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Quantitative risk assessment in a rockfall-prone area: the case study of the Crolles municipality (Massif de la Chartreuse, French Alps)

Évaluation quantitative du risque chutes de blocs: l’exemple de la commune de Crolles (Massif de la Chartreuse, Alpes Françaises)
Manon Farvacque, Jérôme Lopez-Saez, Christophe Corona, David Toe, Franck Bourrier et Nicolas Eckert
p. 7-19

Résumés

L’aléa chute de bloc est lié au détachement d’un bloc rocheux depuis une paroi verticale ou sub-verticale, qui se propage rapidement vers l’aval sous l’effet de la gravité par rebonds successifs. Cet aléa cause chaque année de nombreux dommages aux biens ou aux personnes. Dans ce contexte, une évaluation précise du risque chutes de blocs est devenue cruciale pour les gestionnaires et les pouvoirs publics. Afin de caractériser le risque de manière précise et reproductible, une procédure d’évaluation quantitative du risque adaptée à l’aléa chute de bloc a été utilisée dans cette étude. Le risque pour le bâti a ainsi été calculé à l’échelle de la commune de Crolles, située sur le versant sud-est du Massif de La Chartreuse dans les Alpes Françaises. Cette procédure prend en compte l’intégralité de la distribution des volumes rocheux entre 1 m³ et 20 m³ et inclut les 300 m de parois subverticales qui surplombent le village. Nos résultats, exprimés comme la surface moyenne du bâti détruite chaque année, démontrent (i) l’effet de protection du couvert forestier pour des volumes de 1 m³ à 7 m³, et (ii) la part importante du risque total due aux classes de volume intermédiaires (7-12 m³). Sur un plan spatial, nos résultats permettent d’identifier les secteurs les plus exposés et démontrent qu’une large proportion du risque total est localisée sur quelques habitations situées dans le quartier du Coteau. D’un point de vue pratique, et malgré des incertitudes d’ordre épistémique liées à la magnitude/fréquence des événements rocheux, au paramétrage du modèle trajectographique et à l’absence de courbe de vulnérabilité spécifique au site, notre étude démontre clairement l’intérêt d’une approche quantitative de type QRA pour le zonage et la gestion du risque rocheux.

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Notes de la rédaction

Article soumis le 10 août 2018, reçu sous forme révisée le 28 janvier 2019 et définitivement accepté le 04 mars 2019.

Texte intégral

This research was financially supported by a Ph.D. grant from Rhône-Alpes Region – ARC Environnement 3, the C2ROP (Chutes de blocs, Risques Rocheux, Ouvrages de Protection) national research project and Irstea ZORRINO (Zonage réglementaire du risque en montagne par optimisation des pertes) project. This work is also supported by the French National Research Agency in the Investissements d’Avenir program (ANR-15-IDEX-02). It was conducted within the cross-disciplinary Risk@Univ. Grenoble Alpes program. Irstea is member of Labex Osug@2020.

1. Introduction

1Rockfalls are a common type of fast moving landslide (Hungr et al., 2014) and are a major hazard in mountain areas worldwide, endangering human lives, transportation infrastructures, industry and dwellings (Guzzetti et al., 2004). Abundant literature reports fatalities in alpine environments, e.g., in Switzerland (Straub and Schubert, 2008; Badoux et al., 2016), France (Assali, 2015), Italy (Agliardi et al., 2009) and Austria (Haque et al., 2016). Rockfall protection through rigorous land-use planning based on hazard zoning maps and/or appropriate risk mitigation measures is therefore a crucial issue for authorities and stakeholders in rockfall-prone areas (Corominas et al., 2005; Agliardi et al., 2009).

2However, rockfall risk analysis is inherently complex and difficult. These difficulties derive from several factors such as the lack of historical catalogues, the site-specific nature of rockfalls, the complexity of properly simulating the spatial distribution of the hazard as well the lack of knowledge regarding the vulnerability of the elements at risk (Wang et al., 2014). For these reasons, probabilistic methods are suitable approaches for quantifying rockfall risk. Quantitative risk assessment (QRA) procedures developed for landslides (Fell et al., 2005, 2008; Corominas et al., 2014; Lari et al., 2014) have been adapted to account for the specificities of rockfall processes (Agliardi et al., 2009; Corominas et al., 2005, 2013; Corominas and Mavrouli, 2013; Moos et al., 2017). In QRAs, rockfall risk for exposed elements is estimated by including each term of the risk components – hazard, exposure and vulnerability – in the form of probabilities. Hazard integrates the annual probability of occurrence usually estimated from rockfall inventories (Dussauge-Peisser et al., 2002) and the spatial probability of impact on structures evaluated through rockfall 3D numerical models (Agliardi et al., 2009). Exposure is the probability that a given element at risk is at the impact location at the time of impact (temporal and spatial probabilities). Then vulnerability curves derived from the retro-analyses of documented events are used to evaluate the degree of loss on the elements at risk.

3QRA is a valuable tool for stakeholders because it allows risk to be quantified in an objective and reproducible manner, and the results can be compared from one location to another (Corominas et al., 2014). Furthermore, it is also useful because it allows cost–benefit analyses to be performed, and it provides the basis for the prioritization of management and mitigation actions. However, in practice the quantitative estimation of the different components of risk is challenging (Corominas et al., 2005) due to epistemic and aleatory uncertainties (Baecher and Christian, 2003) that refer to the lack of knowledge on a variable and to the natural randomness of the process, respectively (Wang et al., 2014). As a consequence, quantitative risk analyses remain rare in rockfall-prone regions (Corominas et al., 2014), are mostly site-specific (Ferrari et al., 2016) and are restricted to source areas where a historical inventory of the rockfall events that have occurred in the study area is available (Corominas et al., 2005; Agliardi et al., 2009). In addition, most of these studies only consider a reduced distribution of rockfall volumes that do not account for the spectrum of hazard scenarios.

4In the present study, through the investigation of a 3-km-long limestone cliff from the southernmost slopes of the Chartreuse Mountains, we propose the first quantitative risk analysis for the French Alps. In the municipality of Crolles (fig. 1), where numerous rockfalls have been reported since the beginning of the 20th century (Lopez-Saez et al., 2016), we (i) determined the volume–frequency relationship for rockfall events through detailed historical/field observations, and (ii) performed a quantitative risk analysis including all potential release areas and rock volumes within the range of 1–20 m³.

Fig. 1 – Location and geological setting of the study site.
Fig. 1 – Localisation et contexte géologique du site d'étude.

Fig. 1 – Location and geological setting of the study site.  Fig. 1 – Localisation et contexte géologique du site d'étude.

A: Location at the French Alps scale; B: Situation at the local scale (Crolles is located in the Isère valley, near the city of Grenoble, on the southeastern slopes of the Chartreuse Mountains); C: Overview of the Crolles slopes; D: Geomorphological sketch of the Crolles area; E: Overview of the Crolles urban area and neighborhoods. 1. Location of the 900-m-long transect used to inventory past rockfall events; 2. Berriasian (Marl); 3. Tithonian (Limestone); 4. Callovian-Oxfordian (Marl); 5. Quaternary; 6. Convex change of slope; 7. Ledge; 8. Concave break of slope (talus slope limits); 9. Hydrographic network; 10. Contour line; 11. Rockfall events; 12. Protective structures; 13. Urban front limit.
A : Localisation à l’échelle des Alpes françaises ; B : Situation à l’échelle locale (Crolles est localisée dans le département de l’Isère, dans l’agglomération grenobloise, sur le versant sud-est du Massif de La Chartreuse) ; C : Aperçu des falaises surplombants le village de Crolles ; D : Croquis géomorphologique de Crolles ; E : Vue générale de Crolles et de ses quartiers ; 1. Localisation du transect utilisé pour l’inventaire des chutes de blocs passées ; 2. Berriasien (Marnes) ; 3. Tithonien (Calcaire) ; 4. Callovien-Oxfordien (Marnes) ; 5. Quaternaire ; 6. Changement de pente convexe ; 7. Corniche calcaire ; 8. Rupture de pente concave (limites du talus d’éboulis) ; 9. Réseau hydrographique ; 10. Courbe de niveau ; 11. Evénements rocheux ; 12. Merlons de protection ; 13. Limite du front urbain.

2. Study site

5The village of Crolles is located in the Isère department, northeast of the Grenoble conurbation (fig. 1A-B). It covers an area of 14.2 km² from the Bec Margain (1,036 m a.s.l.) to the Isère River (220 m a.s.l.). The village is situated on the eastern slope of the Chartreuse Mountains (French Alps), with slope angles that decrease gradually from 45–50° in its upper portion to 15° at the urban front, with a marked concavity between 300 and 350 m a.s.l. It is topped by a 300 m-high sub-vertical cliff made of thick-bedded limestones and marls from the upper Jurassic period (fig. 1C-D) (Dussauge-Peisser et al., 2002). The cliff triggers rockfall with sizes varying from gravel clasts to blocks with volumes > 30 m³. The village of Crolles has constantly faced rockfall hazards as reflected in toponymy: the root of Crolles, corrotulare, literally means to roll a block in Latin (Lopez-Saez et al., 2016). Historical archives, fresh blocks, recent impact craters on the ground and visible growth disturbances (i.e., scars, decapitated trees) on the forest stand confirm ongoing numerous rockfall activity on the slopes. Since the mid-20th century, the village has experienced an intense periurban expansion, the total population increasing from 964 inhabitants in 1946 to 8345 in 2015. Several neighborhoods such as Le Fragnès, Magny, Le Coteau, and Ardillais (fig. 1E) have spread over the slopes of the Chartreuse Mountains and experienced an increasing risk related to rockfall activity (fig. 2). As a consequence, since the 1990s, several protective walls have been constructed to reduce rockfall risk (fig. 1E). Above the protective walls, disregarded in our analysis in order to account for homogenous rockfall propagations throughout the study site, the slope is characterized by a dense forest cover and discontinuous grassland plots (fig. 3).

Fig. 2 – Evolution of the southeastern slopes of the Chartreuse Mountains between 1911 (A) and 2017 (B).
Fig. 2 – Évolution de l’occupation du sol du versant sud-est du Massif de La Chartreuse entre 1911 (A) et 2017 (B).

Fig. 2 – Evolution of the southeastern slopes of the Chartreuse Mountains between 1911 (A) and 2017 (B).  Fig. 2 – Évolution de l’occupation du sol du versant sud-est du Massif de La Chartreuse entre 1911 (A) et 2017 (B).

Fig. 3 – Land-use and land-cover (LULC) map of the Crolles slopes in 2017.
Fig. 3 – Carte de l’utilisation et de l’occupation des sols (LULC) du versant de Crolles en 2017.

Fig. 3 – Land-use and land-cover (LULC) map of the Crolles slopes in 2017.  Fig. 3 – Carte de l’utilisation et de l’occupation des sols (LULC) du versant de Crolles en 2017.

Forests cover 68% of the landscape, whereas 9%, 10%, and 12% are occupied by wastelands, screens and thalwegs, grasslands and crops, respectively. Vineyards occupy 1% of the land cover. 1. Historical forest; 2. Forest; 3. Vegetated thalweg; 4. Thalweg; 5. Steep scree; 6. Urban front; 7. Wasteland; 8. Grassland; 9. Vineyard; 10. Crops.
Les forêts recouvrent 68 % des pentes contre 9 %, 10 %, 12 % pour les friches, éboulis et thalwegs, prairies et cultures, respectivement. Les vignes représentent seulement 1% de la surface totale. 1. Forêt ancienne ; 2. Forêt ; 3. Thalweg végétalisé ; 4. Thalweg ; 5. Éboulis ; 6. Front urbain ; 7. Friches ; 8. Prairie ; 9. Vigne ; 10. Culture.

3. Risk framework and numerical model set-up

3.1. General framework and computation

6Rockfall risk can be defined as the simple product of probabilities summed for all the at-risk elements considered, according to the following equation (Agliardi et al., 2009):

  [1]

7where Rw represents the expectations of the consequences (or a certain amount of damage) of hazard activity for the whole system at risk, w. This system is composed of a set of any element or combination of elements z potentially at risk, characterized by an exposure factor q(zw) and a metric zw. The frequency f(Event) of the hazard, the reach probability pz(Event) on an element at risk z and the resulting damage Dz(Event) are derived for all possible events and are representative of the physical and kinetic properties of rockfall.

8Due to the complexity and suddenness of the rockfall process, several parameters such as the real shape or impact characteristics that would be useful for risk assessment are systematically lacking (Eckert et al., 2012; Bourrier et al., 2016). As a consequence, a simplified equation that only includes rock volumes and kinetic energies is generally adopted:

               [2]

9where f(v) corresponds to the occurrence frequency of rockfall events with a volume v, pz(E|v) the reach probability on an element at risk z by a block of volume v with an energy E and Dz(E) the resulting damage on z for an impact energy E.

10Risk analysis is performed numerically on a case-by-case basis by distinguishing each element at risk z identified in the system w. The risk value specific to each element z is approximated by discrete sums on several volume classes. For each of these volume classes, the damaging value is evaluated by the Monte Carlo method as:

                                                         [3]

11where Ek [1, N] is the local distribution of rockfall energies evaluated over N simulations. The risk for the element z is expressed as:

           [4]

12where the volume distribution is discretized in VCL classes.

13Finally, the total risk for the system w is the sum of individual risks for each of the elements z (Eckert et al., 2012):

                                                                              [5]

3.2. Rockfall probability

14Rockfall hazard definition incorporates the concepts of magnitude, recurrence time and geographical location. The first refers to the intensity (volume, energy) of the rockfall event, which conditions its destructive power; the second refers to the temporal frequency of the event; the third (better known as susceptibility) implies the ability to identify the place where the phenomenon may occur (Guzzetti et al., 1999).

15Susceptibility is the likelihood that a block departure event will occur in a specific area based on the local terrain conditions (Brabb, 1984). In this study, potential rockfall release areas have been deduced from a DEM-based geomorphometric approach known as the Slope Angle Frequency Distribution (SAFD) procedure (Loye et al., 2009; Michoud et al., 2012). In this procedure, based on the Histofit routine, slope angle distribution is broken down into several Gaussian distributions that can be considered characteristic of morphological units (such as rock cliffs, steep slopes, foot slopes and plains). The terrain is considered as a potential rockfall source if its slope angle exceeds the frictional angle of the rock mass, which in turn is defined where the Gaussian distribution of the morphological unit “rock cliff” becomes dominant over the “steep slope” unit.

16Statistical analyses of historical data related to natural phenomena (public archives or catalogues developed by, for example, forest rangers, local administrations and road owners) suggest that the volume (magnitude) of events and their frequencies can be fitted by a power law (De Biagi et al., 2017). This approach developed for earthquakes in the 1950s has been transposed to several mass movements such as landslides (Lari et al., 2014), snow avalanches and rockfalls (Dussauge-Peisser et al., 2002; Hantz et al., 2003; Guerin et al., 2014). In the case of rockfalls, it has been expressed as:

                                                                                 [6]

17where V is the rockfall volume, N the cumulative number of rockfalls greater than V, b the cumulative power-law scaling exponent, and α a site-dependent parameter.

18Contrary to previous studies, here we applied the volume–frequency relationship proposed by De Biagi et al. (2017), which separately investigates (i) the temporal occurrence of historical rockfall events, and (ii) their associated volume distribution. For this purpose, 29 fresh blocks (tab. 1) with volumes ranging from 0.2 m³ to 10 m³ were systematically inventoried along a 900-m-long transect located in the Ardillais neighborhood (fig. 1C-E).

19The temporal occurrence was defined with volumes greater than u = 1 m³, the most susceptible to significantly damaging the buildings. Then we used extreme value theory (EVT) to characterize the volume distribution by an asymptotic model from the generalized Pareto (GPD) family (Coles, 2001). The annual cumulative frequency of rockfall events (fig. 4) is given by:

      [7]

20where V represents the volume of the blocks, λ is the temporal occurrence frequency of rockfall per unit of area, and u, σ, ξ the location, the scale and the shape of the distribution, respectively. The circumflex denotes statistical estimates obtained from the data using a maximum likelihood procedure.

Tab. 1 – Rockfall catalogue.
Tab. 1 – Catalogue des événements rocheux.

Tab. 1 – Rockfall catalogue.   Tab. 1 – Catalogue des événements rocheux.

Rockfalls events inventoried along a 900-m-long transect located in the Ardillais neighborhood (fig. 1). According to the parallelepiped shapes of calcareous blocks, their volumes were estimated through the measurement of their x-, y- and z-axes.
Les événements rocheux ont été inventoriés le long d’un transect situé à proximité du quartier d’Ardillais (fig. 1). Sur le terrain, compte-tenu des formes parallélépipédiques des blocs calcaires, le volume de ces derniers a été estimé en mesurant leurs axes x, y et z

Fig. 4 – Rockfall volume–cumulative frequency relationship.
Fig. 4 – Relation volume–fréquence cumulée des événements chutes de blocs.

Fig. 4 – Rockfall volume–cumulative frequency relationship.  Fig. 4 – Relation volume–fréquence cumulée des événements chutes de blocs.

Volume–cumulative frequency relationships in events/yr/hm² and derived from a rock volume inventory made along a 900-m-long transect located in the Ardillais neighborhood. A: Obtained by an asymptotic model of the generalized Pareto distribution (GPD) family. The shaded area illustrates the model 95% confidence interval. B: Relation fitted with a power law (log-log scale).
Fréquences cumulées des événements rocheux en événements/an/hm² obtenues à partir des événements rocheux répertoriés le long d’un transect situé dans le quartier des Ardillais. A : Relation obtenue à partir de la loi de Pareto généralisée (GPD). La surface grisée représente l’intervalle de confiance à 95 %; B : Relation obtenue à partir de la loi puissance (échelle logarithmique).

3.3. Trajectory and maximum runout of falling blocks

21To assess rockfall hazard, knowledge of the spatial distribution of rockfalls is crucial. To obtain this information, we used the probabilistic process-based rockfall trajectory model Rockyfor3D, capable of simulating rockfall processes in three dimensions. The model was described extensively in Dorren (2012), and here we will only briefly illustrate the inputs and outputs. On the basis of slope and surface characteristics, the model provides information on, for example, rock propagation for any location on the study site such as the number, in the simulation sample, of rocks passing through a given surface or the kinetic energy of rocks. At Crolles, the topography was described using a 5-m resolution DEM (RGE, IGN) while slope surface properties were characterized on the basis of a current Land Use and Land Cover (LULC) map. LULC patchiness was derived, according to the cadastral map, from aerial photo interpretation using standard photographic keys (i.e., tone, texture, pattern, shape and size) and information available from the French digital cadaster database. Then soil types (e.g., fine soil material or bedrock) and roughness parameters were associated with each LULC class. For the latter parameter (roughness), three variables representing the obstacle height encountered on 10% (Rg10), 20% (Rg20) and 70% (Rg70) of the surface (tab. 2), respectively, were defined. The oldest forest allotments present in the upper part of the slopes, in contact with the cliff, were mainly located on steep scree slopes susceptible of considerably modifying rockfall propagation. Field observations in these allotments reveal that 10%, 20% and 70% of the total surface was occupied by blocks with heights of 0.25 m, 0.15 and 0.05 m, respectively (tab. 2). On the contrary, a more limited roughness (Rg10:  0.05 m; Rg20: 0.00 m; Rg70: 0.00 m) was associated with flatter allotments occupied by cultivated land (i.e., grassland, culture allotments) and urbanized areas (tab. 2). Finally, the protective walls were removed from the DEM and gaps were corrected by a spatial interpolation.

Tab. 2 – Values used for the parameterization of the Rockyfor3D model.
Tab. 2 – Valeurs utilisées pour le paramétrage de Rockyfor3D.

Tab. 2 – Values used for the parameterization of the Rockyfor3D model.  Tab. 2 – Valeurs utilisées pour le paramétrage de Rockyfor3D.

Rg70, Rg20 and Rg10 represent the roughness (height, in centimeters, of obstacles encountered by the falling block) on 70%, 20% and 10% for the plot surface considered, respectively. The Rn value (normal coefficient of restitution) defines the change in normal velocity during impact and is a function of the soil type. Nb.trees.ha represents the density of the forest stand expressed as the number of stems per hectare. Mean diameter of trees and associated standard deviation are described by DBH mean and DBH std values, respectively. Based on these values, the Rockyfor3D model randomly places a given number of trees within each of the allotments considered (Dorren, 2012).
Rg70, Rg20 et Rg10 désignent des paramètres de rugosité du sol et plus précisément la hauteur des obstacles (en centimètres) rencontrés par les blocs en chutes sur 70 %, 20 % et 10 % de la surface d’une parcelle. Rn (coefficient de restitution normal) définit l’élasticité des différents types de sol et est utilisé par le modèle pour calculer la perte d’énergie lors d’un impact. Nb.trees.ha correspond à la densité (nombre de tiges par hectare) du couvert forestier. DBH mean et DBH std caractérisent le diamètre des arbres (moyenne et écart-type). Ces paramètres sont utilisés par le modèle pour disposer aléatoirement les arbres dans chaque parcelle (Dorren, 2012).

3.4. Reach probability, mean damage and elements at risk

22A total of 20,331 potential cell sources were mapped on the DEM and 10,000 rockfalls with volumes randomly extracted between 1 m³ and 20 m³ were simulated from each source cell. Volumes that exceed 20 m³ were not included in the analysis so as to (i) preserve the efficiency of data storage and processing, and to (ii) remain in the Rockyfor3D model validity range.

23Despite the wide variety of at-risk elements present in Crolles (roads, paths, vehicles, people, etc.), the analysis focused on the buildings mapped on the cadastral map. Simulations were parameterized to stop in case of an impact with a building. The reach probability on building z for blocks belonging to the volume class VCL was computed as:

                                                               [8]

24where Simz(VCL) is the total number of blocks simulated in the volume class VCL that reach the building z and SimTOT(VCL) the total number of blocks simulated in the volume class VCL.

25Knowing the impact energies recorded over the simulations, we derived the degree of loss from the physical vulnerability curve developed by Agliardi et al. (2009). This curve resulting from the back analysis of the 2004 rockfall event in Fiumelatte (Italy) converts the energy of the impact into potential damage varying between 0 (no structural damage) and 1 (total collapse). As a building z can be reached by a large number of simulations in a given volume class VCL, its damage value is set by the mean of the distribution as follows:

                                  [9]

26where ͞z (Vcl) is the mean damage on building z for blocks belonging to the volume class VCL, and Ek is the impact energy (in J) for the block belonging to the VCL class.

27Contrary to vehicles, trains or humans, buildings are static and consequently their exposure factors q(zw) = 1. Finally, the values zw are defined as the floor area (m²) approximated from the current cadastral map. The risk is therefore expressed as the mean surface destroyed each year (m².yr¹).

4. Results

4.1. Rockfall frequency and release areas

28The fitted generalized Pareto model is characterized by maximum likelihood estimators σ and ξ equal to 0.940 and 0.355, respectively (fig. 4A). Based on the relative freshness of the blocks (limited patina, absence of blunt or rounded-off edges, lichens or vegetation on the surface) and on the presence of visible scars on tree stems (Trappmann and Stoffel, 2013), we estimated that the reference period for the computation of rockfall frequency should not reasonably exceed one century. Based on this estimated timeframe, we inventoried 17 blocks > 1 m³ potentially released from a 11.5-hm² cliff section located above the representative transect chosen for field analysis. As a consequence, the rockfall frequency λ was estimated at 0.015 events.yr‑¹.hm². According to the Histofit routine, the threshold slope angle for source areas was set at 49°. The total surface of the potential release areas was evaluated at 127.85 hm² and consequently, the frequency of rockfalls > 1 m³ and > 20 m³ was estimated at 1.890 and 0.005 events.yr¹, respectively.

29These results were compared with those obtained from a more classical approach in which the volume–frequency distribution is fitted by a power law (see eq. 6). Figure 4B shows the cumulative distribution of block volumes recorded along the study transect and the associated power law. The estimators α and b were evaluated at 13.53 and ‑0.97, respectively. Based on the rock wall surface (11.5 hm²) and the timeframe (one century) mentioned above, the parameter α, which represents the rockfall frequency per year and per hm², was estimated at 0.012 events.yr¹.hm². Considering the surface of the whole cliff (127.85 hm²), the frequency of rockfalls > 1 m³ and > 20 m³ was estimated at 1.50 and 0.08 events.yr¹, respectively.

4.2. Probability and energy of rockfall impacts

30Regardless of the volume class, in the simulation campaign we recorded 1,645,834 rockfall impacts on 177 buildings mainly located in the first two rows of houses that compose the urban front. A total of 16,196 (> 1%) of these impacts have been recorded for volume classes up to 7 m³ (fig. 5). Above this threshold, the number of recorded impacts increased linearly and exceeded 250,000 for the class > 19 m³. Regardless of the volume class, 92% of the impacted elements at risk had a reach probability pz < 0.01%, such as buildings ID-1390, ID-452, ID-1352 and ID-455, all located in the Le Fragnès neighborhood, and impacted by 21,529, 25,222, 265 and 9,828 blocks, respectively (fig. 1E, 6). By contrast, two buildings located in the Le Coteau neighborhood (ID-1549, ID-1908) were characterized by a pz value > 0.05%. Interestingly, they account for 10% and 42% of the total number of recorded impacts, respectively. With regard to the intensity of rockfall simulations, 18% of the blocks stopped at the level of the urban front were characterized by a kinetic energy < 100 kJ while 41% of the impacts, mainly related to block with volumes > 10 m³, exceeded 1,000 kJ.

Fig. 5 – Number of rockfall impacts recorded on buildings and distribution of the associated rockfall risk.
Fig. 5 – Nombre d’impacts enregistré sur les bâtiments et distribution du risque chutes de blocs associé.

Fig. 5 – Number of rockfall impacts recorded on buildings and distribution of the associated rockfall risk.  Fig. 5 – Nombre d’impacts enregistré sur les bâtiments et distribution du risque chutes de blocs associé.

A: Distribution of the number of impacts recorded on buildings for each volume class; B: distribution of the rockfall risk (% of the total value) for each volume class. The red curve represents the risk when the physical vulnerability is set at 1 (total destruction of the building in case of impact).
A : Distribution du nombre d’impacts pour chaque classe de volume. B : Distribution du risque chutes de blocs pour chaque classe de volume. La courbe rouge représente la distribution du risque quand le dommage est fixé à 1 (destruction totale du bâtiment à chaque impact).

31These results are very sensitive to Rockyfor3D parameterization, especially with regard to the roughness values. For example, a 5-cm increase in the Rg70, which represents the height of a representative obstacle that a falling block encounters in 70% of the cases during a rebound, induced a sharp decrease in the total number of impacts at the level of the urban front. In the buildings with IDs 452, 455, 1352 and 1390, the respective numbers of impacts decreased from 25,222 to 63; 9,828 to 12; 265 to 0 and 21,529 to 274, for values of the Rg70 in the forest allotments increasing from 0.05 to 0.10 m (fig. 6). With an Rg70 value set at 0.15 m, no impact was recorded on the buildings with IDs 452, 455 and 1,352 while only 19 blocks reached the ID-1390 house.

Fig. 6 – Sensitivity of rockfall modeling to initial parameterization.
Fig. 6 – Sensibilité de la modélisation des chutes de pierres au paramétrage initial.

Fig. 6 – Sensitivity of rockfall modeling to initial parameterization.  Fig. 6 – Sensibilité de la modélisation des chutes de pierres au paramétrage initial.

Number of impacts recorded on buildings IDs 1549 and 1908 located in the Le Coteau neighborhood (A, B) for Rg70 = 0.05 m (C). Number of impacts recorded on buildings IDs 455, 1352, 452 and 1390 in the Le Fragnès neighborhood (A, D) for Rg70 = 0.05 m (E), Rg70 = 0.10 m (F), and Rg70 = 0.15 m (G).
Nombre d’impacts enregistrés sur les bâtiments n° 1549 et 1908 localisés dans le quartier du Coteau (A, B) pour Rg70 = 0.05 m (C). Nombre d’impacts enregistrés sur les bâtiments n° 455, 1352, 452 et 1390 du quartier Le Fragnès (A, D) pour Rg70 = 0,05 m (E), Rg70 = 0,10 m (F), et Rg70 = 0,15 m (G).

4.3. Vulnerability and risk analysis results

32The energies of rockfall impacts at the level of each element at risk were converted to a damage level based on the empirical vulnerability function developed by Agliardi et al. (2009). The mean damage associated with volume classes > 10 m³ systematically exceeded 0.60 and was above 0.75 for the 19- to 20-m³ class volume. Unsurprisingly, the energies were lower for volume classes up to 10 m³ and the mean damage induced by blocks in the 1- to 2-m³ class was 0.4.

33Following eq. 4 and eq. 5, which combine the rockfall frequency, the individual reach probability and the mean degree of loss for each element at risk integrated for each volume class, we computed the risk to buildings in terms of mean annual destroyed surface per year (m².yr¹). Following this approach, the mean total risk Rw was 0.1 m².year¹. In detail, the individual risk was < 0.001 m².yr¹ for a large majority of the impacted buildings (fig. 7). If we consider a typical structure of 150 m², this value corresponds to the complete destruction of the building every 150,000 years. On the other hand, it exceeds 0.01 m².yr¹ (100-year life expectancy) for the ID-1549 building located in the Le Coteau neighborhood (fig. 1, 7).

Fig. 7 – Rockfall risk map.
Fig. 7 – Cartographie du risque chutes de blocs.

Fig. 7 – Rockfall risk map.   Fig. 7 – Cartographie du risque chutes de blocs.

34Figure 5B summarizes the distribution of the risk values for the 19 classes of volumes considered in this study. This distribution was compared with the expected value of risk when the degree of loss is set to a value of 1. The discrepancies between the two distributions induced a 35% difference in the rockfall risk. These differences illustrate the influence of energy on the risk, namely the ability of masonry walls to resist low-energy impacts.

35In addition, the rockfall risk was < 5% of its total value for rock volume classes up to 7 m³ as a result of the reduced number of impacts associated with these classes (fig. 5A). At the upper limit of the volume distribution (> 12 m³), the risk values did not exceed 7% of the total risk value due to the lower frequency of rockfall events in these classes (fig. 4A). Finally, higher risk values were associated with volume classes between 7 and 12 m³.

5. Discussion

5.1. Contributions of the quantitative analysis for rockfall risk management

36In this study, we developed the first quantitative analysis of rockfall risk for the French Alps, in the municipality of Crolles (fig. 1). To integrate a wide spectrum of probability of occurrence, propagation, intensity, impact probability and resulting damage to buildings, the complete distribution of block volumes within the range 1–20 m³ was implemented in our rockfall risk calculation. The results are presented for the different volume classes both at the municipality and individual levels, thus identifying the most critical volume classes for risk management, so that the most risk-prone areas can be mapped.

37The results evidence a nonlinear relationship between the risk and the volume classes with a tipping point in the distribution of risk observed for volumes within the range 7–12 m³ (fig. 5B). The almost comparable distributions of risk values obtained with the empirical vulnerability function developed by Agliardi et al. (2009) and a physical vulnerability set at 1 suggest that this tipping point does not depend on rockfall energy. As a consequence, we hypothesize that the maximum risk associated with volumes within the 7- to 12-m³ range could be attributed to a sharp decrease in the protective function of the forest, which can no longer reduce rockfall propagation. This hypothesis is further supported by the results of Dupire et al. (2016) and Toe et al. (2018), which demonstrated that (i) forest–block interactions reduce both the reach probability and the energy of rockfalls, and (ii) the protective function of the forest is limited for rock volumes > 10 m³. They are also consistent with the findings of Moos et al. (2017) at two sites in the Swiss Alps, which demonstrated that risk is strongly reduced (between 20 and 50%) in forest for volumes < 5 m³ but can remain considerable for greater volumes in case of sufficiently long forested slopes. By contrast, the risk decrease observed for classes above 12 m³ is attributed to the low frequency of high-magnitude events (fig. 4A).

38On a spatial plan, the risk map (fig. 7) shows a rockfall risk limited to the buildings exposed first. The existence of a critical risk-prone area in the Le Coteau neighborhood seems to result from specific terrain conditions and the LULC pattern where the most impacted building (42% of the reach probability, 27% of the total risk) is overhung by a grassland plot (fig. 3), characterized by an absence of roughness (tab. 1), located downslope from of a preferential rockfall path.

39To summarize, these results (i) confirm the protective effect of the forest for rockfall risk reduction for volumes up to 7 m³; (ii) evidence that the risk reduction associated with continuous afforestation can be counterbalanced by the landscape reorganization below the forest front; (iii) show the importance of accounting for intermediate volume classes with propagation poorly affected by the forest stands and still characterized by frequencies significant enough to influence the risk.

5.2. Pros and cons of the quantitative risk analysis approach undertaken at Crolles

40Previous quantitative rockfall risk analyses mainly focused on back analysis of historical events (Corominas et al., 2005; Agliardi et al., 2009). They are restricted to a limited number of release areas and to specific block volumes. By contrast, by including all potential release areas from a 300-m-high sub-vertical cliff that threatens the village of Crolles, the risk map proposed here provides, for each building, a probability of physical losses due to rockfalls in a wide spectrum of volumes. In addition, in current practices, the risk is usually expressed as damage in monetary value (Agliardi et al., 2009; Moos et al., 2017). This makes them tributary of the economic values affected to each element at risk, which are susceptible to change over time and space. Conversely, we deliberately quantified the risk as a physical loss expressed in m².yr-1 in order to express the risk in an objective and reproducible manner. We believe that the holistic approach chosen here is a major interest for stakeholders in charge of risk management because it allows for prioritization and dimensioning protective structures (Corominas et al., 2005, 2013). Yet, one must keep in mind several limitations related to (i) the magnitude/frequency of rockfall, (ii) the parameterization of Rockyfor3D and (iii) the absence of a site-specific vulnerability curve for Crolles buildings.

5.2.1. Uncertainties related to the frequency–volume relationship

41The first limitation related to the absence of a historical catalogue was overcome through detailed field observations along a representative transect. Despite the care taken during the fieldwork, our survey resulted in different uncertainties relating to the representativeness of the transect, the temporal window (one century) and the surface (11.5 ha) of the cliff considered as a potential source for the sampled blocks. The reliability of the survey is also hampered by several inaccuracies related to (i) the simplification of rockfall shape to parallelepipeds, (ii) the high probability of rock removed in the lower part of the slope (fig. 2) and (iii) potential biases on the volume estimations related to fragmentation during rockfall propagation (Corominas and Mavrouli, 2013).

42The second limitation is associated with the choice of the model used to fit the volume–frequency relationship. Here, following the recommendations of De Biagi et al. (2017), we characterized the volume distribution using the extreme value theory rather than the more frequently used power law model (Dussauge-Peisser et al., 2002; Guerin et al., 2014). The generalized Pareto model (GPD) was demonstrated to be more suitable to quantify, in a generic way, the stochastic behavior of large occurrences of any process (Coles, 2001). The choice of the GPD instead of the power law has limited impacts on the characterization of low-magnitude high-frequency events but induces significant differences at the tail of the distribution. The return periods associated with rockfall events > 20 m³ thus increase from 12.5 years to 200 years when the GPD is used instead of the power law model.

5.2.2. Sensitivity of rockfall modeling to initial parameterization

43Regarding rockfall propagation (Bourrier et al., 2009), technical restrictions concern the ability of the Rockyfor3D model to properly simulate rockfall trajectories. The soil mechanical properties attributed to each of the allotments remain difficult to estimate. This difficulty is even more detrimental in that our results, in agreement with Corona et al. (2017), demonstrate that a slight increase in roughness parameters may significantly reduce reach probabilities (fig. 6). Furthermore, soil mechanical properties have been attributed to each LULC type on the basis of field surveys in representative allotments. Yet, they do not account for the strong heterogeneity possible in each LULC type. Similarly, no roughness was attributed to the urban area despite the variety of elements in this environment (asphalt roads, enclosure walls, public gardens, etc.).

44Finally, the Rockyfor 3D model was coded to stop the rockfall simulation when it intersects an element at risk. This assumption is warranted by the absence of precise knowledge on the rockfall–building interaction. It may induce, however, an underestimation of the risk since the retroanalysis of past events, e.g., in Fiumelatte or Tramin in Italy (Agliardi et al., 2009), demonstrated that a block could pass through a building or damage several neighboring houses. In the future, better characterization of these interactions could significantly improve the risk analysis in an urban context.

5.2.3. Absence of site-specific vulnerability function and inaccuracy in exposed housing areas

45The damage assessment is based on the vulnerability function specifically developed by Agliardi et al. (2009) in the aftermath of the Fiumelatte event (Italy) in November 2004. The use of this function was driven by (i) comparable slope lengths (> 500 m) and rockfall volume classes at Crolles and Fiumelatte, (ii) the lack of damaging events at Crolles that would have enabled a site-specific retroanalysis, and (iii) the scarcity of continuous vulnerability functions for structural elements in the literature. For example, the approach developed by Mavrouli and Corominas (2010) was not applicable in this study because (i) it accounts for the impact location of the rock requiring detailed information on the structure (information not available at our study site scale), and (ii) it is developed for a smaller volume range (up to ~ 4 m³) than those of the study.

46Yet, the results of the present study should be considered cautiously given that the vulnerability curve of Agliardi et al. (2009) was calibrated on a limited number of documented events and it is impossible to precisely evaluate the relevance of its transposition to our case study.

47With respect to the issue, additional uncertainties are related to the evaluation of housing areas (zw) potentially exposed to rockfall hazard. Indeed, despite the existence of multi-storey housing in Crolles, this study only accounts for surfaces affected on the ground floor. In addition, these can be overestimated due to the resolution of the raster file used in Rockyfor3D (25 m²). For example, a building with a ground floor of 70 m² that overlaps four cells of our raster file will be assigned a total surface of 100 m² in our risk calculation.

48In view of these different limitations, the risk values obtained in this study can be considered as indicative (Corominas et al., 2014), but cannot be used as is for zoning purposes, for example. As a consequence, additional work is required to further assess the weight of the different assumptions and limitations presented above on the final risk estimates. Specifically, a systematic quantification of uncertainties associated with each of the risk components would greatly improve the reliability of the results (Straub and Schubert, 2008; Wang et al., 2014).

6. Conclusion and outlooks

49In this study, we developed a quantitative analysis of rockfall risk in the municipality of Crolles that integrates volumes in the 1- to 20-m³ range. The approach developed here (i) accounts for all distributions of rockfall volumes, (ii) precisely maps the elements highly subjected to risk, and (iii) evidences the volume classes making a major contribution to total risk. Epistemic uncertainties mainly related to the magnitude and frequency of rockfall, the parameterization of the trajectory model and the absence of a vulnerability curve for the study site, for example, are the most critical steps of the risk analysis procedure. Hence, we strongly believe that a better estimation of the rockfall frequency relationship through Lidar monitoring (Guerin et al., 2014), for example, or tree-ring analyses (Favillier et al., 2017) would greatly increase the reliability of QRA studies. In addition, we also encourage more systematic coupling between rockfall modeling and field-based dendrogeomorphic approaches as the potential of the latter repeatedly demonstrated its potential for the calibration of rockfall simulations (Stoffel et al., 2006; Corona et al., 2017). Finally, to our knowledge, vulnerability curves that are potentially usable for rockfall QRAs have been developed by Agliardi et al. (2009) and Mavrouli and Corominas (2010). Owing to the efforts needed to develop such vulnerability functions, we are aware that specific curves cannot be developed at each study site. However, additional retroanalyses of past events should be encouraged in the future in order to assess existing models.

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Annexe

Version française abrégée

L’aléa chute de bloc est défini comme le détachement brutal et rapide d’une masse rocheuse depuis une paroi verticale ou sub-verticale, qui se propage vers l’aval sous l’effet de la gravité par rebonds successifs. Ces événements, fréquents en zones de montagne, induisent un risque majeur pour les biens et les personnes. Par exemple, le détachement d’un volume rocheux de 30 m³ en 2014 a provoqué le déraillement d’un train près de Pignes-près-d’Annot, faisant deux victimes et de nombreux blessés. Cet événement illustre bien notre vulnérabilité face à cet aléa et souligne les besoins en matière de méthode de diagnostic et d’analyse du risque pour l’aménagement des territoires de montagne et le choix de mesures de mitigation optimales. Dans ce contexte, cette étude propose une méthodologie d’évaluation du risque par une approche de type QRA « Quantitative Risk Assessment » adaptée à la spécificité du processus chute de bloc (Corominas et al., 2014). Cette étude, pionnière à l’échelle des Alpes françaises, a été réalisée sur la commune de Crolles, localisée dans le département de l’Isère, sur le versant sud-est du Massif de La Chartreuse (fig. 1). Les archives historiques (catalogue d’évènements, photographies), les cicatrices d’impacts observées sur les arbres, les cratères sur le sol, ainsi que les blocs récents de plusieurs m³ observés le long du versant témoignent de l’intensité du phénomène. Considérant des volumes rocheux de 1 à 20 m³ issus des 300-m de parois sub-verticales qui surplombent le village, le risque rocheux a été évalué pour chaque bâtiment référencé dans le plan cadastral de Crolles.

Les résultats obtenus, exprimés en surface moyenne de bâti détruite chaque année, ont été calculés en croisant des modèles d’aléa et de dommage issus de la littérature scientifique, d’études de terrain et d’approches numériques. La relation volume-fréquence des événements rocheux a été élaborée en utilisant la statistique des valeurs extrêmes – loi de Pareto généralisée (Coles, 2001; De Biagi et al., 2017) – appliquée à un catalogue d’événements répertoriés sur le versant de Crolles (fig. 4). La propagation des événements rocheux a été modélisée au moyen du logiciel de simulation trajectographique Rockyfor3D (Dorren, 2012), en prenant en compte l’hétérogénéité de l’occupation et de l’usage des sols (rugosité, type de sol, densité du couvert forestier). Par ailleurs, les énergies des blocs fournies par le logiciel Rockyfor3D ont été utilisées pour calculer le taux de dommage moyen associé à chaque enjeu. Ce dernier est estimé à partir de la courbe de vulnérabilité d’Agliardi et al. (2009), qui transforme l’énergie d’un bloc (en J) en un dommage dont la valeur est comprise entre 0 (pas de dommage) et 1 (destruction totale du bâti). Cette courbe est issue de la rétro-analyse de l’évènement chutes de blocs observé en 2004 à Fiumelatte (Italie).

Sur le plan spatial, la cartographie du risque rocheux démontre que les enjeux menacés sont principalement situés sur la première rangée de bâtiment (fig. 7). Le risque individuel excède rarement 0.01 m² détruits par an, mais le quartier du Coteau fait exception puisque le risque peut dépasser cette valeur. Dans ce quartier, l’augmentation du risque résulte de conditions d’utilisation et d’occupation des sols particulières, où l’absence de rugosité induite par la présence d’une parcelle de prairie (fig. 3) directement en sortie d’un thalweg est à l’origine d’une augmentation des probabilités d’impacts.

Par ailleurs, le risque rocheux pour le bâti de Crolles a été calculé pour 19 classes de volume comprises entre 1 et 20 m³. La distribution qui résulte de cette analyse met en évidence la proportion importante du risque total liée aux classes de volumes comprises entre 7 et 12 m³. La décroissance du risque pour des volumes supérieurs résulte de la diminution des fréquences d’occurrence pour des événements de fortes magnitudes (fig. 4A). A l’inverse, pour des classes de volume inférieures, le risque diminue du fait de la protection induite par le couvert forestier.

L’approche développée ici présente un caractère holistique puisqu’elle intègre conjointement tous les volumes et l’intégralité des zones de départ potentielles de la falaise calcaire surplombant le village de Crolles. Elle permet de cartographier avec précision les éléments les plus exposés et de mettre en évidence les classes de volume qui contribuent le plus au risque total. Le caractère quantitatif de cette approche lui confère un intérêt pour l’aménagement du territoire et l’optimisation du positionnement et du dimensionnement des ouvrages de protection. Cependant, en raison de plusieurs incertitudes d’ordre épistémique, les valeurs de risque rocheux calculées ici n’ont qu’un caractère indicatif. Ces limites, discutées dans cet article concernent chaque composante du calcul de risque. Elles sont liées, par exemple, aux incertitudes concernant (i) les relations magnitude/fréquence des événements rocheux, (ii) le paramétrage du modèle trajectographique ou (iii) l’absence de de courbe de vulnérabilité spécifique à notre site d’étude. Néanmoins, nous pensons que l’intégration plus systématique d’analyses dendrogéomorphologiques, des archives historiques, d’observations de terrain ou de données issues du suivi des parois pourraient augmenter considérablement la fiabilité de l’analyse quantitative du risque.

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Table des illustrations

Titre Fig. 1 – Location and geological setting of the study site. Fig. 1 – Localisation et contexte géologique du site d'étude.
Légende A: Location at the French Alps scale; B: Situation at the local scale (Crolles is located in the Isère valley, near the city of Grenoble, on the southeastern slopes of the Chartreuse Mountains); C: Overview of the Crolles slopes; D: Geomorphological sketch of the Crolles area; E: Overview of the Crolles urban area and neighborhoods. 1. Location of the 900-m-long transect used to inventory past rockfall events; 2. Berriasian (Marl); 3. Tithonian (Limestone); 4. Callovian-Oxfordian (Marl); 5. Quaternary; 6. Convex change of slope; 7. Ledge; 8. Concave break of slope (talus slope limits); 9. Hydrographic network; 10. Contour line; 11. Rockfall events; 12. Protective structures; 13. Urban front limit. A : Localisation à l’échelle des Alpes françaises ; B : Situation à l’échelle locale (Crolles est localisée dans le département de l’Isère, dans l’agglomération grenobloise, sur le versant sud-est du Massif de La Chartreuse) ; C : Aperçu des falaises surplombants le village de Crolles ; D : Croquis géomorphologique de Crolles ; E : Vue générale de Crolles et de ses quartiers ; 1. Localisation du transect utilisé pour l’inventaire des chutes de blocs passées ; 2. Berriasien (Marnes) ; 3. Tithonien (Calcaire) ; 4. Callovien-Oxfordien (Marnes) ; 5. Quaternaire ; 6. Changement de pente convexe ; 7. Corniche calcaire ; 8. Rupture de pente concave (limites du talus d’éboulis) ; 9. Réseau hydrographique ; 10. Courbe de niveau ; 11. Evénements rocheux ; 12. Merlons de protection ; 13. Limite du front urbain.
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Titre Fig. 2 – Evolution of the southeastern slopes of the Chartreuse Mountains between 1911 (A) and 2017 (B). Fig. 2 – Évolution de l’occupation du sol du versant sud-est du Massif de La Chartreuse entre 1911 (A) et 2017 (B).
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Titre Fig. 3 – Land-use and land-cover (LULC) map of the Crolles slopes in 2017. Fig. 3 – Carte de l’utilisation et de l’occupation des sols (LULC) du versant de Crolles en 2017.
Légende Forests cover 68% of the landscape, whereas 9%, 10%, and 12% are occupied by wastelands, screens and thalwegs, grasslands and crops, respectively. Vineyards occupy 1% of the land cover. 1. Historical forest; 2. Forest; 3. Vegetated thalweg; 4. Thalweg; 5. Steep scree; 6. Urban front; 7. Wasteland; 8. Grassland; 9. Vineyard; 10. Crops. Les forêts recouvrent 68 % des pentes contre 9 %, 10 %, 12 % pour les friches, éboulis et thalwegs, prairies et cultures, respectivement. Les vignes représentent seulement 1% de la surface totale. 1. Forêt ancienne ; 2. Forêt ; 3. Thalweg végétalisé ; 4. Thalweg ; 5. Éboulis ; 6. Front urbain ; 7. Friches ; 8. Prairie ; 9. Vigne ; 10. Culture.
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Titre Tab. 1 – Rockfall catalogue. Tab. 1 – Catalogue des événements rocheux.
Légende Rockfalls events inventoried along a 900-m-long transect located in the Ardillais neighborhood (fig. 1). According to the parallelepiped shapes of calcareous blocks, their volumes were estimated through the measurement of their x-, y- and z-axes. Les événements rocheux ont été inventoriés le long d’un transect situé à proximité du quartier d’Ardillais (fig. 1). Sur le terrain, compte-tenu des formes parallélépipédiques des blocs calcaires, le volume de ces derniers a été estimé en mesurant leurs axes x, y et z
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Titre Fig. 4 – Rockfall volume–cumulative frequency relationship. Fig. 4 – Relation volume–fréquence cumulée des événements chutes de blocs.
Légende Volume–cumulative frequency relationships in events/yr/hm² and derived from a rock volume inventory made along a 900-m-long transect located in the Ardillais neighborhood. A: Obtained by an asymptotic model of the generalized Pareto distribution (GPD) family. The shaded area illustrates the model 95% confidence interval. B: Relation fitted with a power law (log-log scale). Fréquences cumulées des événements rocheux en événements/an/hm² obtenues à partir des événements rocheux répertoriés le long d’un transect situé dans le quartier des Ardillais. A : Relation obtenue à partir de la loi de Pareto généralisée (GPD). La surface grisée représente l’intervalle de confiance à 95 %; B : Relation obtenue à partir de la loi puissance (échelle logarithmique).
URL http://journals.openedition.org/geomorphologie/docannexe/image/12778/img-12.png
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Titre Tab. 2 – Values used for the parameterization of the Rockyfor3D model. Tab. 2 – Valeurs utilisées pour le paramétrage de Rockyfor3D.
Légende Rg70, Rg20 and Rg10 represent the roughness (height, in centimeters, of obstacles encountered by the falling block) on 70%, 20% and 10% for the plot surface considered, respectively. The Rn value (normal coefficient of restitution) defines the change in normal velocity during impact and is a function of the soil type. Nb.trees.ha represents the density of the forest stand expressed as the number of stems per hectare. Mean diameter of trees and associated standard deviation are described by DBH mean and DBH std values, respectively. Based on these values, the Rockyfor3D model randomly places a given number of trees within each of the allotments considered (Dorren, 2012). Rg70, Rg20 et Rg10 désignent des paramètres de rugosité du sol et plus précisément la hauteur des obstacles (en centimètres) rencontrés par les blocs en chutes sur 70 %, 20 % et 10 % de la surface d’une parcelle. Rn (coefficient de restitution normal) définit l’élasticité des différents types de sol et est utilisé par le modèle pour calculer la perte d’énergie lors d’un impact. Nb.trees.ha correspond à la densité (nombre de tiges par hectare) du couvert forestier. DBH mean et DBH std caractérisent le diamètre des arbres (moyenne et écart-type). Ces paramètres sont utilisés par le modèle pour disposer aléatoirement les arbres dans chaque parcelle (Dorren, 2012).
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Titre Fig. 5 – Number of rockfall impacts recorded on buildings and distribution of the associated rockfall risk. Fig. 5 – Nombre d’impacts enregistré sur les bâtiments et distribution du risque chutes de blocs associé.
Légende A: Distribution of the number of impacts recorded on buildings for each volume class; B: distribution of the rockfall risk (% of the total value) for each volume class. The red curve represents the risk when the physical vulnerability is set at 1 (total destruction of the building in case of impact). A : Distribution du nombre d’impacts pour chaque classe de volume. B : Distribution du risque chutes de blocs pour chaque classe de volume. La courbe rouge représente la distribution du risque quand le dommage est fixé à 1 (destruction totale du bâtiment à chaque impact).
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Titre Fig. 6 – Sensitivity of rockfall modeling to initial parameterization. Fig. 6 – Sensibilité de la modélisation des chutes de pierres au paramétrage initial.
Légende Number of impacts recorded on buildings IDs 1549 and 1908 located in the Le Coteau neighborhood (A, B) for Rg70 = 0.05 m (C). Number of impacts recorded on buildings IDs 455, 1352, 452 and 1390 in the Le Fragnès neighborhood (A, D) for Rg70 = 0.05 m (E), Rg70 = 0.10 m (F), and Rg70 = 0.15 m (G). Nombre d’impacts enregistrés sur les bâtiments n° 1549 et 1908 localisés dans le quartier du Coteau (A, B) pour Rg70 = 0.05 m (C). Nombre d’impacts enregistrés sur les bâtiments n° 455, 1352, 452 et 1390 du quartier Le Fragnès (A, D) pour Rg70 = 0,05 m (E), Rg70 = 0,10 m (F), et Rg70 = 0,15 m (G).
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Titre Fig. 7 – Rockfall risk map. Fig. 7 – Cartographie du risque chutes de blocs.
URL http://journals.openedition.org/geomorphologie/docannexe/image/12778/img-18.png
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Référence papier

Manon Farvacque, Jérôme Lopez-Saez, Christophe Corona, David Toe, Franck Bourrier et Nicolas Eckert, « Quantitative risk assessment in a rockfall-prone area: the case study of the Crolles municipality (Massif de la Chartreuse, French Alps) », Géomorphologie : relief, processus, environnement, vol. 25 – n° 1 | 2019, 7-19.

Référence électronique

Manon Farvacque, Jérôme Lopez-Saez, Christophe Corona, David Toe, Franck Bourrier et Nicolas Eckert, « Quantitative risk assessment in a rockfall-prone area: the case study of the Crolles municipality (Massif de la Chartreuse, French Alps) », Géomorphologie : relief, processus, environnement [En ligne], vol. 25 – n° 1 | 2019, mis en ligne le 04 avril 2019, consulté le 25 mai 2019. URL : http://journals.openedition.org/geomorphologie/12778 ; DOI : 10.4000/geomorphologie.12778

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Auteurs

Manon Farvacque

Université de Grenoble Alpes, Irstea, UR ETNA – 2 rue de la papeterie, 38402 St‑Martin‑d’Hères, France (manon.farvacque@irstea.fr). Tel: +33 (0)4 76 76 27 27.

Jérôme Lopez-Saez

Climate Change Impacts and Risks in the Anthropocene, Institute for Environmental Sciences, University of Geneva – 66 bd Carl Vogt, 1205 Geneva, Switzerland (jerome.lopez-saez@unige.ch).

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Christophe Corona

Université de Clermont Auvergne, CNRS, GEOLAB UMR – 4 rue Ledru, 63057 Clermont‑Ferrand, France (christophe.corona@uca.fr).

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David Toe

Université de Grenoble Alpes, Irstea, UR LESSEM – 2 rue de la papeterie, 38402 St‑Martin‑d’Hères, France (david.toe@irstea.fr).

Franck Bourrier

Université de Grenoble Alpes, Irstea, UR LESSEM – 2 rue de la papeterie, 38402 St‑Martin‑d’Hères, France (franck.bourrier@irstea.fr).

Nicolas Eckert

Université de Grenoble Alpes, Irstea, UR ETNA – 2 rue de la papeterie, 38402 St‑Martin‑d’Hères, France (nicolas.eckert@irstea.fr).

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