Probabilistic Approach to the Seismic Vulnerability of RC Frame Structures by the Development of Analytical Fragility Curves

Fragility curves are very useful in quantifying the physical and economic damage of buildings that have undergone an earthquake. This paper presents the development of analytical fragility curves representative of mid-rise residential structures built with reinforced concrete, taking into account the specific structural characteristics of Algerian buildings. The derivation of the analytical fragility curves is based on the capacity spectrum method (CSM), which combines a non-linear static analysis (pushover) with a response spectrum analysis. Observation of the consequences of earthquakes of a given intensity shows that the damage to buildings is not identical, even though their construction is similar. This variability of damage can be explained by the variability of a large number of factors such as the local intensity of the hazard, the heterogeneity of the terrain, and the mechanical and geometrical characteristics of the constructions. The materials and patterns of demand spectra were considered as random variables using the Latin Hypercube Sampling Technique. Most of the existing methods that model the damage to structures accept a log-normal distribution hypothesis, where the log-normal law is a model controlled by two parameters: its mean value and its standard deviation. To set these parameters, Monte Carlo simulations (MCS) are performed to generate 1000 samples. The resulting fragility curves following these analyses were applied to two real-life cases of buildings affected by the earthquake of Beni-Ilmane 2010 (Msila, Algeria), so as to assess the damage.