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Quantitative risk assessmenent for buildings due to rock- falls : some achievements and challenges

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Résumé An application example of Quantitative Risk Assessment due to rockfalls for a developed area is presen-ted in this paper. The methodology aims at the calculation of the risk for buildings which are situated at the bottom of a rockfall prone slope and may be impacted by rock blocks and of the global risk by aggre-gation of the results. It can be applied at either site-specific or local scales and it is analytical. Frequency of the rockfall events has been obtained from historical records and dendrochronology. The probability of a rockfall reaching the developed area is obtained by trajectographic modelling. A key issue is the consi-deration of fragmental rockfalls. Falling rock masses are expected to break apart after first impacts on the ground, leading to individual blocks that will follow independent paths. Different impact energy le-vels may lead to four potential damage states: 1. non-structural damage, 2. local structural damage, 3. partial collapse, and 4. extensive to total collapse. For every building, the risk is expressed in terms of the annual probability of loss and it is the sum, for all rockfall magnitudes, of the products of the rockfall frequency with the conditional probability of a rock block reaching the building with a certain kinetic energy sufficient to cause a specific state of damage and its associated vulnerability. The details of the proposed methodology are presented here through an application example in the Principality of Andorra. Mots clefs: Rock falls, Quantitative Risk Assessment, Pyrenees.
JRDN 2011 Quantitative Risk Assessment for Rockfalls for buildings - 1
Quantitative risk assessmenent for buildings due to rock-
falls : some achievements and challenges
Jordi Corominas & Olga-Christina Mavrouli1
1 Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia (UPC),
Barcelona, Spain; e-mail: jordi.corominas@upc.edu, ph. +34 93 4016861
Résumé
An application example of Quantitative Risk Assessment due to rockfalls for a developed area is presen-
ted in this paper. The methodology aims at the calculation of the risk for buildings which are situated at
the bottom of a rockfall prone slope and may be impacted by rock blocks and of the global risk by aggre-
gation of the results. It can be applied at either site-specific or local scales and it is analytical. Frequency
of the rockfall events has been obtained from historical records and dendrochronology. The probability of
a rockfall reaching the developed area is obtained by trajectographic modelling. A key issue is the consi-
deration of fragmental rockfalls. Falling rock masses are expected to break apart after first impacts on
the ground, leading to individual blocks that will follow independent paths. Different impact energy le-
vels may lead to four potential damage states: 1. non-structural damage, 2. local structural damage, 3.
partial collapse, and 4. extensive to total collapse. For every building, the risk is expressed in terms of the
annual probability of loss and it is the sum, for all rockfall magnitudes, of the products of the rockfall
frequency with the conditional probability of a rock block reaching the building with a certain kinetic
energy sufficient to cause a specific state of damage and its associated vulnerability. The details of the
proposed methodology are presented here through an application example in the Principality of Andorra.
Mots clefs: Rock falls, Quantitative Risk Assessment, Pyrenees.
1. Introduction
Quantitative Risk Assessment (QRA) is progres-
sively becoming a requirement for the administra-
tions in charge of landslide risk management.
QRA aims to provide objective evaluation of risk
in a reproducible and consistent way, avoiding the
use of ambiguous terms, and thus favouring the
comparison of risk level between distant loca-
tions. The QRA may provide information on the
potential loss (i.e. in €/year) due to a potential
hazardous event thus allowing the interpretation
based on risk acceptability criteria. The QRA
results can be used by administrative authorities
for urban planning and/or mitigation measure
purposes, as well as by insurance companies for
the application of their policies.
The methodologies for the QRA due to landslides
which are used globally vary according to the
type of mechanism, the applied scale, and the
available input data. In what concerns the rockfall
risk, several important contributions to the field of
the QRA, have been made by Hungr et al. 1999;
Bell and Glade, 2004; Roberds, 2005; Corominas
et al. 2005; Agliardi et al. 2009; Li et al. 2009.
The objective of this communication is to present
a methodology for the quantification of the risk
for buildings which are located at the bottom of a
slope and are exposed to rockfalls (Corominas
and Mavrouli, 2010). The proposed methodology
takes into account the fragmental nature of the
rockfalls and the structural characteristics of the
impacted buildings. It is analytical and it includes
individual sub-procedures allowing their refine-
ment according to information available, the scale
of work, and the desired degree of the detail. The
local conditions are taken into account including
the topographical relief and the limits of the built
area.
First of all, the methodology with its sub-
procedures is presented through an application
example of the Andorra Principality. At the end, a
discussion is made on its possibilities and limita-
tions.
The study area is a slope situated next to the ur-
ban area of Santa Coloma, in the Principality of
Andorra, located in the east-central Pyrenees
2 – COROMINAS & MAVROULI
(Figure 1). It experiences a relatively high rate of
rockfall activity and has been the object of several
studies on rockfall hazard during the last years
(i.e. Copons, 2004; Copons et al. 2005; Coromi-
nas et al. 2005). The outcropping rock consists of
densely fractured granodiorite and was shaped by
Pleistocene glaciers that after their retreat gener-
ated the steep slopes of the valley. The intense
rockfall activity has produced thick talus deposits
which have been partly developed mainly during
the 70s and 80s.
Fig. 1 Partial view of the study area of Santa Co-
loma, Principality of Andorra. Potential sources,
trajectories, stop points and volumes of some re-
cent rockfall events are shown.
2. Methodology
2.1 General procedure
For the QRA of rockfall threatened developed
areas, an integrated analytical methodology is
proposed here, for application at site-specific sca-
le. The general equation of the rockfall risk is
given as follows :
R= λ(Ri)xP(D:Ri)xP(S:T)xV(E:S)xC (1)
Where
R: expected loss due to rockfall
λ(Ri): frequency of a rockfall of magnitude i
P(D:Ri): probability of a rockfall reaching the
element at risk
P(S:T): the temporal spatial probability of the
element at risk
V(E:S): vulnerability of the exposed element at
risk to impact by a rock fall of magnitude i
C: value of the element at risk
The terms λ (Ri) and P(D:Ri) represent the hazard,
P(S:T) the exposure and V(E:S) the vulnerability.
Equation 1 allows the calculation of the risk due
to the occurrence of a single rockfall size only. To
obtain total risk, all potential rockfall sizes must
be considered. On the other hand, in the case that
elements at risk consist of buildings, the damage
capability of the rockfall is given by its velocity
or kinetic energy rather than by its size. Conse-
quently equation 1 must be substituted by the
following equation to obtain the expected annual
risk:
[ ]
xC))xV(RR:)xP(E(R=(P)R
ijiji
j
1=j
i
1=i
ΣΣ
λ
r
(2)
Rf(P): expected annual loss to the property due to
rockfall, relative to the value of the building;
λ
(Ri): annual frequency of a rockfall with a mag-
nitude “i”;
P(Ej:Ri): probability of a rockfall reaching the
building with a kinetic energy. The latter is calcu-
lated as a function of the magnitude (volume) “i”
and the velocity “j”. The kinetic energy levels are
those leading to the respective damage states (de-
fined in table 6).
V(Rij): vulnerability of the building for a rockfall
of magnitude “i” and velocity “j”;
C: value of the building.
The temporal spatial probability of the element at
risk P(S:T) for static elements such as buildings
is 1. Consequently, it is not considered in equa-
tion 2.
2.2 Frequency of rockfalls
λ
(Ri)
Frequency of rockfalls can be calculated by
means of statistical analyses of rockfall records.
(i.e. Hungr et al., 1999; Dussauge-Peisser et al.,
2002; Guzzetti et al., 2003).
Unfortunately, the availability of such records is
restricted to a few road and railway maintenance
offices and national park services. Historical
records are often too short in comparison with the
time scale of large rockfall events. In the case of
Santa Coloma, the available rockfall record cov-
ers a span of time of about 50 years but it is com-
plete only for the last 15 years when the Andorran
administration established a systematic inventory
of all the rockfall events occurring in the area.
This inventory covers exclusively rockfall events
larger that 1m3 that were noticed by the inhabi-
tants of the area and by annual surveys with heli-
copter flights. The rockfall series has been com-
pleted by intensive dendrogeomorphological ana-
lyses of damaged trees (Moya et al. 2010) and has
JRDN-11 Quantitative Risk Assessment for Rockfalls for buildings - 3
allowed extending the rockfall record to the last
40 years. The average annual frequency λT for all
rockfall sizes is 0.5 events per year. This figure
must be considered a minimum value because the
occurrence of small-size rockfall events without
producing impacts on trees cannot be absolutely
disregarded.
The magnitude (volume) - frequency relation of
the inventoried rockfalls in the entire Santa Colo-
na area is shown in table 1 and it is assumed to be
the same for the study site.
λ
(Ri) is the product of
λT with the relative frequency of each volume
class. Volume corresponds to that measured at the
source.
Source
volume
(m3)
Number
of events λ(Vi) λ(Ri)
≤ 5 14 0.667 0.333
10 4 0.19 0.095
25 2 0.095 0.047
150 1 0.048 0.024
Table 1. Rockfall events observed in Santa Colo-
ma area. λ(Vi) is the relative frequency of each
volume class and λ(Ri) its annual frequency
However, the volume to consider in the trajecto-
graphic analysis is not an evident issue. A rockfall
may involve the displacement of a single or sev-
eral blocks. It may also begin by the detachment
of a more or less coherent rock mass that after the
first impact with the slope face splits into several
pieces. The latter is the case of a fragmental rock-
fall which is characterized by the independent
movement of individual rock fragments after de-
tachment from a rock face (Evans and Hungr,
1993). The fragmentation mechanism is not cur-
rently included in trajectographic models and may
strongly affect the reliability and validity of the
results. The detachment of large rock masses
without considering their fragmentation after the
first impacts on the ground will give unrealistic
travel distances in excess of what should be ex-
pected. The important effect of the number and
mean size of fragmented rocks on the hazard due
to a single event has been discussed by
Jaboyedoff et al. (2005), who proposed the em-
pirical evaluation of the latter.
Table 2 shows the average distribution of block
sizes from several rockfall events of the Santa
Coloma area inventoried during the last decade.
Both the number and size of the blocks increase
with the volume of the detached rock mass. The
assumption made in the methodology presented
here is that the frequency of falling blocks of a
given size has to be increased by adding the fre-
quency of the blocks of the same size produced
by fragmentation of larger rockfall events.
Block
size
(m3)
Volume of the rock mass detached at
the source area (m
3
)
5
10
25
150
1
2
4
12
1
1
1
8
0
0
1
2
0
0
0
1
Table 2. Number of fragmented blocks of each
size class for different volumes of the rock mass
detached at the source area.
Thus the frequency of rockfalls of a defined block
size “s” is given by the following expression:
[ ]
)(R)xN(R=(Rs)
isi
i
1=i
Σ
λλ
(3)
where
λ (Rs) is the frequency of blocks of “s” size
λ(Ri) is the frequency of rockfalls of “i” volume
Ns(Ri): the number of blocks of size “s” per every
rockfall of volume “i”
Table 3 shows the annual frequency of each block
class in Santa Coloma area calculated using equa-
tion 3.
Block size (m3) λ
(Rs)
1
1.000
2,5
0.667
10
0.095
30
0.024
Table 3. Frequency of different block sizes in the
area of Santa Coloma area calculated from Eq.3
2.3 Trajectographic analysis P(Ej:Rs)
For each range of block volume, a three-
dimensional probabilistic trajectory analysis has
been performed with ROTOMAP32 to define the
percentage of possible rockfall paths reaching
each exposed building with a given level of ki-
netic energy. This level is defined by the potential
damage states caused to the buildings (Mavrouli
and Corominas, 2010a) which are: non-structural
damage, local damage, partial collapse or exten-
sive to total collapse. The thresholds of the E that
distinguish between the damage states are calcu-
lated by the analysis of the response of the ex-
posed structure to the block impact. More infor-
mation on this is given at section 2.4.
4 – COROMINAS & MAVROULI
ROTOMAPS32 code provides different rockfall
paths from different initial velocities, respective
directions and exact locations of the rockfall
sources. Some rockfall sources produce paths
that have higher probability of affecting some
buildings than others and this is taken into ac-
count in the analysis. The potential range of ki-
netic energy E of the rock blocks reaching the
buildings is also calculated. The blocks that reach
a particular building are classified into groups
with respect to their E, and the probability of each
group is evaluated.
The model was calibrated to comply with histori-
cal rockfall events data (Corominas and Mavrouli,
2010). The results were considered acceptable
when the stop points from the simulation ap-
proximated those of the real events. In the case of
the blocks of 30 m3 size, the velocity of impact
onto the buildings is not known and the restitution
coefficients and limit angles were calibrated
through successive trials to reproduce the path of
the block. However, the obtained velocities from
the calibration indicate extremely high levels of
E, the reliability of which should be validated
with the back-analysis of future rockfall events.
After the calibration, the trajectory analysis was
performed. Given the detailed work scale, the risk
in this example is evaluated using Equation 4 and
the probability of reaching directly a target build-
ing with a certain E was obtained by:
T
nΕ
sj n
)R:P(E =
(4)
where:
nE: number of block paths reaching any particular
building with a certain E;
nT: total number of block paths
Fig. 2 Rockfall paths for blocks of 2.5 m3 size.
The obtained values for the P(Ej:Rs) are shown in
Table 4. Additionally, Figure 2 presents an exam-
ple of all the potential paths produced by a block
of 2.5 m3, their associated rockfall sources and the
potentially affected buildings. The total number
of simulations for every magnitude class was
1500.
Build-
ing Block
volume
(m3)
Kinetic Energy (KJ)
<14 14-28 >28
A 1 0.003 0.008 0.008
2.5 0 0 0.013
10 0 0 0.020
30 0 0 0.104
B 1 0.001 0.003 0.002
2.5 0 0 0.004
10 0 0 0.001
30 0 0 0.037
C 1 0.003 0 0.004
2.5 0 0 0.011
10 0 0 0.029
30 0 0 0.060
D 1 0 0 0
2.5 0 0 0
10 0 0 0
30 0 0 0
E 1 0 0 0
2.5 0 0 0
10 0 0 0
30 0 0 0.015
F 1 0 0 0
2.5 0 0 0
10 0 0 0
30 0 0 0.033
G 1 0 0 0
2.5 0 0 0
10 0 0 0
30 0 0 0.017
Table 4. Probability of reaching the building with
an energy P(Ej:Rs) as calculated in the trajecto-
graphic analysis
JRDN-11 Quantitative Risk Assessment for Rockfalls for buildings - 5
The used thresholds that may lead to different
damage states that, for this example, were ob-
tained during the sub-procedure that is described
in section 2.4 (Table 6). They are: < 14 kJ for
non-structural damage, 14 28 kJ for local or
partial structural damage and > 28 kJ for exten-
sive to total collapse.
2.4 Vulnerability of the exposed building
The exposed elements here are considered to be
the buildings which are situated at the bottom of
the slope. A single structural typology is consid-
ered: a 2-storey frame reinforced-concrete frame
(RC) structure.
The vulnerability is quantified considering the
potential repair cost of the building, with respect
to its reconstruction value. To evaluate it, the
step-by-step procedure for the response of RC
buildings to single rock impacts on their basement
column(s), proposed by Mavrouli and Corominas
(2010a), is used. It is an analytical methodology
that can be adapted to various structural typolo-
gies, for the assessment of the physical damage in
case of loss of structural and non-structural ele-
ments of a building, taking into consideration the
potential of a cascade of failures (progressive
collapse) which extends to a part or to the entire
building, due to the initial loss of the element.
For simple regular frame RC frame buildings the
damage extent and the potential of progressive
collapse depends on the number and damage of
the struck element(s) for a rockfall impact of a
given E, and their importance for the overall sta-
bility of the building. Potential damage can be
classified into four damage states: a. non-
structural damage of the infill walls, b. local
structural damage, c. partial collapse and d. exten-
sive to total collapse.
In the worked example, it is considered the same
building typology as used in Corominas and Mav-
rouli (2010b) and is shown in Fig.3. The results of
the analysis for the considered building, which is
composed by two frames (three columns) at its
exposed façade, 3 frames perpendicularly to it,
along its length, and 5 m infill walls in-between
the columns, indicate the conditions that lead to
the proposed damage states. The four following
initial damage scenarios are investigated: loss of a
central column, of a corner column, an infill wall
and two or more central or corner columns per-
pendicularly to the exposed façade, depending on
the impact location and the kinetic energy that
determines the capacity of a block to destroy one
or more columns. The considered scenarios are
unfavourable regarding the direction of the rock
blocks perpendicularly to the exposed façade and
are considered here from the safety side.
The proposed vulnerability is calculated as the
sum of the products of the probability of encoun-
ter of the rock block with a structural or non-
structural element and the associated RRC:
)RRC x(P=)V(R kke,
k
1=k
ij Σ
(5)
where,
V(R ij): vulnerability for a rock bloc with a magni-
tude i” and velocity “j”;
Pe,k: encounter probability of a rock with a possi-
ble structural and non-structural element of the
building “ k” that may be struck by a rock block
of magnitude “i”;
RRCk: relative recovery cost that corresponds to
the damage of one or more structural and/or non-
structural element(s) of the building “k” by a rock
block of magnitude “i” and velocity “j”.
To calculate the probability of each impact loca-
tion, the following Equations are used:
sinψ a dl
c
+
= P
ec
(6)
sinψ a dl
1
c
+
=n
P
s
(7)
sinψ a dl
1
w
w
+
=n
P
(8)
where:
Pec: the probability of encounter with any exposed
column;
Ps: the probability of encounter with a specific
column;
Pw: the probability of encounter with an infill
wall;
n: the number of projected columns on a line ver-
tical to the rock path;
lc: column width;
lw: infill-wall width;
a: distance between centers of columns;
d: rock block diameter;
ψ: angle between the rock path and the façade
plane.
Using Equations (6) to (8) for the given building,
the probability of encounter with a non-structural
or a structural member is given by Table 5. The
impact location is expected to occur exclusively
in the structural elements present at the first level
of the building.
6 – COROMINAS & MAVROULI
Fig. 3 Typical structural typology of the area
Building
m3 Central
column
Corner
column
Any
column
A, B, C, D,
E, F, G
1
9.91E-02
1.98E-01
2.97E-01
2.5
1.27E-01
2.53E-01
3.80E-01
10
1.88E-01
3.77E-01
5.65E-01
30
2.62E-01
5.24E-01
7.86E-01
Table 5. Probability of encounter with a non-
structural or a structural member
The RRC expresses the cost of the repair in rela-
tion to the value of the building. It is calculated in
function of the physical structural and non-
structural damage, translated into economical
cost, for every potential location of the impact
(Mavrouli and Corominas 2010b).
For the considered building, the RRC is provided
by Table 6, for every scenario (impact location
and kinetic energy sufficient to cause the loss of
one or more elements)
Damage state Damaged
element E
(kJ)
RRC
No damage Any col-
umn
< 14 0
Non-structural
damage External
infill wall 0.01
Local struc-
tural damage
Central
column
14 - 28 0.2
Partial struc-
tural collapse
Corner
column
14 - 28 0.4
Generalised
damage Two or
more col-
umns > 28 1
Table 6. Conditions leading to every damage state
and associated RRC
Considering these, the vulnerability is calculated
in function of the block diameter and kinetic en-
ergy as shown in Table 7.
Building m E (kJ)
< 14 14 - 28 > 28
A, B, C, D,
E, F, G
1 1.00E-02 1.09E-01 3.07E-01
2.5 1.00E-02 1.37E-01 3.90E-01
10 1.00E-02 1.98E-01 5.75E-01
30 1.00E-02 2.72E-01 7.96E-01
Table 7 Vulnerability V(Rij) for every possible
impact energy
2.5 Calculation of the relative risk
For every building, the relative risk to its value is
calculated here, using Eq. (2) just substituting the
rockfall frequency λ(Ri) by the block size fre-
quency λ (Rs) as discussed in section 2.2. The
results are presented in Table 8.
The global risk for an area is then evaluated by
summing up the products of the relative risk for
all the exposed buildings with their values:
C)*(P)R( R(P) r
Σ
=
where
R(P): global risk for an area;
Rr(P): relative risk for a building;
C: value of the building
The total relative risk for the entire area is the
sum of the relative risk for all buildings and equal
to 2.16E-02.
In buildings A, B, and C, the risk is higher for
small rock sizes (1 and 2.5 m3). This is due to the
higher frequency associated to them. Instead,
buildings E, F, G are affected by the largest
blocks only. This is because, for these particular
cases, only blocks of 30m3 are able to reach the
building locations with the required energy level
to produce damage (see table 4). It has to be taken
into account that these are results of a simulation
and they should be validated with real cases.
Building D has no risk because none of the mod-
elled trajectories passes through the building loca-
tion.
JRDN-11 Quantitative Risk Assessment for Rockfalls for buildings - 7
Buildi
ng m3 Rr(P) for every
magnitude i
Total Rr(P) for
the building
A
1
1,32E-03
7,86E-03
2.5
3,46E-03
10
1,09E-03
30
1,99E-03
B
1
9,12E-04
2,69E-03
2.5
1,04E-03
10
3,64E-05
30
7,01E-04
C
1
1,26E-03
6,78E-03
2.5
2,78E-03
10
1,60E-03
30
1,15E-03
D
1
0,00E+00
0,00E+00
2.5
0,00E+00
10
0,00E+00
30
0,00E+00
E
1
0,00E+00
2,92E-04
2.5
0,00E+00
10
0,00E+00
30
2,92E-04
F
1
0,00E+00
6,36E-04
2.5
0,00E+00
10
0,00E+00
30
6,36E-04
G
1
0,00E+00
3,31E-04
2.5
0,00E+00
10
0,00E+00
30
3,31E-04
Table 8 Relative risk for every building Rr(P)
3. Conclusions
The calculation of risk using the proposed meth-
odology is quantitative and may be expressed in
terms of annual loss
The proposed procedure takes into account the
fragmentation on the detached rock masses which
otherwise would have produced longer runout
distances and higher impact energies in the trajec-
tographic analyses. The increase of the number of
blocks of small size caused by the fragmentation
of the detached rock mass has been included in
the assessment of the frequency of the different
block sizes. However, this may not prevent an
underestimation of their kinetic energy and runout
distance. It is thus necessary a validation with
further rockfall events.
In what concerns the vulnerability the methodolo-
gy includes a weighted vulnerability that takes
into account the encounter probability of the
block with key structural and non-structural ele-
ments and the subsequent damage. Thus, the vul-
nerability can be integrated into the risk equation.
The worked example includes only a particular
structural building typology and it is necessary to
add other typologies before generalizing the pro-
cedure.
The methodology that has been presented here
may be used for the calculation of the risk for a
building that is impacted at its basement by a sin-
gle block fragmented rockfall, as well as for the
calculation of the global risk for a built area, by
aggregation.
The application example was carried out at site-
specific scale. This analysis indicated that not all
the exposed buildings have the same impact pro-
bability; instead rockfalls follow preferential
paths towards some of them. As a result the risk
for each building is different even though the vul-
nerability and their location with reference to the
topographic elevation under the rockfall source
are the same. This can be useful for the optimiza-
tion of the cost/benefit relationship of protection
measures.
Acknowledgements : This work has been per-
formed within the projects Safeland, funded by
the European Union (7th Framework Program)
grant agreement 226479 and Big Risk, funded by
the Spanish Ministry of Science and Innovation,
contract number BIA2008-06614. Partial support
was given to the second author by the European
Reintegration Grant for the project RISK-LESS,
grant agreement 268180
The authors appreciate Julien Godefroy’s assis-
tance with the calibration of the trajectory model.
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... A comprehensive exposure analysis takes into account not only the extent of the landslide and its frequency but also the spatial and temporal probability that an element at risk (static or dynamic) is within the landslide path. In practice, the calculation of exposure depends mostly on the scale of analysis and landslide type and it can vary from individual elements (buildings and people inside buildings exposed to rockfalls, Corominas et al. 2005;Corominas and Mavrouli 2011;Agliardi et al. 2009), pixel level (people, linear infrastructure and buildings exposed to debris flow and shallow landslides, Jaiswal et al. 2011;Zêzere et al. 2008), up to municipal level (Pellicani et al. 2014). Fell et al. (2005) and Corominas et al. (2014) propose different approaches for computing exposure of static and dynamic elements at risk taking into account multiple scenarios. ...
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... Corominas et al. (2005) showed an example of the quantification of the risk of blocks hitting people inside buildings. A methodology for the analysis of rockfall risk for buildings for application at the site-specific scale was proposed by Corominas and Mavrouli (2011a), which included the analytical probabilistic vulnerability of buildings as a function of the location of rock block impact. Ferlisi et al. (2012) provided a methodology for calculating the risk taken by people moving along a road while inside vehicles. ...
... Different types of approaches have been applied which are dependent on the available information and the specific location of the assessment. In the case of rockfalls, Corominas and Mavrouli (2011) developed an application for a developed area by calculating the risk for buildings which are situated at the bottom of a rockfall prone slope and may be impacted by rock blocks. The frequency of the rockfall events was obtained from historical records and dendrochronology, while the probability of a rockfall reaching the developed area was estimated by trajectographic modelling. ...
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... Corominas et al. (2005) showed an example of the quantification of the risk of blocks hitting people inside buildings. A methodology for the analysis of rockfall risk for buildings for application at the site-specific scale was proposed by Corominas and Mavrouli (2011a), which included the analytical probabilistic vulnerability of buildings as a function of the location of rock block impact. Ferlisi et al. (2012) provided a methodology for calculating the risk taken by people moving along a road while inside vehicles. ...
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The two main transportation corridors of southwestern British Columbia are subject to a range of rock slope movements (rock falls, rock slides, and rock avalanches) that pose significant risks to road and rail traffic travelling through the region. Volumes of these landslides range from less than 1 m3 to over 4.0 x 107 m3. A database of rock falls and slides was compiled for rail and highway routes in each transportation corridor using maintenance records spanning four decades. The records number approximately 3500, of which about one half includes information on volume. Magnitude - cumulative frequency (MCF) relationships were derived for each corridor. A scaled sampling procedure was used in part to reduce the effects of censoring. Both corridors yield MCF curves with significant linear segments on log-log plots at magnitudes greater than 1 m3. The form of both railway and road plots for each corridor shows similarity over several orders of magnitude. The slope of the linear segments of the curves depends on geological conditions in the corridors. Temporal histograms of the data show a trend towards reduction of rock fall frequency as a result of rock slope stabilization measures, implemented during the 1980s and 1990s. A risk analysis methodology using the slope of the magnitude-frequency relationship is outlined. The major part of the risk to life in the case examined results from rock falls in the intermediate-magnitude range (1-10 m3). [Journal Article; 25 Refs; In English; Summary in English and French]
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