# Comparison of Damage Indexes for Assessing Seismic Fragility of Bearings in an Offshore Bridge
## 4 Results and Discussion  
### Incremental Dynamic Analysis  
Incremental dynamic analysis (IDA) is a technique of performing a range of nonlinear time-domain dynamic evaluations of a structure by varying the magnitude of one (or more) seismic records [30]. At this time, the curve connecting the increasing _IM_ with the corresponding structural response is called the \"IDA curve\". Currently, three typical methods are commonly used for IDA: (1) Equal step method: he IM is increased in equal \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Name** & **Event** & **Time (Year)** & **Site** & **PGA (g)** & **Magnitude (M)** \\ \hline
1 & RSN-138 & Tabas, Iran & 1978 & Boshrooyeh & 0.24 & 7.35 \\
2 & RSN-164 & Imperial Valley-06 & 1979 & Cerro Prieto & 0.37 & 6.53 \\
3 & RSN-286 & Irpinia, Italy-01 & 1980 & Bisaccia & 0.25 & 6.90 \\
4 & RSN-776 & Loma Prieta & 1989 & Hollister-South and Pine & 0.32 & 6.93 \\
5 & RSN-827 & Cape Mendocino & 1992 & Fortuna-Fortuna Blvd & 0.22 & 7.01 \\
6 & RSN-880 & Landers & 1992 & Mission Creek Fault & 0.31 & 7.28 \\
7 & RSN-1008 & Northridge-01 & 1994 & LA-W 15 th St & 0.32 & 6.69 \\
8 & RSN-1100 & Kobe, Japan & 1995 & Abeno & 0.31 & 6.90 \\
9 & RSN-4840 & Chuetsu-oki, Japan & 2007 & Joetsu Kita & 0.30 & 6.80 \\
10 & RSN-6886 & Darfield, New Zealand & 2010 & Canterbury Aero Club & 0.35 & 7.00 \\ \hline \end{tabular}
\end{table} 
Table 7: Information from 10 original seismic records. Figure 7: Seismic response spectrum. steps. The step size should be different for different structures. (2) Variable step method: The step size may be larger or smaller for a certain seismic record. The differences in the IM of curves approaching a horizontal line make the analysis steps required for each IDA curve different. The step value can be increased or decreased based on the convergence of the calculations. (3) Hunt and fill method: This method is based on the variable step method. An IM value is selected from the IM interval corresponding to the maximum convergence and minimum non-convergence for analysis until the interval is less than the allowable value. After that, the median value of the two IM values with the largest interval is taken for analysis until the maximum convergent IM interval is less than the allowable value [29,32]. In this study, the equal step method was selected to improve the calculation efficiency [9]. A single IDA curve can fully reflect the entire process of a structure from elasticity to failure with increasing ground motion intensity. Figure 8 shows that as the PGA increases, the IDA curves of the relative displacement of the bearings do not exhibit an evident yield platform. The slope of the curves changes slightly and can be approximately regarded as a straight line. Further, IDA curves for bearings 1#-6# subject to the Cape Mendocino ground motion (Figure 9) during their entire life cycles are also studied (Figure 10). When the service life is 100 years, the maximum relative displacements of bearings 1#-6# under the Cape Mendocino ground motion are 0.68 m, 0.68 m, 0.69 m, 0.69 m, 0.71 m, and 0.71 m, respectively. The relative displacements of the bearings above the same pier are basically the same, and the relative displacements of bearings 5# and 6# are the largest. Therefore, as representatives, the bearings 1#, 3#, and 5# were selected for comparative analysis of the IDA curves under PGA \(\geq\) 0.5 g, with bearings in service for 0 years, 50 years, and 100 years serving as examples. Figure 10g indicates that the IDA curves of bearings 1# and 3# on piers 1# and 4# are basically the same in the service period, which is slightly lower than the IDA curve of bearing 5# located at the pier 5#. This observation can be explained by the fact that the heights of piers 1# and 4# are comparable, whereas pier 5# is about 1.7 times taller than the former two. In terms of a given cross-section, a pier with greater height possesses relatively greater flexibility.