Stochastic approach for analytical fragility curves

One of the main problems is the assessment of “residual reliability” or “vulnerability” of a single existing structure, or of a given class of similar structures, against seismic actions. The fragility curves describe the probability of a structure to suffer a given damage level when it is subject to a given seismic excitation level. This research work is focused on an analytical method for constructing fragility curves of existing structures based on a stochastic approach. Analysed structure is modelled by a simple one degree of freedom system subject to a nonstationary Kanai-Tajimi process. The numerical values of the parameters of its constitutive law, here suitably described by means of a hysteretic model, are selected using an identification procedure with the non linear pushover analysis performed on the real assessed structure. To develop fragility curves, a displacement based damage index is adopted. Fragility curves are obtained in terms of probability of exceeding a given damage level by using an approximate crossings theory of stochastic processes.