Keywords: natural hazard, masonry, failure, probability, floods, risk, vulnerability.

This paper develops a new integrated probabilistic methodology in order to assess the mechanical reliability of masonry constructions against natural hazards such as floods and earthquakes. The flood hazard as well as the mechanical vulnerability are described within a probabilistic framework. The risk of failure is then assessed quantitatively. The procedure helps in analysing the risks at a large scale: cities, regions, large set of masonry constructions.

The flood hazard is defined as the probability of exceeding a given value of hydraulic load. For this purpose, probabilistic models are considered in order to study the discharges at the channel (or river) entrance, the water depth and velocity that are produced downstream in the floodplain where the constructions under study are erected. The discharges are well described by exponential distributions while the maximal hydraulic load is well expressed by a Gumbel distribution. Monte Carlo simulations are run for this purpose.

The mechanical vulnerability of the existing structures is also expressed in probabilistic terms. The mechanical risks or structural reliability are therefore derived in terms of the probabilities of failure. This methodology is a global approach combined with a mechanical analysis and a reliability analysis.

A simplified mechanical model is considered in order to calculate the bearing capacity of the masonry walls under the water pressure. The theoretical results are compared to experimental values collected from the existing literature: they are in good agreement. This mechanical model considers therefore the structural parameters as random variables, i.e. the joints strength and the hydraulic in a first stage. The probabilities of mechanical failure are thus calculated using the Monte Carlo simulations and level-2 method such as the Lind-Hasofer index is calculated. Sensitivity analysis is performed in order to find the most influential structural parameters that may require detailed modelling.

A simplified approach is also proposed in order to help engineers to find a near value of the mechanical risk. Actually, fourteen governing parameters (dimensions, geometry, materials properties,- topography, etc) are selected. An original methodology, called "the global approach", based on an existing probabilistic method (developed in the case of earthquakes) is also proposed in this paper.

The probabilities of failure obtained by the two methods (detailed mechanical approach or the global approach) remain very close. Finally, these two methodologies are run and integrated in a geographic information system ( GIS) in order to provide quantitative risks maps that may help in the analysis and management of the natural risks for either urban or regional scales. A simulation is done with real data and the risks maps are obtained for the case of a city (Cheffes sur Sarthe, France) that suffered significant damage due to water floods in 1995.

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