Cloud analysis is based on linear regression in the logarithmic space using least squares, in which a large number of nonlinear dynamic analyses are required to ensure the regression accuracy. Thus, it needs significant computational effort to derive fragility curves especially for the complicated structures. This article proposed the Enhanced Cloud approach (E-Cloud) to enhance the efficiency but maintain the accuracy of Cloud analysis. The basic concept of the E-Cloud method aims to utilize both maximum and additional seismic responses with corresponding intensity measures (IMs) from ground motions for the logarithmic linear regression in Cloud analysis. The additional seismic responses can be obtained from the engineering demand parameter (EDP)-IM curve, which is generated at the specific time duration when structures are subjected to intensifying dynamic excitations in nonlinear time–history analysis. The required number of nonlinear time–history analyses in Cloud analysis is reduced since additional seismic responses (with their corresponding IM value) are used as additional Cloud points for the Cloud regression. The proposed E-Cloud method is applied for the case study of a typical reinforced concrete (RC) frame structure. By comparison of probabilistic seismic demand models and fragility curves from the E-Cloud method to Cloud analysis, it is demonstrated that the proposed E-Cloud method can significantly improve the computational efficiency of the Cloud analysis, which also leads to accurate fragility estimates of the structures.

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Residual displacements between the girder and piers were observed in previous strong earthquakes. These are caused by the limited re-centering capacity of sliding isolation bearings. With this concern, a spring re-centering device is proposed to improve the re-centering capacity of sliding isolation systems. The working mechanism is illustrated, and the force–deformation relationship of this device was investigated in theoretical, experimental, and finite element methods. An extra-dosed multi-pylon cable-stayed bridge was introduced to demonstrate the re-centering effect. The results show that this spring re-centering device could slightly mitigate the seismic forces and significantly mitigate the residual displacement between the girder and piers. After that, the parametric analysis was conducted to investigate the effect of critical parameters of re-centering bearings on seismic performances.