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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).
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
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
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
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
(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
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
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
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
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
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
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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Standard errors of the regression coefficient for 2 causal factors (slope angle
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Parameter sconst sS sparam sDr r 2
PGA (m/s/s) 0.064 0.001 0.056 0.331 0.871
PGV (m/s) 0.058 0.001 0.003 0.406 0.776
Ia (m/s) 0.043 0.001 0.095 0.428 0.722
Const ¼ constant; S ¼ slope angle; PGA ¼ peak ground acceleration;
PGV ¼ peak ground velocity; Ia ¼ Arias intensity; Dr ¼ landslide relative
density; r ¼ regression coefficient.
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