# Collapse Potential of an Existing Reinforced Concrete Bridge Structure
## 2 Materials and Methods
### Damage Levels  
The Turkish Bridge Seismic Design Code [1] defines 4 different performance levels: Uninterrupted Occupancy Performance Level, Limited Damage Performance Level, Controlled Damage Performance Level, and Collapse Prevention Performance Level. The Uninterrupted Performance Level defines no or negligible damage in the main structural system elements. The Limited Damage Performance Level represents limited and easily repairable damage in the main structural system elements. The Controlled Damage Performance Level corresponds to the damage level in the main structural system elements that is not severe and is mostly repairable. Each performance level has a damage limit in terms of plastic rotation. This study aims to evaluate the probability of exceeding the collapse prevention performance level of an existing bridge in accordance with the current Turkish Bridge Seismic Design Code [1]. Therefore, the collapse limit has been established based on the damage criterion specified in the aforementioned code. The Code requires that this type of bridge must meet the collapse prevention performance level for an earthquake with a 2% probability of exceedance. The Turkish Bridge Seismic Design Code [1] defines the Collapse Prevention Performance Level as the onset of collapse where the bridge's structural elements experience extensive severe damage. The acceptable damage levels, in terms of the plastic rotations of an RC section for each Performance Level, are given in Equations (13)-(15).  
\[\theta_{p}^{(LD)} =\left(\phi^{LD}-\phi_{y}\right)L_{p} \tag{13}\] \[\theta_{p}^{(CD)} =\left(0.5\phi_{u}-\phi_{y}\right)L_{p}\] (14) \[\theta_{p}^{(CP)} =\left(0.67\phi_{u}-\phi_{y}\right)L_{p} \tag{15}\]  
where \(\phi_{y}\) and \(\phi_{u}\) are yielding curvature and ultimate curvature of the section, respectively. \(\phi^{LD}\) is the curvature calculated based on the existing longitudinal and transverse reinforcement and the unit strain capacities given by the Turkish Bridge Seismic Design Code [1], with 0.004 for concrete and 0.015 for reinforcement. The interstory drift ratio, obtained from IDA, which initiates the exceedance of the plastic rotation limits previously mentioned above, is accepted as the limit of the bridge's structural performance level, and the corresponding spectral acceleration level is taken as the limit value of spectral acceleration for the reached or exceeded bridge performance level. Table 2 shows the bridge performance level and section damage levels based on the approach explained above.  
Figure 14: Mean acceleration spectrum of matched ground motions and spectrum of maximum earthquake.  
\(d_{f\!r}\) is the displacement limit of the bearing calculated based on friction resistance, as given in Equation (16).  
\[d_{f\!r}=\mu P/K_{r} \tag{16}\]  
where \(\mu\), \(P\), and \(K_{r}\) are the friction coefficient, the axial force of the bearing, and \(K_{r}\) stiffness, respectively. \(d_{pud}\) is the dimension of the elastomeric bearing in the direction of motion. \(d_{ums}\) refers to the displacement associated with the bridge deck sliding off the cap beam, and \(d_{gap}\) refers to the distance between the shear key and the adjacent structural element. Finally, \(d_{u}\) is the displacement corresponding to the shear strength of the shear key, which is calculated by dividing shear strength by its stiffness.