Framework for the mainshock-aftershock fragility analysis of containment structures incorporating the effect of mainshock-damaged states

In earthquake events, aftershocks triggered by a mainshock can impose further damage on buildings and then increase the seismic risk. This paper proposes a framework for the fragility evaluation of containment structures under mainshock-aftershock excitations, which can incorporate the impact of mainshock-damaged states effectively. In the proposed method, a joint seismic demand model of two random variables is established by using copula technique for the dependence modelling. To consider the influence of mainshock-damaged levels on the residual seismic capacity, bi-dimensional limit-state functions are used to measure the performance level of a structure during seismic sequences. Finally, the Monte Carlo method is adopted to develop fragility curves, allowing the influence of mainshock-damaged levels to be directly considered in the computation of failure probability. An example of a containment structure is presented to illustrate the use of this proposed methodology, and the sensitivity analysis of fragility curves is also carried out. The results confirm the importance of considering the impact of mainshock-damaged levels in the fragility analysis of containment structures under mainshock-aftershock sequences.