Multi-dimensional damage measure for seismic reliability analysis

A new multi-variate approach for assessing the seismic performance of structures is proposed. The classical safety factor formulation in structural reliability is adopted considering multi-dimensional limit state functions that are defined in terms of demand-over-capacity ratios. Variable definitions of multi-dimensional limit state functions represent additional epistemic uncertainty in reliability problems. The use of different multi-dimensional limit state functions is investigated either in terms of variability on the resulting fragility curves and as effect on the risk by calculating the probability of exceeding prescribed limit states. The proposed method is demonstrated by analyzing four non-ductile reinforced concrete structures and by considering bi-dimensional damage measures in terms of maximum inter-story drift and residual drift. Results show that for limit states where the structure behaves elastically, there is no significant effect on the fragility and risk when alternative multi-dimensional measures are adopted. Conversely, average variations up to 10% on the assessment of the probability of failure are observed for limit states where the structure behaves nonlinearly; such variations can be as large as 50% for some particular cases.