Vulnerability of built elements to rockfalls: a French application in the Valley Favier, P., Bourrier, F., Berger, F.

Univ. Grenoble Alpes, Grenoble, LESSEM and ETNA, Irstea Grenoble, Grenoble, France

Cheers Final Conference 06/07/2021

Vulnerability of built elements to rockfalls: a French application in the p. 1 06/07/2021 / Favier et al. Summary

I. Definitions II. Derivation methods III. Application of the Fratch tool to the Ubaye Valley IV. Vulnerability assessment of Four à Chaux V. Conclusion et perspectives

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 2 06/07/2021 / Favier et al. I. Definitions In the community of natural hazard risk engineering: Fragility = the distribution of physical damage, function of the value of the intensity measure of the studied natural hazard; Vulnerability = the distribution of losses, function of the value of the intensity measure of the studied natural hazard.

Intensity measures examples: pressure for snow avalanche, peak ground acceleration for earthquake.

Loss is commonly estimated via the quantification of deaths, dollars/euros or downtimes. For cultural heritage assets, the estimation of loss is based on a much wider range of criteria/values (e.g., historical, aesthetic/artistical, spiritual, educational values).

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 3 06/07/2021 / Favier et al. I. Definitions: example Fragility of the Gallivaggio Sanctuary (Photo credits: Daniela Lattanzi)

Structural damage

Non-structural damage

Contents damage

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 4 06/07/2021 / Favier et al. I. Definitions Fragility quantification

[1] O. Mavrouli and J. Corominas, “Vulnerability of simple reinforced concrete buildings to damage by rockfalls,” Landslides, vol. 7, Jun. 2010, pp. 169–180. [2] O. Mavrouli and J. Corominas, “Rockfall vulnerability assessment for reinforced concrete buildings,” Natural Hazards and Earth System Sciences, vol. 10, 2010, pp. 2055–2066.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 5 06/07/2021 / Favier et al. I. Definitions Vulnerability curves can be derived from fragility curves by the law of 푛 total probability: 퐸 퐿|퐼푀 = σ푖=1 푙푖 푝 푑푠푖 퐼푀 None to few Moderate High-level Full damage damage damage damage

Fragility: damage state 푑푠퐼 푑푠퐼퐼 푑푠퐼퐼퐼 푑푠퐼푉

Vulnerability: loss 푙퐼 = 12.5% 푙퐼 = 50% 푙퐼 = 87.5% 푙퐼 = 100%

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 6 06/07/2021 / Favier et al. II. Derivation methods

Empirical approaches consist in using damage or loss database, which are collected in the aftermath of a natural disaster event. Disasters data collection and feedbacks are essential for widening the knowledge of the effect of natural hazards on the built cultural heritage environment. However, it often suffers incompleteness and is usually not publically accessible.

Numerical approaches consist in using numerical models, which are capable of predicting the structural/physical damages or losses of an element function of the intensity measures of the hazard of interest.

Expert judgment-based approaches consist in using the knowledge of experts to build fragility or vulnerability relations.

Hybrid methods are methods that gather at least two of the three methods previously described (e.g., via Bayesian approaches).

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 7 06/07/2021 / Favier et al. II. Derivation methods

Examples from Palazzi, N. C., Favier, P., Rovero, L., Sandoval, C., & de la Llera, J. C. (2020). Seismic damage and fragility assessment of ancient masonry churches located in central Chile. Bulletin of Earthquake Engineering, 18(7), 3433-3457.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 8 06/07/2021 / Favier et al. II. Derivation methods Large rockfall-induced damage database and intensity measures from past events are scarce (e.g. after the landslide/rockfall above the Gallivaggio Sanctuary).

Photo credits: Daniela Lattanzi

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 9 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley a. Elements at stake: Our study is located in the Ubaye Valley, in the French . The cultural heritage list is composed of 14 entities. # Name CH Group CH subgroup Municipality 1 Tour Cardinalis Religious Tower 2 Villa Bleue Vernacular Villa Barcelonnette Faucon-de- 3 Cimetière de Faucon Local Cemetery Barcelonnette 4 Chateau des Magnans Vernacular Castle Eglise paroissiale Saint-Nicolas de 5 Religious Church Jausiers Myre Eglise Notre Dame du Mont 6 Religious Church Larche Camel 7 Eglise de St Martin du désert Religious Church Maljasset Ouvrage Maginot de St-Ours 8-10 haut Military Maginot Line Meyronnes (3 buildings) Eglise paroissiale Saint-Pierre et 11 Religious Church Saint-Paul-sur-Ubaye Saint-Paul Eglise Saint Jean-Baptiste et son 12 Religious Church Saint-Paul-sur-Ubaye enclos de Fouillouse 13 Military Fort Saint-Paul-sur-Ubaye

14 Four à Chaux Vernacular Kiln Saint-Paul-sur-Ubaye 15 Museum Museum Museum Barcelonnette

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 10 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley a. Elements at stake

https://sites.google.com/site/carnetsditinerance/escapades/alpes/haute-vallee-de-l-ubaye

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 11 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley a. Elements at stake

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 12 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley b. Susceptibility map

Rock-EU mapping* is a hazard characterization tool. It has been developed within the framework of the Interreg RockTheAlps project. This tool provides trajectographic simulations outputs at the municipal level. *https://www.alpine-space.eu/projects/rockthealps/en/results-and-download/platrock

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 13 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley b. Susceptibility quantification Cheers Fracth exposure ratings Negligible 0 Probable 6 Extremely unlikely 1 Likely 7 Very unlikely 2 Very likely 8 Unlikely 3 Extremely likely 9 Improbable 4 Inevitable 10 Possible 5 Match of rockfall susceptibility levels to exposure ratings Susceptibility level Exposure ratings Not reached by any blocks Negligible At less than 25 m from a reaching zone Very unlikely Zone reached by blocks from 28°-42° Possible slopes Zone reached by blocks from >28° Very likely slopes Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 14 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley c. Exposure to Rockfalls Among the 14 CH entities, five are prone to rockfall hazard: three churches, one military fort, and one lime kiln.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 15 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley c. Exposure to Rockfalls • The church Eglise paroissiale Saint-Nicolas de Myre: the housing row is taken into account in the "Measures in place" column of the Fratch tool by selecting "Very few measures in place". • Tournoux military fort: measures in place consist in unstable rocks removal and few meters of nets protection. The "Measures in place" column of the Fratch tool is filled in by "Very few measures in place".

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 16 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley d. Vulnerability assessment The vulnerability rating is assessed using literature of masonry building vulnerability (Vallero et al, 2020) and using expert-based judgment: • quality of the masonry; • number of spans composing the structures (several spans allows the possibility of partial collapses, reducing the overall vulnerability); • past events analysis.

Name Quality of masonry Number of spans Past events analysis Eglise paroissiale Saint-Nicolas several-spans can be severely Moderately strong de Myre structures damaged several-spans can be severely Eglise de St Martin du désert Moderately strong structures damaged Eglise Saint Jean-Baptiste et son several-spans can be severely Moderately strong enclos de Fouillouse structures damaged Only partial damage is several-spans Fort de Tournoux Strong expected with very structures local damage suffer total collapse Four à Chaux Low NA with a single rock

Vallero, G., De Biagi, V., Barbero, M., Castelli, M., & Napoli, M. L. (2020). A method to quantitatively assess the vulnerability of masonry structures subjected to rockfalls. Natural Hazards, 103, 1307-1325.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 17 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley d. Vulnerability assessment: past events

The churches have been assessed to be in the "Possible" vulnerability rating,

the military fort in the "Unlikely" vulnerability rating

and the kiln in the "Likely" vulnerability rating.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 18 06/07/2021 / Favier et al. III. Application of the Fratch tool to the Ubaye Valley e. Risk analysis Name CH Group CH subgroup Risk index Eglise paroissiale Saint- Religious Church L3 Nicolas de Myre Eglise de St Martin du Religious Church M6 désert Eglise Saint Jean-Baptiste Religious Church L4 et son enclos de Fouillouse Fort de Tournoux Military Fort M5 Four à Chaux Vernacular Kiln H7

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 19 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux

Numerical approach steps:

• Mechanical modeling • Failure criteria • Statistical uncertainty • Curves fitting

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 20 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux Numerical approach step I: Mechanical modeling • Siconos : nonsmooth numerical simulation* developed by Inria • C++ and Python software to model mechanical systems (rigid or solid) with unilateral contact and Coulomb friction and impact (nonsmooth mechanics, contact dynamics, multibody systems dynamics or granular materials).

*https://nonsmooth.gricad-pages.univ-grenoble-alpes.fr/siconos/index.html

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 21 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux Numerical approach step II: Failure criteria • Maximal displacement at impact zone; • Number of fallen bricks from the impact zone; • Partial to total collapse, where a large number of bricks fell from the impact zone and above.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 22 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux Numerical approach step III-IV: • Statistical uncertainty: the impact point is assumed to follow a uniform law all over the structure; • Curves fitting: a lognormal distribution is fitted to the failure outputs data.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 23 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux Numerical approach step III-IV: • Statistical uncertainty: the impact point is assumed to be uniform all over the structure; • Curves fitting: a lognormal distribution is fitted to the failure outputs data.

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 24 06/07/2021 / Favier et al. IV.Vulnerability assessment of Four à Chaux Towards continuous approach of risk Risk quantified as the mean expected loss Legend: Annual rate of Distribution of RISK NH occurence intensity measure EXPOSITION VULNERABILITY HAZARD Exposition rate Expected loss conditioned to Actualization rate intensity measure

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 25 06/07/2021 / Favier et al. IV.Conclusion and perspectives • The three derivation methods of fragility/vulnerability have been herein illustrated: • Empirical approach via an example from literature; • Expert-based all through the Fratch tool; • Numerical using the Four à Chaux case.

• Practical applications show that: • The expert-based approach is adapted to a large area studied zone where detailed collection database are not available. • The numerical approach suits well precise case study where data and measures in situ are well known. • Empirical approaches are efficient for study where a large damage/loss database from past events is available.

• Risk quantification for the Four à Chaux is a work under progress (hazard definition and calculation implementation). Thank you for your attention !

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 26 06/07/2021 / Favier et al. Thank you for your attention !

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Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley

Favier, P., Bourrier, F., Berger, F.

Univ. Grenoble Alpes, Grenoble, France LESSEM et ETNA, Irstea Grenoble, Grenoble, France

Vulnerability of built elements to rockfalls: a French application in the Ubaye Valley p. 27 06/07/2021 / Favier et al.