## 1 Introduction
Therefore, relevant scholars have conducted extensive research and proposed several seismic fragility analysis methods for entire bridges, including the wide bound method [13], the Monte Carlo sampling method [14], and the multivariate copula function [15]. However, most studies have only considered the correlation between the seismic responses of different components, while ignoring the correlations between their seismic capacities. In view of this, [PERSON] et al. proposed multi-dimensional fragility analysis (MFA) based on multiple evaluation indexes in order to consider the correlation between the seismic capacity of different components, which has been widely applied to large structures [16]. [PERSON] et al. applied MFA to the seismic performance evaluation of large-scale bridges based on the displacement of bridge bearings and the ductility ratio of the bridge pier, considering the uncertainty of both ground motions and structural performance limit states [17]. [PERSON] et al. applied MFA to seismic performance evaluation of large multi-tower structures based on the probability density evolution method [18]. According to the fundamental theory of MFA, a reasonable internal relationship of different indexes is a primary basis for fragility analysis [16]. However, most current papers only provide a qualitative value to represent the relationships between vulnerable components, and do not reveal the internal correlation mechanism to obtain rational correlation coefficients [17; 19]. Therefore, the internal correlation mechanism between vulnerable components must be clarified, and the correlation coefficients under different seismic performance limit states should be further developed to propose an improved MFA. In this paper, we employ the improved MFA to achieve an accurate seismic risk analysis of an offshore bridge while taking into account chloride ion erosion and the seismic correlations between vulnerable components. In this paper, a reinforced concrete simply-supported beam bridge in an offshore tidal environment is employed as an example. Considering the adverse effects of chloride ion erosion and the uncertainty of both structural material parameters and ground motions, we first establish 300 bridge-ground motion analysis sample pairs. The seismic response process of the example bridge is simulated employing the IDA method, with the plate rubber bearing and the pier selected as vulnerable components. Based on linear regression analysis and first-order reliability theory, 1D seismic fragility curves are obtained for both single components and the entire bridge. The internal relationship mechanism between the seismic demand and the seismic capacity of different components is further explored in order to clarify the correlation coefficients of the vulnerable components and obtain the 2D seismic fragility curves of the entire bridge while considering the seismic correlations between vulnerable components. The seismic risk probability of the entire bridge is further determined based on discrete conditional probability in combination with hazard analysis at the bridge site and seismic loss analysis. This research can provide scientific and technical support for seismic design and seismic risk assessment of offshore bridges. The flowchart of this paper is shown in Figure 1.