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A probabilistic approach for seismic risk assessment based on vulnerability functions. Application to Barcelona

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Abstract

Risk assessment and management is an important step towards resilient and sustainable cities. Among many other perils, both natural and manmade, seismic risk is a major threat for resilience and sustainability. In recent decades, several methods for seismic risk assessment have been proposed, including the well-known Vulnerability Index Method (VIM). In this study, a probabilistic version of the VIM, which we call the Vulnerability Index Method-Probabilistic (VIM_P), is proposed. The VIM_P requires essential information on the seismic hazard and on the vulnerability of the building stock. Seismic hazard is determined using the exceedance rates of macroseismic intensities, as defined in the European Macroseismic Scale (EMS). Seismic vulnerability is defined by means of vulnerability probability density functions (pdf) that describe the probability distribution of the corresponding vulnerability index. Beta-like functions are used for these pdfs. VIM_P quantifies seismic vulnerability by means of three vulnerability curves, Lower, Best and Upper, according to the quantity and quality of available information, thus allowing three estimates of seismic vulnerability and risk. Then, seismic risk is computed via the convolution of seismic hazard and seismic vulnerability, considering semi-empirical damage functions. Seismic risk is given through the exceedance frequencies of the damage grades. To highlight the capabilities of the VIM_P, the seismic risk of about 70,000 residential buildings in Barcelona was assessed. According to the results, the exceedance frequency of the collapse damage state for more than the 50% of the buildings in the Eixample district would be greater than 1 × 10−5. This confirms the relatively high seismic risk in the city, mainly due to the high vulnerability of the built environment. Specific software, USERISK20015, has been developed for routine applications of VIM_P. It is hoped that VIM_P and this new tool for seismic risk assessment will be useful to stakeholders and civil protection authorities for risk management and prioritizing actions that can help to create more resilient, sustainable cities.

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Fig. 1

(adapted from Aguilar-Meléndez et al. 2018)

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(adapted from Secanell et al. 2004)

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(adapted from Aguilar-Meléndez et al. 2018)

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Notes

  1. Note that Eq. (11) is deterministic. The development of a specific probabilistic damage function is an improvement of VIM_P that is pending, to become a fully probabilistic approach.

  2. Processor Intel® Core™ i7-4600U CPU @ 2.10 GHz 2.70 GHz, and installed RAM of 8.00 GB.

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Acknowledgements

This study was made possible by the support of the Barcelona Supercomputing Center (BSC), CONACyT, and the Universidad Veracruzana. The research was partially funded by the Ministry of Economy and Competitiveness (MINECO) of the Spanish Government and by the European Regional Development Fund (ERDF) of the European Union (EU) through projects with references CGL2011-23621 and CGL2015-65913 -P (MINECO/ERDF, EU).

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Authors and Affiliations

  1. Barcelona Supercomputing Center (BSC), Barcelona, Spain

    Armando Aguilar-Meléndez & Josep de la Puente

  2. Faculty of Civil Engineering, Universidad Veracruzana (UV), Poza Rica, Mexico

    Armando Aguilar-Meléndez

  3. Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya (UPC), BarcelonaTech, Barcelona, Spain

    Luis G. Pujades, Alex H. Barbat & Nieves Lantada

  4. Institute of Engineering, Universidad Nacional Autónoma de México (UNAM), Mexico City, Mexico

    Mario G. Ordaz

  5. Faculty of Engineering, Universidad Autónoma de Sinaloa (UAS), Culiacán, Mexico

    Héctor E. Rodríguez-Lozoya

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  1. Armando Aguilar-Meléndez
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  2. Luis G. Pujades
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  3. Alex H. Barbat
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Corresponding author

Correspondence to Armando Aguilar-Meléndez.

Appendix

Appendix

See Tables 10 and 11.

Table 10 Relevant methodologies for seismic risk assessment in urban areas
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Table 11 Summary of the main features of the VIM and VIM_P methodologies
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Aguilar-Meléndez, A., Pujades, L.G., Barbat, A.H. et al. A probabilistic approach for seismic risk assessment based on vulnerability functions. Application to Barcelona. Bull Earthquake Eng 17, 1863–1890 (2019). https://doi.org/10.1007/s10518-018-0516-4

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