## 3 Application
### Definition of Seismic Damage to Isolated Grider Bridges
#### 3.4.2 Isolation Bearing  
The failure state of the isolated bearing is mainly determined by the displacement and shear strain of the bearing. Five damage states, including basically intact, minor damage, moderate damage, severe damage, and collapse, were defined by [PERSON] according to the displacement of the bearings [44]. Here, displacement of the isolated bearing based on bearing shear strain was adopted as the basis for evaluating earthquake damage. The definition of the deformation rate of the bearing under different damage states is given in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Random Variable** & \
\begin{tabular}{c} **Probability** \\ **Distribution** \\ \end{tabular} & **Average Value** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Unit** \\ \hline Fy & normal & 385.42 & 28.32 & Mpa \\ Fc & normal & 27.68 & 5.23 & Mpa \\ \(\rho\) & normal & 28,930 & 2530 & N/m3 \\ K1 & uniform & 12,357 & — & kN/m \\ Qy & uniform & 54.83 & — & kN \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistics of the random variables.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Damage State** & **Intact** & **Minor Damage** & **Medium Damage** & **Serious Damage** & **Collapse** \\ \hline Failure criterion & \(\phi\leq\phi^{\prime}_{y}\) & \(\phi^{\prime}_{y}\leq\phi\leq\phi_{y}\) & \(\phi_{y}\leq\phi\leq\phi_{d}\) & \(\phi_{d}\leq\phi\leq\phi_{u}\) & \(\phi\geq\phi_{u}\) \\ \hline \hline \end{tabular} Note: \(\phi^{\prime}_{y}\) is the first reinforcement yielding, concrete cracking; \(\phi_{y}\) is the appearance of the plastic hinge of the section; \(\phi_{d}\) is the maximum value of the bending capacity; \(\phi_{u}\) is the limit bending state.  
\end{table}
Table 2: Damage status and description of damage index for piers.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**State** & **Intact** & **\begin{tabular}{c} **Minor** \\ **Damage** \\ \end{tabular} & **\
\begin{tabular}{c} **Moderate** \\ **Damage** \\ \end{tabular} & **
\begin{tabular}{c} **Severe** \\ **Damage** \\ \end{tabular} & **Collapse** \\ \hline Index & \(d_{\Delta}\leq 100\%\gamma\) & \(d_{\Delta}\leq 150\%\gamma\) & \(d_{\Delta}\leq 200\%\gamma\) & \(d_{\Delta}\leq 250\%\gamma\) & \(d_{\Delta}>250\%\gamma\) \\ \hline \hline \end{tabular} Note: \(d_{\Delta}\) is relative horizontal displacement, \(\gamma\) is the total thickness of the rubber layer.  
\end{table}
Table 3: Description of isolated bearing damage indexes (unit: mm).  
3.4.3. The Girder End and the Abutment Collision  
Under the action of near-fault ground motion, a large relative displacement may occur at the girder end. When the relative displacement of the motion reaches or exceeds the width of the expansion joint between the girder end and the abutment, a collision may occur between the girder end and the abutment. Furthermore, this paper assumed that the expansion between the girder ends and the abutment joint width was 100 mm (gap = 100 mm). In the analysis, the change in temperature and the effect of material variation on the width of the expansion joint were considered. Under the action of a strong earthquake, when the relative displacement of the girder end reached or exceeded 100 \(\pm\) 10 mm, the girder end was considered to collide with the abutment.