Keywords: earthquakes, seismic damage, reliability, probability of failure, risk maps, structures.

In order to quantify the damage that structures may have suffered during an earthquake, a new probabilistic proposal is developed in this paper. Each country has its own sheet evaluation for its structures. Once an earthquake has occurred, the engineers complete these sheets, for each structure inspected, and take technical decisions regarding its supposed ability to resist loads and future quakes. The author develops a new integrated methodology to assess the residual mechanical reliability in the case of masonry structures that suffered earthquakes. This new methodology may be very helpful in the few hours or days that follow an earthquake. Actually, evaluation sheets are usually filled by the engineers in order to evaluate the damage level that affects the structures inspected. Based on expert knowledge and engineering feedbacks, these sheets require the evaluation of several parameters that are supposed to govern the mechanical resistance of the structures. The engineer in charge of this evaluation has therefore to define final and global mechanical damage. A decision is then taken: evacuate and demolish the construction in the case of very serious damage, evacuate until the structure is strengthened in case of medium damage, and slight repair in case of very slight damage. In various countries, the engineer inspecting the structure classifies finally the structure into five categories:

• "1=Light Green": the damage is very slight, so the structure requires very slight repair and may follow in use
• "2=Dark Green": the damage is very reduced, so the structure requires repair but does not present any danger to the inhabitants
• "3=Light Orange": the damage is significant, so the structure must be evacuated and requires important repair
• "4=Dark Orange": the damage is important, so the structure should be evacuated and requires very important strengthening
• "5=Red": the damage is very important, so the structure is out of service and is not able to remain in service.

The author proposes herein an integrated probabilistic methodology. He assumes that the five categories 1 up to 5 correspond to risk levels ranging from 0 (no damage) up to 1 (complete damage). Six relationships between the categories and the probability of failure are considered. The structural components are the infrastructure, the vertical bearing elements and the elements resisting horizontal loads (floors, slabs, roof). The structural damage is then expressed, within a probabilistic framework. Three probabilistic models are considered in order to derive the structural failure based on the individual failure probability of each of the four governing components. This methodology might therefore be integrated in a geographic information system (GIS) in order to provide maps and information that may help in the analysis and management of the natural risks at either urban or regional scales. The integrated probabilistic methodology may be summarised as follows:

• After an earthquake occurrence, the engineers fill their usual evaluation sheets.
• The structure being considered as a mechanical system with elementary components (foundations, columns, beams and floors, roofs and slabs), a probabilistic methodology transforms the qualitative engineer evaluation into a quantitative probabilistic contribution of each governing component (residual mechanical risk ranging from 0 up to 1, i.e. total damage up to no damage).
• The engineer may base his final evaluation of this so calculated residual risk, derived from probabilistic events (intersection and union of elementary probabilities).
• The socio-economical consequences may then be derived and damage maps may be generated, in order to help the decision making.

This methodology was run and its theoretical results are expected to be compared to the observed damage maps during the Boumerdes earthquake (Algeria, May 21, 2003), in order to improve, the relationships between the damage category and the probability of failures, and the probabilistic combination of the structural components reliability to derive the global structural failure.

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