Development of fragility surfaces for reinforced concrete buildings under mainshock-aftershock sequences

A single intensity measure (IM) is commonly used to develop fragility curves for structures subjected to mainshock-aftershock (MS-AS) scenarios. This study aims to propose a framework to develop MS-AS fragility surfaces by characterizing the MS-AS sequences with two IMs. To do this, the well-known Park & Ang damage index, which increases monotonically with the ground motion duration, is adopted to represent the accumulative structural damage during sequential excitations. The MS-AS accumulative damage of structures is thus represented by the combination of the initial damage caused by MS and the incremental damage caused by AS. Based on total probability theorem, the process of assessing MS-AS fragility is consequently divided into two parts, namely the MS fragility assessment and the AS fragility assessment, respectively, where the cases of dynamic instability are considered. The proposed framework is illustrated using a typical four-story reinforced concrete frame building. The peak ground velocity values of both MS and AS are taken as the representative IMs for the MS-AS sequences. The fragility results for MS only and MS-AS sequences are compared to scrutinize the effects of AS on structural damage. It is found that the MS-AS sequence can cause significantly larger exceedance probabilities of limit states compared to the MS only. The MS-AS sequence also leads to a reduction of the MS-AS fragility median conditioned on a given AS intensity. Such reduction increases with the increase of the AS intensity.