A Simplified Approach of Analytical Seismic Fragility Analysis Using the Endurance Time Method

The endurance time (ET) method is an effective dynamic analysis method for seismic response analysis of structures. It has been recently used for analytical fragility analysis. However, the available ET-based fragility analysis methods have two limitations: 1) the prediction error of the structural median responses estimated by the ET method is ignored; and 2) the record-to-record variability inherent earthquake ground motions is not well considered. To overcome the above limitations, another ET-based fragility analysis method is proposed, where only three times of ET nonlinear analyses are required. To do this, three specific endurance time excitation functions (ETEFs) are generated in correspondence to the mean and 16% and 84% percentile of response spectra of a selected suite of ground motion records (i.e. ${\rm{ ETE}}{{\rm{F}}_m}$ETEFm, ${\rm{ETE}}{{\rm{F}}_{v1}}{\rm{ }}$ETEFv1 and ${\rm{ETE}}{{\rm{F}}_{v2}}$ETEFv2, respectively). The structural response under ${\rm{ ETE}}{{\rm{F}}_m}$ETEFm is used to estimate the median response of structures under the selected suite of ground motion. Moreover, the structural responses under ${\rm{ETE}}{{\rm{F}}_{v1}}{\rm{ }}$ETEFv1 and ${\rm{ ETE}}{{\rm{F}}_{v2}}{\rm{ }}$ETEFv2 are used to quantify the record-to-record variability in earthquake ground motions. The fragility relationships are developed by both point and interval estimate methods since another logarithmic standard deviation is introduced to account for the difference between the median responses predicted using ${\rm{ ETE}}{{\rm{F}}_m}$ETEFm and those predicted by the dynamic analysis. To validate the proposed method, two RC frame structures with six and nine stories are taken as the study cases. The fragility results based on the proposed ET-based method and those based on the cloud method are compared. It is found that the proposed ET-based fragility analysis method could generate reliable fragility estimation, whereas requiring limited computation cost. The proposed method would provide another simplified way for the rapid fragility assessment of structures.