Long-span cable-stayed bridge is a prevalent bridge type for sea-crossing passages and occupies an essential role in the transportation system. Non-uniform excitations significantly impact the response of long-span cable-stayed bridges, especially the site-response effect (ESR), which is one of the three primary characteristics. This paper employs a long-span sea-crossing cable-stayed bridge with consideration of hydrodynamic and pile-soil effects to systematically study the influence regularity and parameter sensitivity of the site parameter ωc on the response of critical components, and develop probabilistic seismic demand models between each component and ωc. The results reveal that the fragility of each component exhibits dissimilar sensitivities related to ωc, specifically, the changing amplitude of bearing fragility is greater than that of the bridge pylon. Consequently, when the soil type at the pylons changes from soft to solid, the damage sequence of the main pylon, pier and bearing has been changed, which exhibits different damage mechanism and failure mode. Furthermore, the mathematical model between the seismic parameters and damage mechanism is established to quantify the impact of ESR on the failure mode of sea-crossing cable-stayed bridges. Thus, it could provide a theoretical basis for the earthquake damage assessment and seismic optimization of long-span cable-stayed bridges.
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