Probabilistic demand models and fragilities for reinforced concrete frame structures subject to mainshock-aftershock sequences

• A bivariable function considering both mainshock and aftershock intensity measures is used to develop demand model. • A Bayesian approach is used to calibrate demand models. • The Gardoni bounds is used to quantify the variability in the fragility estimates. • The uncertainties in the seismic fragility estimates are quantified. This paper presents a formulation for developing seismic demand models and estimating fragilities for reinforced concrete (RC) structures under mainshocks (MSs) only and mainshock-aftershock (MS-AS) sequences. The demand model for the MS only is a function of the MS intensity, while the model for the MS-AS sequence is a function of two variables, one describing the MS and one describing the AS. A Bayesian method is used to calibrate the demand models. The demand models are then used to estimate the fragility of RC structures. Predictive fragility curves are developed to include the uncertainties in the model parameters estimated by Bayesian approach, and confidence bounds of the fragility curves are developed to separate the effects of the uncertainty in the model parameters from the other sources of uncertainties. The proposed formulation is illustrated using a typical five-story RC frame building. The results show that the fragility curves for MS only tend to significantly underestimate the fragility curves for MS-AS sequences. Also, the uncertainty in the fragilities for the MS-AS sequence is, as expected, larger than that considering only the MS.