Probabilistic seismic risk assessment and comparison of steel reinforced concrete frame with/without buckling-restrained braces

Two analytical formulations for seismic reliability analysis of structures proposed by Prof. Cornell are revisited from two different aspects of Total Probability Theorem (TPT). Analytical formulations for seismic fragility analysis are elaborated. The analytical seismic reliability formulations based on hazard and fragility are applied to a Steel Reinforced Concrete (SRC) frame structure and a steel reinforced concrete frame structure with buckling-restrained braces (SRC-BRB). To assess and compare the probabilistic seismic risk of two types of buildings, the probabilistic seismic demand analysis is firstly implemented through nonlinear dynamic time-history analysis of the structures and regression analysis of structural displacement demands and intensity parameters of strong earthquake motions. And then, the probabilistic seismic capacity analysis based on a multi-level force-controlled random pushover analysis is performed on the structures. The seismic fragility analysis is run by combining the results of probabilistic seismic demand analysis and probabilistic seismic capacity analysis, and it is further integrated with the hazard curves of probabilistic seismic hazard analysis via the analytical reliability formulation to derive the point estimated values of the seismic risk of being different damage states of the structures. Finally, the seismic risk curves of these types of buildings are obtained. The failure probabilities of the structures corresponding to four damage states are analyzed. Considering the uncertainties in only seismic demand and in both seismic demand and structural capacity, the seismic risk of the structures are compared. The seismic reliability and probabilistic seismic risk of SRC frame with or without buckling-restrained braces are compared.