# Comparison of Damage Indexes for Assessing Seismic Fragility of Bearings in an Offshore Bridge
## 3 Problem Definition  
### Detailed Numerical Model of the Bridge Structure  
An offshore bridge is taken as the example. The girder section has an equal height, a single box, and a chamber (C50 concrete). Piers 1#, 4#, and 5# are piers with bearings (C40 concrete); piers 2# and 3# are rigid frame piers (C50 concrete); the bridge piers are all constructed as solid diamond-shaped piers. For more details on the material properties of concrete, please refer to Table 2. The longitudinal reinforcement and stirrup are made of HRB 335 and R235 reinforcement, respectively, with diameters of 32 mm and 16 mm, respectively. The thicknesses of the protective layers for the two are 103 mm and 90 mm, respectively. For more details on the material properties of longitudinal reinforcement and stirrup, please refer to Table 3. The bearings are spherical movable steel bearings. The address environment of the example bridge is a fortified area with a basic earthquake intensity of 7 degrees, located in a class II site, with good foundation conditions, mostly weakly weathered rock and slightly weathered rock, with relatively high stiffness. The detailed structure of the bridge is shown in Figure 4[10; 17]. As for the superstructure, the bridge structure is primarily prone to damage at the piers and bearings under earthquakes. Unless the bridge girder collapses, it does not undergo plastic deformation, and the dynamic response of the superstructure under earthquakes is primarily characterized by elastic deformation. Therefore, it is assumed that the superstructure behaves as an elastic component [9; 26]. All loads borne by the superstructure are equivalent to the nodal masses acting on the girder. In the concept of ductility design, the accuracy of the computational modeling of bridge piers is vital [19]. The Open System for Earthquake Engineering Simulation (OpenSees) provides two types of elements for simulating the nonlinear mechanical behavior of components: (1) The displacement-based \"beam column element\" (i.e., fiber elements based on the stiffness method) can be obtained through the three-time hermit difference. However, this method cannot well reflect the curvature distribution at the end of the element after yielding, and the calculation convergence speed is slow. (2) The force-based \"beam column element\" (i.e., fiber elements based on the flexibility method) only needs to be obtained by linear difference, which is more conducive to the simulation of curved beam-column elements, and the calculation convergence speed is faster. Thus, the nonlinear mechanical behavior of the piers is modeled using the \"nonlinear beam column element\" by the flexibility method. As for the fiber section of a pier, the Gauss-Lobatto integration algorithm mandates that the fiber section characteristics of each integration point must be consistent. Among them, the fibers of the confined concrete section are divided into 30 layers along the transverse direction and 15 layers along the longitudinal direction. The fibers of the unconstrained concrete section corresponding to the short side are divided into 1 layer along the transverse direction and 15 layers along the longitudinal direction; the fibers of the unconstrained concrete section corresponding to the long side are divided into 30 layers along the transverse direction and 1 layer along the longitudinal direction, and each longitudinal reinforcement is a fiber section. In addition, to reconstruct the plastic deformation of the ductile member (pier) under earthquakes, a plastic hinge area is set on the pier. With the \"zero-length element\", the plastic hinge is set at the bottom of the 1#, 4#, and 5# piers (piers with bearings), and at the top and bottom of the 2# and 3# piers (rigid frame piers). Among them, the top of the rigid frame pier and the bottom of the girder at the same position are treated as common nodes. The connection between the top of the  
Figure 4: Detailed structure of the bridge (unit: m).