Reliability estimation of incremental retrofitted structures considering cumulative seismic damages

Incremental retrofitting consists of two or more retrofitting stages scheduled discretely during the lifetime of the building in order to decrease initial costs and to avoid long period of activities interruption. Retrofitted building achieves limited or partial performance objectives in each incremental retrofitting. The objective of this paper is to assess the reliability of incremental retrofitted buildings in seismic zones considering the accumulated damages with simplified probabilistic method. In this work, we consider that structural damage is accumulated in a series of seismic ground motions until a damage level is reached or exceeded. The proposed method consists in 7 steps: (1) Definition of the global damage states (GDS) that results of the division of the capacity curve of the building in a non-damage state, obtained through a static nonlinear analysis (Pushover Analysis) according to Vision 2000, (2) Estimation of the modified moment-rotation curves of each damaged element of the building associated to each defined GDS with an approximate approach. This method is based on the evaluation of the plastic hinge rotation through the estimation of the moment-rotation curve for each structural element, (3) Estimation of the building capacity curve for each GDS considering the damage elements through their modified moment-rotation curves, (4) Elaboration of seismic fragility curves for each GDS with the capacity spectrum assessment method using the software FRACAS, which uses inelastic response spectra derived from earthquake ground motion accelerograms to construct fragility curves, (5) Determination of damage transition probability matrices for different seismic intensity levels using the values obtained in the previous step, (6) Implementation of a Markov Chains Model to obtain the probability distribution function of each GDS after a determinate number of earthquakes, and (7) Estimation of the structural reliability taking into account the damage accumulation process during probable future earthquakes assuming a Poisson process. This methodology is applied to compare the reliability of two retrofitted Peruvian school buildings, one with partial performance objectives and the other with full performance objectives. It is obtained that the reliability at the end of the service life of the first one i s 20% less than the reliability of the second one. We recommend this methodology to assess reliability for life cycle cost benefit analysis of new and retrofitting projects.