Seismic base isolation faces the challenge of the large displacement demands for the isolators in case of long-period ground motions. Semi-active control has the potential to mitigate the risk against such extreme scenarios and therefore increase the seismic reliability of base-isolated structures. However, the superstructural nonlinearity and the time delay in the control system are always neglected in related studies. Such a knowledge gap may overestimate the benefit of semi-active control in enhancing the seismic reliability of base-isolated buildings. This study explores the seismic reliability of semi-actively base-isolated buildings with realistic considerations of the superstructural nonlinearity and the time delay in a practical hydraulic control system in a fully probabilistic framework. It features the use of the probability density evolution method (PDEM) and the development of a MATLAB-OpenSees interaction technique. The reliability of the semi-actively isolated structure and its passive counterpart are compared, highlighting the effects of nonlinearity and time delay. The results show the superstructural nonlinearity and the inevitable time delay in a practical hydraulic control system may significantly degrade the control performance of semi-actively base-isolated buildings, potentially leading to higher failure probabilities than passive buildings.
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