A methodology based on the progressive incremental dynamic analysis has been introduced in this paper to estimate the structural response and the corresponding annual probability of failure. The proposed methodology employs the genetic algorithm optimisation technique and an equivalent single-degree-of-freedom system corresponding to the first-mode period of a considered structure. The proposed methodology can significantly reduce the number of ground motion records needed for estimating the annual probability of failure. The numerical results indicate that the proposed method can effectively reduce the computational effort needed for computation of probability of failure for the first-mode dominated structures, which is advantageous as the structure becomes larger. A relatively huge set of single-degree-of-freedom systems as well as three multi-degree-of-freedom systems including 3, 8 and 12 storeyed reinforced concrete structures was taken into account to test the proposed methodology. It has been shown that the probability of failure can be estimated within ±15% error with 95% confidence. The proposed method can speed up the decision-making process in the probability-based seismic performance assessment of structures, and it also incorporates the randomness of strong ground motions explicitly.
