# Comparison of Damage Indexes for Assessing Seismic Fragility of Bearings in an Offshore Bridge
## 1 Introduction  
Bridge bearings are important components in the seismic analyses of bridge structures. They are also one of the most fragile components under earthquakes [1]. Although bearings are replaceable throughout the operational lifespan of the bridge, their damage during the replacement period can seriously affect the normal serviceability of bridges. Therefore, it is necessary to analyze the dynamic response of bearings and quantify and classify their damage state under earthquakes. Previous studies proposed various methods for defining the damage states of bearings. These methods are based on different parameters, such as relative displacement, shear strain, and relative displacement ductility ratio. [PERSON], [PERSON] [2] defined a damage index for a neoprene bearing pad by considering the shear force of the bearing as the demand parameter. They then presented an analytical method for the development of fragility curves of highway bridges based on the classification of the damage state. [PERSON] [3] updated damage index limits for movable and fixed steel bearings using a Bayesian theory. After that, scholars further updated the quantification method of damage states for bearings based on the displacement under the earthquake-induced excitation, encompassing the shear strain, displacement, and displacement angle. Among them, [PERSON] and [PERSON] [4] proposed classification criteria for different damage states under earthquakes using shear strain, displacement, and displacement angle. Furthermore, the establishment of damage criteria for bearings aimed to establish a relationship between the response quantities ofthe components and the overall damage states of bridges. A damage index was proposed by [PERSON], [PERSON] [1], which is using the displacement and displacement ductility ratio values corresponding to different damage states. They found that such bridges' bearings are more susceptible to earthquakes than piers and abutments, especially the movable bearings at the abutments. [PERSON], [PERSON] [5] proposed damage indexes for elastomeric pads and sliding bearings and analyzed the earthquake resistance of a highway bridge retrofitted with laminated rubber bearings and shape memory alloy (SMA) restrainers. To improve the precision of evaluating the impact of bearings on the operational reliability of bridges subjected to seismic activity, researchers such as [PERSON], [PERSON] [6], [PERSON], [PERSON] [2], and [PERSON] [3] proposed a fragility analysis theory based on traditional reliability theory. This theory employs a joint failure probability analysis method to investigate the earthquake resistance for the components and their implications for the operational characteristics of structural systems. [PERSON] and [PERSON] [7] analyzed the fragility curves for bearings along two horizontal directions and provided solutions for retrofitting existing bridges. Furthermore, [PERSON] and [PERSON] [8] conducted a seismic fragility analysis and found that movable steel bearings are highly vulnerable to failure under seismic excitation. Recent developments in research on fragility analyses of bearings showed the significant influence of time-varying deterioration of materials on the operational effectiveness of bearings. [PERSON], [PERSON] [9] and [PERSON], [PERSON] [10] conducted an analysis of the seismic behavior of bearings in offshore bridges based on their relative displacement. Their findings indicate that material deterioration leads to an increase in the dynamic response and failure probability of bearings under earthquake loading. Moreover, [PERSON] and [PERSON] [11] discovered that the peak deformation of bearings increases significantly when an aging factor is taken into account. The effect of corroded steel bearings on the component-level seismic fragility of a bridge was examined by [PERSON] and [PERSON] [12]. Their study emphasized the significance of using realistic bearing degradation models for bridges located in seismic regions that experience corrosion deterioration.