Multivariate Joint Fragility And Probabilistic Safety Prediction Of RC Frame Structures Under Mainshock-aftershock Sequences

Several aftershocks often occur following a serious mainshock.An earthquake sequence will cause more serious damage than the mainshock only.However the current seismic design method and provisions don’t comprehensively consider the damage potential due to earthquake sequences.This shortcoming affects structural safety subjected to mainshock-aftershock sequences.Therefore,this study will assess the probabilistic safety of reinforced concrete frame structures under mainshock-aftershock sequences based on seismic fragility.The main contents are summarized in the followings:(1)Multivariate probabilistic seismic demand analysis.The maximum inter-story drift and the residual inter-story drift are both adopted as structural demand parameters.Based on a two-step stripe method,the multivariate probabilistic seismic demand model using the selected structural demand parameters is developed,which is further modified by considering the effect of collapse.(2)Multivariate joint probabilistic seismic demand analysis.The developed multivariate probability seismic demand models which are established in content(1)in terms of maximum inter story drift and residual inter story drift are used to generate multivariate joint probabilistic seismic demand model by using the Copula theory.(3)Multivariate joint seismic fragility analysis.The multivariate joint seismic fragility is calculated for structures subjected to mainshock-aftershock sequences by using the multivariate joint probabilistic seismic demand model in content(2)and the limit states described in terms of maximum inter story drift and residual inter story drift.A vulnerability index is computed to examine the effect of mainshock-aftershock sequences on structural performance in a probabilistic way.(4)Probabilistic seismic safety prediction.In light of the correlation between the structural damages induced by mainshock only and mainshock-aftershock earthquake sequences,their joint probability distribution is developed by using the Copula theory,which is used to predict the failure probability due to mainshock-aftershock sequences is predicted on the condition of the mainshock-induced damages of different levels.Moreover,the copula-based joint probability distribution of the failure probabilities due to mainshocks and mainshock-aftershock sequences is developed to predict the safety level of the structures under mainshock-aftershock sequences.