A probabilistic framework for performance-based seismic assessment considering residual deformations
Recent advances in performance based design and assessment procedures have highlighted the importance of considering residual deformations in addition to maximum deformations as a complementary damage indicator. A combined 3-dimensional performance matrix, where maximum and residual deformations are combined to identify performance levels coupled with various seismic intensity levels is presented within a probabilistic formulation of a performance based assessment procedures. Combined fragility curves providing the probability of exceedence of performance levels defined by pairs of maximum-residual deformations are derived using bivariate probability distributions, due to the statistical dependence of the two parameters. Numerical examples on equivalent SDOF systems with extensive non-linear time history analyses under a properly selected suite of earthquakes are performed to derive the fragility curves for various performance levels. The effects of hysteretic systems and strength ratios on fragility curves are examined. The significance of accounting for residual deformations in addition to maximum deformation indices when evaluating the actual performance level is confirmed by using joined fragility curves. In conclusion, for a given strength ratio and performance level, joined fragility spectra are generated for a range of effective secant periods of SDOF systems providing a measure of confidence in achieving the targeted performance.