induced by earthquakes: a statistical approach

S. Marzoratia, L. Luzia, M. De Amicisb,*

aIstituto Nazionale di Geofisica e Vulcanologia, via Bassini 15, 20133 Milano, ItalybDipartimento di Scienze dell’Ambiente e del Territorio, Universita degli Studi di Milano-Bicocca, Piazza della Scienza 1, 20126 Milano, Italy

Accepted 1 May 2002

Abstract

During September and October 1997 a seismic sequence of moderate magnitude struck the Umbria and Marche regions, central Italy. As a

consequence of the main shocks several rock falls were triggered along the flanks of the Valnerina valley, an important canyon formed by the

erosion of the Nera river on limestone formations. This landslide data set was used to explore the correlation existing among rock falls and

several causal factors, like slope angle, geology and strong ground motion parameters. All the data have been digitised and georeferenced

with the aid of a Geographic Information System in the form of digital thematic layers. The landslide inventory has been overlaid to the maps

of causal factors, and the result arranged in order to create a data structure suitable to perform a multivariate statistics. A multiple regression

allowed to formulate a predictive rule that can be used to produce a rock fall susceptibility map in case of an earthquake, in regions with

similar geologic and geomorphologic characteristics. q 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Rock fall; Earthquake; Geographic Information System; Umbria; Marche

1. Introduction

The study of landslides induced by an earthquake plays an

important role in the determination of seismic risk, as

earthquakes can induce considerable damage to infrastruc-

tures and cause life loss and injuries. Generally landslide

hazard determination is approached by two main strategies:

the detailed examination of single landslide cases, or the study

of the distribution of mass movements over wide areas. The

first approach to the problem investigates the physical

behaviour of the phenomena and requires a detailed knowl-

edge of limited areas, achieved by accurate surveys and in field

measurements. The second one, on the contrary, requires large

georeferenced data sets, to characterise the different distri-

bution of environmental factors related to the landslide

occurrences, and makes use of statistical analysis.

Fundamental studies in landslide hazard induced by

earthquakes have been conducted by Keefer [15,16], who

analysed the distribution of types and magnitude of mass

movements in active tectonic regions. He subdivided them

according to type, material involved and velocity, after

examining a set of 40 historical earthquakes. A general

summary of the results achieved is shown in Table 1. Rock

falls are not only the most abundant among landslide types,

but also the ones that mostly endanger human lives. In fact

about 90% of the movements classified as rock avalanches

has caused the highest number of casualties, because of their

extreme rapidity.

Keefer and Wilson [24] have also been pioneers in

evaluating dynamic slope stability over large areas, by

applying the theory proposed by Newmark [20] to the

territory of Los Angeles California. The model based on

Newmark’s theory [20] still represents the simplest and at

the same time most reliable among the ones proposed in

literature. It models the landslide as a block sliding on an

inclined surface, that represents the slope, and has a

resistance to the movement expressed by an inertial force

corresponding to the critical acceleration coefficient kc £ g

where g is the acceleration due to gravity. The critical

acceleration is the minimum ground acceleration required to

initiate movement. The acceleration history is crucial to

establish the amount of displacement, which is obtained by

solving the equation of motion. Fig. 1 exemplifies the basis

of the analysis. The acceleration is overlaid on the

horizontal line represents the critical acceleration when

the ground motion exceeds the critical threshold movement

starts, when the ground motion does not exceed the critical

acceleration, the slope remains stable.

Many refinements of this technique have been proposed,

0267-7261/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.

PII: S0 26 7 -7 26 1 (0 2) 00 0 36 -2

Soil Dynamics and Earthquake Engineering 22 (2002) 565–577

www.elsevier.com/locate/soildyn

* Corresponding author. Fax: þ39-2-6448-2895.

E-mail address: [email protected] (M. De Amicis).

Page 2: Rock falls induced by earthquakes: a statistical approach

such as the accounting for soil strain softening with

displacement, or liquefaction.

The main limitation of the analysis described is that it is

applicable only to those landslides which occur along pre-

defined or newly formed sliding planes, such as translational

or rotational slides. Different solutions should be therefore

sought for mass movements such as rock and soil falls or

avalanches.

When analysing those landslide types, the primary task

should be the identification of the areas where rock blocks or

boulders may detach. Then, a second phase consists in the

delimitation of the portions of slopes where boulders crush

in smaller parts, bounce and finally stop.

A deterministic approach, based on the knowledge of the

mechanical characteristics of rock slopes, is not frequently

adopted because of the great difficulty in determining the

many fundamental parameters needed.

Alternatively, a scenario analysis can evaluate qualitatively

the conditions that allow the sliding of blocks along planes and

discontinuities present in rock masses. It states that the

movement can initiate whenever the inclination of any

discontinuity exceeds the frictional resistance of the rock

mass. This second approach also requires detailed surveys of

slope discontinuities and is therefore not applicable when

calculating hazard over large areas.

The method here discussed is not based on a physical

theory, but on the observation in a large landslide data set.

The core of the analysis is represented by the quantification

of the spatial variability of mass movements and their

triggering factors, that can be easily achieved with the aid of

a Geographic Information System (GIS) [5]. The quantifi-

cation of the relations existing among the landslides and

their causal factors may be obtained by a statistical analysis,

that allows the formulation of most appropriate predictive

relation to describe the phenomenon.

This approach is limited too, as it can only detect the

areas where block and boulders can probably detach, but

does not account for the scenario of the landslide, that is the

determination of the block paths and their maximum run out

distance.

However, despite these limitations, it can be very useful

for land use planning and scenario definition, in case of an

earthquake.

2. Brief description of the area and the seismic sequence

The investigated area is located in the Umbria–Marche

Apennines, central Italy, where the Umbria–Marche sedimen-

tary sequence crops out. It is composed of a multi-layered

alternation of limestones, marly limestones, marls and flysch

sequences [7,3], that was first deformed by a compressive

structural phase, and subsequently dissected by normal faulting

during the Quaternary. Fig. 2 depicts a geological sketch of the

central Apennines and a zoom on the investigated area.

According to recent studies [19], the extensional

patterns are related to the crustal thinning processes

occurring in the Tyrrhenian Tuscan area. The Quaternary

normal faults led to the formation of intramountain

basins, of which the Colfiorito plain is a clear example,

and the seismicity of the area is mainly related to the

activity of these faults.

The seismic sequence, object of the study, lasted several

months, from September 1997 to May 1998, and was

characterised by a large number of shocks of moderate to

low intensity and shallow depth. The main shocks, with

moment magnitudes of 5.7 and 6.0, both occurred on

Table 1

Relative abundance of landslides in historical earthquakes (from Keefer [16])

Landslides type Number of cases

Rock falls, disrupted soil slides, rock slides Very abundant: .100.000

Soil lateral spreads, soil slumps, soil block slides, soil avalanches Abundant: 10.000–100.000

Soil falls, rapid soil flows, rock slumps Moderately common: 1.000–10.000

Sub-aqueous landslides, slow earth flows, rock block slides, rock avalanches Uncommon: 100–1.000

Fig. 1. Landslide displacement according to the model proposed by

Newmark [20]; the acceleration is overlaid to an horizontal line

representing the kc; as long as the ground motion does not exceed the

critical acceleration the slope remains stable.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577566

Page 3: Rock falls induced by earthquakes: a statistical approach

September 26th and affected an area close to the village of

Colfiorito, in the north. Subsequently, the seismic activity

migrated to the south in the zone close to the village of Sellano

where an earthquake with moment magnitude of 5.7 occurred

on October 14th [1,8]. The epicentral distributions of the

sequence shows a NW–SE trend, for a total length of about

30 Km (Fig. 3).

The area selected for the case study is the so called

‘Valnerina’ valley, where the shock of October 14th caused

the trigger of several rock falls. It is huge canyon formed by

the deepening of the river Nera through the Umbria–

Marche sedimentary sequence. The predominant formations

are layered and massive limestones, that are highly fractured

because of the intense tectonic deformations they experi-

enced; their resistance to erosion gives rise to very steep

slopes, whose predominant angles are in the range 35–458,

but can reach up to 708.

Most of the rock falls activated by the earthquake

occurred on pre-existing movements and only few of them

were newly formed. This testifies the high degree of

vulnerability of the territory before the earthquake.

The rock falls did not cause any casualties, but several

Fig. 2. Geologic sketch of the central Apennines and zoom over the investigated area.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 567

Page 4: Rock falls induced by earthquakes: a statistical approach

infrastructures were damaged, main and secondary roads and

tunnels. This caused the interruption of the communications

between the zone of Colfiorito and Norcia for several weeks.

In Fig. 4 two examples of rock fall show the spectrum of

the size of the blocks and the magnitude of the phenomena.

3. Data collection and mapping strategy

The selection of a statistical procedure for landslide

hazard zoning requires a remarkable amount of information

regarding the environmental variables connected to the

occurrence of rock falls and the tectonic activity. The

approach generally followed consists in the ‘slicing’ of the

territory into thematic pieces of information, termed data

layers, such as geology, topography, landslide inventory,

etc. Each layer is digitised, georeferenced and stored in a

GIS, so that the information regarding each site can be

accessible at once.

The research required the following information: (a) rock

fall distribution; (b) geology, (c) topography, and (d)

location of the accelerometric recording stations.

Fig. 3. Spatial distribution of the epicentres of the Umbria Marche sequence.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577568

Page 5: Rock falls induced by earthquakes: a statistical approach

The mass movement inventory was almost entirely mapped

in the field immediately after the earthquake. The zones not

accessible during the fieldwork were subsequently investi-

gated by the aerial photo interpretation of a set of photo’s taken

few days after the event. The resulting inventory of about 200

mass movements was drawn on ortophotomaps at 1:10,000

scale, with the intention of keeping separated trigger and

accumulation zones. They were subsequently digitised with

the aid of a manual digitiser (Fig. 5).

The geology map was obtained by digitising a set

of existing geologic sheets at different scales, produced by

the Umbria Region and by the Geologic Survey of Italy. About

80% of the area was covered by a set of maps at 1:10,000 scale

[21]. The remaining territory, in the east, was covered by the

1:100,000 scale maps produced by the National Survey of

Italy: the sheet n. 131, Foligno, and the sheet n. 132, Norcia.

As the small scale maps had coarse information about

superficial deposits, their detail was improved by adding the

results of the photo interpretation and the 1:2000 scale maps

produced for the microzoning study of the area. The picture of

the final map has been shown already in Fig. 2. The subsequent

elaboration of the geologic map consisted in its generalisation

into three classes, by aggregating the formations with the same

geotechnical performance: (a) massive and stratified lime-

stones; (b) stratified calcareous marls and marly limestones;

(c) superficial deposits, mainly formed by calcareous debris

Fig. 4. Example of rock falls occurred during the shock of October 14th

1997: (a) typical landslide morphology, (b) size of rock blocks.

Fig. 5. Landslide inventory map.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 569

Page 6: Rock falls induced by earthquakes: a statistical approach

(conglomerates and breccias with scarce matrix) and

alluvial terraces (conglomerates and breccias with abundant

matrix).

The topographic information was obtained from a set of

ortophotomaps at 1:10,000 scale, with 10 or 5 m contour

intervals in flat areas, and 50 m intervals in very steep

slopes. The procedure adopted was: (a) manually drawing of

the contours on a transparent sheet, (b) scanning, (c)

georeferencing of the tic points and (d) vectorising. The

Digital Elevation Model (DEM) was obtained by using the

Arc/Info ‘Topogrid’ algorithm [9], which is based on the

procedure by Hutchinson [11,12] that generates hydrologi-

cally correct DEM’s in a raster format. A picture of the

shaded relief of the area is shown in Fig. 6.

A DEM is the fundamental layer for obtaining the slope

angle distribution, which is a very meaningful parameter in

landslide hazard zoning. It is obtained by filtering the

topographic field to get the directional gradients. Here the

standard function ‘slope’ of the software Arc/Info [9] was

used.

Finally the map with the location of the accelerometric

recording stations, activated by the shocks, was of great

importance in determining the spatial variation of the strong

ground motion (Fig. 7).

All the maps that have been described above were

digitised in order to have a standard error smaller than 2 m,

that represents a good degree of accuracy when working at

1:10,000 scale. The small error in the digitising procedure

results in a good degree of confidence in the overlay

operations, that represent the core of the subsequent

analysis.

4. Determination of the seismic input

The study of the rock falls induced by the earthquake

needs a model that can reproduce the spatial variability of

the ground motion of the actual shock, and, at the same time,

can be easily implemented into a GIS. The straightforward

way is, with no doubt, the interpolation of the recorded

values. Unfortunately, the recording stations were very few

and so unequally spaced, that no geostatistics could be

performed without introducing large errors. A more suitable

approach was indeed the application of a predictive relation,

a formula for estimating the strong motion parameter at any

site as a function of the distance from the seismic source, the

earthquake magnitude and the soil type. The accuracy of

several relations proposed in literature could be tested using

the acceleration time histories recorded on October 14th,

made available by the Italian National Energy Company.

From the accelerometric records the following significant

parameters were selected: (a) the peak ground acceleration,

PGA (m/s2), (b) the peak ground velocity, PGV (m/s) and

(c) the Arias intensity Ia (m/s) [2]. The first two indices

represent the maximum recorded values of the acceleration

and velocity during the entire time history, that may

represent the triggering values for landslide initiation. The

Arias intensity is proportional to the integral of the squared

acceleration in time and can also be reasonably associated

with landslide occurrence [13].

Some of the most popular sets of predictive relations

have been tested proposed by: (1) Joyner and Boore [14]; (2)

Boore et al. [4]; (3) Campbell and Bozorgnia [6]; (4) Sabetta

and Pugliese [22]; and (5) Spudich et al. [23].

All the listed sets of relations provide an equation to

evaluate the PGA, three of them can determine the PGV and

only the one proposed by Sabetta and Pugliese [22]

estimates the Ia.

The accuracy test is based on the difference between the

theoretical and actual value, normalised on the actual value,

expressed in percentage, as:

Diff ¼Theoretical 2 Actual

Actual100 ð1Þ

The results for the PGA tell that all the proposed relations

overestimate the actual accelerations. The equation that best

fits the data is the one proposed by Spudich [23], if the

results is reduced of one standard deviation. This conclusion

is reasonable, as the relation is valid for extensional

structures, like the one analysed, and the data set on

which is based also includes Italian earthquakes. The

Fig. 6. Shaded relief of the investigated area.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577570

Page 7: Rock falls induced by earthquakes: a statistical approach

Fig. 7. Location of the accelerometric stations triggered by the shock of October 14th 1997.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 571

Page 8: Rock falls induced by earthquakes: a statistical approach

Fig. 8. Actual strong ground motion parameters versus predictive curves: (1) PGA; (2) PGV and (3) Arias Intensity.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577572

Page 9: Rock falls induced by earthquakes: a statistical approach

Spudich attenuation relation is given by,

log PGA ¼ 0:299 þ 0:229ðM 2 6Þ2 1:052 log D

þ0:112G^ s ð2Þ

where PGA is the peak ground acceleration (g ); M, the

moment magnitude; D ¼�r2

jb þ h2�1/2; where rjb is the

closest distance from the fault projection (km) and h is 7.27;

G is 0 for rock sites and 1 for soil sites; s ¼�s2

1 þ s22

�1/2;where s1 is 0.172 and s2 is 0.108.

Two of the predictive relations proposed by Sabetta and

Pugliese [22] best approximate the actual PGV and Ia.

The PGV relation is:

log PGV ¼ 20:828 þ 0:489M 2 logðR2 þ h2Þ1/2 þ 0:116S1

þ 0:116S2 ^ s ð3Þ

where PGV is the peak ground velocity (cm/s); M, the local

magnitude; R, the distance from the epicentre (km); h, 3.9;

S1 is 1 for shallow deposits and 0 in other cases; S2 is 1 for

deep deposits and 0 in other cases; and As is the standard

deviation (0.249).

The latter is:

log Ia ¼ 0:729 þ 0:911M 2 1:818 logðR2 þ h2Þ1/2

þ0:244S1 þ 0:139S2 ^ s ð4Þ

where Ia is the Arias Intensity (cm/s); M, the local

magnitude; R, the distance from the epicentre (km); h,

5.3; S1 is 1 for shallow deposits and 0 in other cases; S2 is 1

for deep deposits and 0 in other cases; and s is the standard

deviation (0.397).

The actual values of the strong ground motion par-

ameters, plotted against the predictive curves, are shown in

Fig. 8.

The spatial variability of the strong motion parameters,

that depends on the distance from the source and the soil

type, was calculated with the aid of a GIS. The predictive

relations were input in a raster map calculation and as an

example of the final result, the spatial variability of PGA, is

shown in Fig. 9.

5. Determination of a predictive rule for rock fall hazard

estimation

As already stated, the aim of the research was the

formulation of a predictive relation for rock fall hazard

estimation.

It was initially supposed that the main causal factors of

rock falls were; lithology, slope angle and strong ground

motion parameters. Therefore, the subsequent step of the

investigation was mapping the location of mass movements

and the distribution of triggering factors, a task that could be

easily achieved with the aid of a GIS.

The observations stored in the form of maps, represent

the spatial distribution of landslides and causal factors and

have to be converted into values indicating the degree of

hazard. A standard procedure in GIS is map overlay, a tool

that allows the calculation of the frequency of landslide

occurrences, given the concurrency of specified environ-

mental factors. After the overlay, the combinations of

presence/absence of landslide, geology type, slope angle,

and value of the strong ground motion parameter are stored

in a table.

The area of each unique combination is automatically

calculated, and the relative density of landslides is simply

the ratio of the landslide area present in each area, over the

total area:

Dr ¼Aland > Auc

Auc

ð5Þ

where Dr is the landslide relative density, Aland is the area

covered by the rock falls and Auc is the area of the unique

combination of several triggering factors.

This relative density can be treated as the conditional

probability of landslide occurrence, given a certain

combination of causal factors. It is worth noting that

whenever the term ‘landslide’ is used, it always refers to the

landslide trigger zone, that is the area where boulders and

blocks detached from.

The procedure needed a central decision, that is the

selection of the proper terrain unit on which perform the

analysis.

Fig. 9. PGA spatial distribution according to the predictive law proposed by

Spudich [23].

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 573

Page 10: Rock falls induced by earthquakes: a statistical approach

Usually landslide hazard determination is conducted on

elementary catchments or slope units, that have a geo-

morphic meaning. Their use is very appropriate when

dealing with mass movements occurring along defined

failure surfaces, where water plays an important role. Here,

for rock fall hazard evaluation, it was preferred a

subdivision of the territory into regular square cells, with

a size of 15 m, subsequently indicated with the term pixels.

In fact there is no evident geomorphic relation between

elementary catchments and the steep slopes where block or

boulder detach from.

A very preliminary test on the correlation of landslides

and triggering factors resulted from the overlay of the map

of the trigger zones, in a binary format (0 ¼ no landslide,

1 ¼ landslide), with the data layers representing the slope

angle, the geology and each strong ground motion

parameter.

The results showed how the landslide occurrence is

related to the slope angle and strong ground motion

parameters. Fig. 10 visually demonstrates that, for each

geologic unit, and inside each slope interval, the relative

density of landslides increases with increases of the value of

the strong motion parameter. Therefore a multivariate

statistics was necessary to quantify the inter-correlation

existing among all factors. However, before performing the

subsequent analysis, one should bear in mind that most of

the rock falls occurred on limestones, that usually crop out

along very steep slopes, as consequence of their resistance

to erosion. Therefore the conditional dependence of the two

layers cannot be disregarded, as it can introduce redundancy

of information.

With this assumptions, a multiple regression was chosen

as a tool to correlate the landslide density, the dependent

variable, to the triggering factors (geology, slope angle and

seismic parameters), that are the independent variables. The

method of least squares was used to find the regression

coefficients and their associated errors. First order and

logarithmic regression have been attempted:

log y ¼ ax1 þ bx2 þ cx3 þ d ð6Þ

log y ¼ a log x1 þ b log x2 þ c log x3 þ d ð7Þ

where y is the landslide density; x1, the slope angle; x2, the

geology layer; and x3 is one of the three ground motion

parameters, respectively PGA, PGV, or Ia.

The geology layer is introduced into the calculation as a

set of three binary maps, C is the limestone lithotechnic unit,

M is the marl unit and D is the surface deposit unit. When

using three independent variables (geology, slope and

seismic parameters), the best correlation is found with the

PGA and the equation is:

log Dr ¼ 24:220 þ 0:054S þ 0:232 PGA þ 0:078 C

þ 0:284 M þ 0:333 D ð8Þ

where Dr is the landslide density; S, the slope angle; C, M

and D assume the value 1 in case of presence and the value 0

in case of absence. Table 2 gives the standard errors for each

regression coefficient.

As geology and slope strictly depend one on the other,

the geologic information has been subsequently disre-

garded, obtaining a much finer correlation.

Even when analysing two independent variables, slope

Fig. 10. Landslide relative density in function of the slope angle and Peak Ground Acceleration.

Table 2

Standard errors of the regression coefficients for 3 causal factors (geology,

slope angle and one seismic parameter)

sconst sS sPGA sC sM sD sDr r 2

0.113 0.001 0.117 0.104 0.106 0.105 0.390 0.780

Const ¼ constant; S ¼ slope angle; PGA ¼ peak ground acceleration;

C ¼ massive and stratified limestones; M ¼ calcareous marles and marls;

D ¼ superficial deposits; Dr ¼ landslide relative density; r ¼ regression

coefficient.

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577574

Page 11: Rock falls induced by earthquakes: a statistical approach

angle and one of the strong ground motion parameter, the

best correlation is found when using the PGA. The

regression equation states:

log Dr ¼ 24:565 þ 0:056 S þ 0:670 PGA ð9Þ

Table 3 shows the errors of the regression coefficients

obtained for the PGA as well as for the other strong ground

motion parameters in this case.

When plotting the actual landslide densities against the

theoretical ones, as shown in Fig. 11, one can observe that at

very small slope angles the data are very sparse. This is due

to the fact that angles of about 158 have been introduced in

Fig. 11. Plot of calculated landslide relative density versus actual values.

Fig. 12. Hazard map resulting from the application of the Eq. (9) to the data set (values indicate the probability of detachment of rock blocks).

S. Marzorati et al. / Soil Dynamics and Earthquake Engineering 22 (2002) 565–577 575

Page 12: Rock falls induced by earthquakes: a statistical approach

the regression, as a results of small errors in the overlay

procedure. Therefore, a threshold for the analysis should be

set at this value.

The only test of accuracy that can be performed with the

available data is the simple creation of a hazard map with

the data set itself and overlay it to the landslide occurrences.

As it should be reasonably expected, about 90% of the

trigger zones are classified as highly hazardous. Fig. 12, that

represents the hazard map, with a zoom over the zones with

highest hazard, shows the match visually.

6. Discussion

The method here discussed is useful for the zonation of

areas where earthquakes can trigger rock falls. The results of

the application of Eq. (9) is a hazard map, where the

territory is subdivided into classes having different prob-

ability of block or boulders detachment. This layer of

information is meaningful for any risk calculation or

emergency planning. In fact, the impact of rock falls on

inhabited areas can cause damage to buildings and, as

consequence, endanger human lives. Moreover, mass

movements can damage man made infrastructures, creating

barriers to transportation during the emergency phase and

additional costs for reparation in the reconstruction phase.

The main limitation of the result is the lack of any

information regarding the size of the detached blocks and

the calculation of the run out distance of the mass

movement. The two limitations can be overcome by

introducing further layers of information. A geomechanic

map, for instance, may give indication about the fracture

spacing of the rock masses, whereas calculation of paths

along topographic gradients, a standard procedure in GIS

analysis, can be used to calculate the run out distances.

Before applying Eq. (9) additional accuracy tests should

be conducted with other data sets. The intention of the

authors is, in fact, the use of the rock fall data set triggered

by the Friuli 1976 earthquake, already available in analogue

format [10].

One additional remark should be made about data

collection. A very determinant layer of information is

represented by the topography, that should be always

affected by the smallest error possible, as it is one of the

fundamental triggering factors in rock fall occurrence.

Finally, this particular data set has demonstrated that

geology can be disregarded in the calculation, as in the

Valnerina area slopes are highly correlated to lithology.

This may not be valid for other area.

7. Conclusion

After the occurrence of the Umbria–Marche 1997

earthquake, central Italy, several rock fall landslides were

triggered. The field surveys conducted soon after the

occurrence of the shocks and the availability of a set of

aerial photographs, allowed the creation of a data set to

study the influence of environmental and seismic factors on

rock fall occurrences. The data have been georeferenced and

stored into a GIS and a series of map overlays allowed to set

up a data structure to perform a multivariate statistics.

A multiple regression analysis was conducted to

establish the relations existing among environmental and

seismic factors and rock fall occurrences. In particular,

among environmental factors, the slope angle showed the

strongest correlation, whereas peak ground acceleration

gave the best fit among the strong ground motion

parameters. The predictive relation thus obtained allows

the creation of a rock fall susceptibility map in case of an

earthquake. This is an intermediate step for risk calculation,

mitigation and emergency planning.

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