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



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:, ph. +34 93 4016861
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
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-
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
(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)
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
[ ]
Rf(P): expected annual loss to the property due to
rockfall, relative to the value of the building;
(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
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
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.
(Ri) is the product of
λT with the relative frequency of each volume
class. Volume corresponds to that measured at the
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.
Volume of the rock mass detached at
the source area (m
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:
[ ]
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
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.
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:
sj n
)R:P(E =
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
ing Block
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,
ij Σ
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
= P
sinψ a dl
sinψ a dl
Pec: the probability of encounter with any exposed
Ps: the probability of encounter with a specific
Pw: the probability of encounter with an infill
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
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.
Fig. 3 Typical structural typology of the area
m3 Central
A, B, C, D,
E, F, G
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
No damage Any col-
< 14 0
damage External
infill wall 0.01
Local struc-
tural damage
14 - 28 0.2
Partial struc-
tural collapse
14 - 28 0.4
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
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-
JRDN-11 Quantitative Risk Assessment for Rockfalls for buildings - 7
ng m3 Rr(P) for every
magnitude i
Total Rr(P) for
the building
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-
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
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
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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Romania represents one of Europe’s most active landslide hotspots. The importance of studying these phenomena is both fundamental (establishing the morphogenetic and morphodynamic frameworks) and applied (quantifying and predicting the potential losses inflicted by such processes). The analysis of agents–processes–forms can be directed toward predictive assessments through susceptibility–hazard–risk studies. The complexity of landslides conditioning factors as well as the available data in terms of quantity (multi-temporal and typological more or less complete landslide inventories) and quality (point and polygon-based inventories, uncertainties induced by the correlation between the used method and the working scale) are imposing local-to-regional and regional-to-national approaches, aiming to highlight, in a predictive manner (based either on heuristic, statistic, or probabilistic predictions) the spatial and temporal sequences more or less prone to future processes, as well as the potential consequences and their mitigation strategies.
... 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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Quantitative landslide risk assessment requires information about the temporal, spatial and intensity probability of hazardous processes both regarding their initiation as well as their run-out. This is followed by an estimation of the physical consequences inflicted by the hazard, preferentially quantified in monetary values. For that purpose, deterministic hazard modelling has to be coupled with information about the value of the elements at risk and their vulnerability. Dynamic run-out models for debris flows are able to determine physical outputs (extension, depths, velocities, impact pressures) and to determine the zones where the elements at risk can suffer an impact. These results can then be applied for vulnerability and risk calculations. Debris flow risk has been assessed in the area of Tresenda in the Valtellina Valley (Lombardy Region, northern Italy). Three quantitative hazard scenarios for different return periods were prepared using available rainfall and geotechnical data. The numerical model FLO-2D was applied for the simulation of the debris flow propagation. The modelled hazard scenarios were consequently overlaid with the elements at risk, represented as building footprints. The expected physical damage to the buildings was estimated using vulnerability functions based on flow depth and impact pressure. A qualitative correlation between physical vulnerability and human losses was also proposed. To assess the uncertainties inherent in the analysis, six risk curves were obtained based on the maximum, average and minimum values and direct economic losses to the buildings were estimated, in the range of 0.25–7.7 million €, depending on the hazard scenario and vulnerability curve used.
... 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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This paper presents recommended methodologies for the quantitative analysis of landslide hazard, vulnerability and risk at different spatial scales (site-specific, local, regional and national), as well as for the verification and validation of the results. The methodologies described focus on the evaluation of the probabilities of occurrence of different landslide types with certain characteristics. Methods used to determine the spatial distribution of landslide intensity, the characterisation of the elements at risk, the assessment of the potential degree of damage and the quantification of the vulnerability of the elements at risk, and those used to perform the quantitative risk analysis are also described. The paper is intended for use by scientists and practising engineers, geologists and other landslide experts.
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A procedure is presented for investigating the response of reinforced concrete buildings to rockfall impact. The method considers a single rock hit on the basement columns, and it includes four steps: (a) calculation of the probability of a rock impact on a member of the load-bearing system, taking into account the block size and the design of the structure; (b) evaluation of the response of one or more structural elements to the hit based on element capacity; (c) in the case of structural element failure, assessment of the robustness of the whole structural system, calculating the potential for progressive collapse; and (d) calculation of a damage index (DI), which is the ratio of structural elements that fail to the total number of structural elements. The proposed method is applied to a reinforced concrete building for a range of rockfall paths and intensities. The analysis has been carried out for a 2-m-diameter block and velocities < 3.5m/s. The possible damage range is found to be highly variable, with DI values ranging from 0.01 to 1 depending on the impact location and block velocity. KeywordsVulnerability-Buildings-Rockfalls-Impact-Risk-Progressive collapse
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Quantitative Risk Assessment (QRA) has become an indispensable tool for the management of landslide hazard and for planning risk mitigation measures. In this paper we present the evaluation of the rockfall risk at the Solà d’Andorra slope (Andorra Principality) before and after the implementation of risk mitigation works, in particular, the construction of protective fences. To calculate the risk level we have (i) identified the potential rockfall release areas, (ii) obtained the volume distribution of the falling rocks, (iii) determined the frequency of the rockfall events, and (iv) performed trajectographic analysis with a 3D numerical model (Eurobloc) that has provided both the expected travel distances and the kinetic energy of the blocks. The risk level at the developed area located at the foot of the rock cliff has been calculated taking into account the nature of the exposed elements and their vulnerability. In the Forat Negre basin, the most dangerous basin of the Solà d’Andorra, the construction of two lines of rockfall protection fences has reduced the annual probability of loss of life for the most exposed person inside the buildings, from 3.8×10−4 to 9.1×10−7 and the societal risk from 1.5×10−2 of annual probability of loss of life to 1.2×10−5.
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The vulnerability of buildings to the impact of rockfalls is a topic that has recently attracted increasing attention in the scientific literature. The quantification of the vulnerability, when based on empirical or heuristic approaches requires data recorded from historical rockfalls, which are not always available. This is the reason why appropriate alternatives are required. The use of analytical and numerical models can be one of them. In this paper, a methodology is proposed for the analytical evaluation of the vulnerability of reinforced concrete buildings. The vulnerability is included in the risk equation by incorporating the uncertainty of the impact location of the rock block and the subsequent damage level. The output is a weighted vulnerability that ranges from 0 to 1 and expresses the potential damage that a rock block causes to a building in function of its velocity and size. The vulnerability is calculated by the sum of the products of the probability of block impact on each element of the building and its associated damage state, the latter expressed in relative recovery cost terms. The probability of exceeding a specific damage state such as non-structural, local, partial, extensive or total collapse is also important for the quantification of risk and to this purpose, several sets of fragility curves for various rock diameters and increasing velocities have been prepared. An example is shown for the case of a simple reinforced concrete building and impact energies from 0 to 4075 kJ.
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Although various methods to carry out quantitative landslide risk analyses are available, applications are still rare and mostly dependent on the occurrence of disasters. In Iceland, two catastrophic snow avalanches killed 34 people in 1995. As a consequence the Ministry of the Environment issued a new regulation on hazard zoning due to snow avalanches and landslides in 2000, which aims to prevent people living or working within the areas most at risk until 2010. The regulation requires to carry out landslide and snow avalanche risk analyses, however, a method to calculate landslide risk adopted to Icelandic conditions is still missing. Therefore, the ultimate goal of this study is to develop such a method for landslides, focussing on debris flows and rock falls and to test it in Bíldudalur, NW-Iceland. Risk analysis, beside risk evaluation and risk management, is part of the holistic concept of risk assessment. Within this study, risk analysis is considered only, focussing on the risks to life. To calculate landslide risk, the spatial and temporal probability of occurrence of potential damaging events, as well as the distribution of the elements at risk in space and time, considering also changing vulnerabilities, must be determined. Within this study, a new raster-based approach is developed. Thus, all existent vector data are transferred into raster data using a resolution of 1m x 1m. The specific attribute data are attributed to the grid cells, resulting in specific raster data layers for each input parameter. The calculation of the landslide risk follows a function of the input parameters hazard, damage potential of the elements at risk, vulnerability, probability of the spatial impact, probability of the temporal impact and probability of the seasonal occurrence. Finally, results are upscaled to a resolution of 20m x 20m and are presented as individual risk to life and object risk to life for each process. Within the quantitative landslide risk analysis the associated uncertainties are estimated qualitatively. In the study area the highest risks throughout all of the analyses (individual risk to life and object risk to life) are caused by debris flows, followed by rock falls, showing that risk heavily varies depending on the process considered. The resultant maps show areas, in which the individual risk to life exceeds the acceptable risk (defined in the aforementioned regulation), so that for these locations risk reduction measures should be developed and implemented. It can be concluded that the newly developed method works satisfactory and is applicable to further catchments in Iceland, and potentially to further countries with different environmental settings.
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Rockfall hazard zoning is usually achieved using a qualitative estimate of hazard, and not an absolute scale. In Switzerland, danger maps, which correspond to a hazard zoning depending on the intensity of the considered phenomenon (e.g. kinetic energy for rockfalls), are replacing hazard maps. Basically, the danger grows with the mean frequency and with the intensity of the rockfall. This principle based on intensity thresholds may also be applied to other intensity threshold values than those used in Switzerland for rockfall hazard zoning method, i.e. danger mapping. In this paper, we explore the effect of slope geometry and rockfall frequency on the rockfall hazard zoning. First, the transition from 2D zoning to 3D zoning based on rockfall trajectory simulation is examined; then, its dependency on slope geometry is emphasized. The spatial extent of hazard zones is examined, showing that limits may vary widely depending on the rockfall frequency. This approach is especially dedicated to highly populated regions, because the hazard zoning has to be very fine in order to delineate the greatest possible territory containing acceptable risks.
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We study the rock fall volume distribution for three rock fall inventories and we fit the observed data by a power-law distribution, which has recently been proposed to describe landslide and rock fall volume distributions, and is also observed for many other natural phenomena, such as volcanic eruptions or earthquakes. We use these statistical distributions of past events to estimate rock fall occurrence rates on the studied areas. It is an alternative to deterministic approaches, which have not proved successful in predicting individual rock falls. The first one concerns calcareous cliffs around Grenoble, French Alps, from 1935 to 1995. The second data set is gathered during the 1912–1992 time window in Yosemite Valley, USA, in granite cliffs. The third one covers the 1954–1976 period in the Arly gorges, French Alps, with metamorphic and sedimentary rocks. For the three data sets, we find a good agreement between the observed volume distributions and a fit by a power-law distribution for volumes larger than 50 m<sup>3</sup> , or 20 m<sup>3</sup> for the Arly gorges. We obtain similar values of the b exponent close to 0.45 for the 3 data sets. In agreement with previous studies, this suggests, that the b value is not dependant on the geological settings. Regarding the rate of rock fall activity, determined as the number of rock fall events with volume larger than 1 m<sup>3</sup> per year, we find a large variability from one site to the other. The rock fall activity, as part of a local erosion rate, is thus spatially dependent. We discuss the implications of these observations for the rock fall hazard evaluation. First, assuming that the volume distributions are temporally stable, a complete rock fall inventory allows for the prediction of recurrence rates for future events of a given volume in the range of the observed historical data. Second, assuming that the observed volume distribution follows a power-law distribution without cutoff at small or large scales, we can extrapolate these predictions to events smaller or larger than those reported in the data sets. Finally, we discuss the possible biases induced by the poor quality of the rock fall inventories, and the sensibility of the extrapolated predictions to variations in the parameters of the power law.
With the rapid development of the west region of China, a great number of highways are being or to be built in the western mountainous regions. Rockfalls constitute a major hazard in numerous adjacent rock cuts or steep natural rock slopes along these highways. In this paper, the connotations, extensions and characteristics of rockfall are discussed and the triggering mechanism is analysed. The widely accepted relative rockfall rating systems are introduced. Based on the Italian modified rockfall hazard rating system, the weights of all categories including five rockfall hazard factors and four vehicle vulnerability factors are introduced to enhance the major categories and weaken the minor categories. In addition, according to the different influence degrees of risk environment and road forms, the modified coefficients are introduced to improve the initial results. Finally, an example with this method to assess a section along Shuifu-Maliuwan highway in Yunnan Province was developed. Through rockfall hazard assessment, in this section, we find four intervals which are very hazardous. Some further analysis and investigation on geotechnical stability was recommended. And some necessary measures should be taken to reduce rockfall hazards in these four intervals.
The determination of the frequency of rockfall events continues to challenge quantitative hazard assessments in most mountain areas. Dendrogeomorphological analysis was used to assess rockfall frequency on talus slopes at Solà d'Andorra (Eastern Pyrenees, Andorra). Rockfall events were dated at two sites: one at the outlet of a chute, and the other below a rock wall. The impact wounds visible on the tree surface were analyzed with a seasonal temporal resolution. At each site, trees were sampled in three forest strips 15 to 30 m wide located at different heights on the talus. All the trees with visible injuries in the strips were sampled.Rockfall frequency cannot be assessed by a simple analysis of time series of tree damage. A satisfactory assessment requires a prior interpretation of the location of the damaged trees in relation to a number of rockfall events. At Solà d'Andorra, the rockfall chronology was reconstructed for the last 25 years by dating visible wounds. For older periods, the tree wound record of rockfalls is incomplete owing to progressive closure of wounds. Wounds exceeding 40 years in age had already disappeared from the tree surface in the study area. Our results show a clear reduction of the rockfall frequency down the talus, a noticeable lateral change in frequency, and an influence of source morphology (chute or wall) on rockfall activity on the talus.
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]
Fragmental rockfall is characterized by the independent movement of individual rock fragments after detachment from a rock face. The continued operation of the process leads to the accumulation of talus slopes. On talus slopes the rockfall shadow extends beyond the base of the talus and consists of scattered boulders that have run out beyond the base of the slope. The landing probability of boulders in the shadow is examined; return periods of the order of 1000 years relative to a house site are typical. Rockfall behaviour particularly with respect to run out into the shadow can be assessed using geological evidence, empirical methods, physical modelling, and computer-based analytical models. Documentation of the three rockfall incidents shows that, in each case, rockfall fragments impacted on homes at equivalent shadow angles of 30[deg] or more. This would suggest that a review of existing development within rockfall shadow areas at the base of talus slopes may be in order. -from Authors [Journal; In English]