## 4 Results
### Simply Supported Deck Scheme  
The results of the assessment for the simply supported decks are summarized in the matrix shown in Figure 13. For each seismic scenario, the deck type and pier height, the assessment may provide one of three outcomes: retrofit is not necessary (the elastic resource of the piers overcomes the seismic demand); retrofit is necessary and deck isolation is effective; or retrofit is necessary but deck isolation is not effective, as the seismic forces associated with the mass of the pier alone exceed the elastic resource of the latter).  
The parametric study also allows for drawing some interesting conclusions regarding the effectiveness of deck isolation.  
The pier with a circular cross-section requires the retrofit of the bridge in all seismic scenarios and for all heights, except in the case of tall piers (20 m high) in moderately low-seismicity areas. In this case, the flexibility of the piers lengthens the fundamental period of the bridge by reducing the As-Built acceleration below the Elastic Resource acceleration. The parametric analyses further reveal that in the high-seismicity zone, tall piers do not have sufficient elastic resources to resist the seismic forces associated with their own mass. In fact, in zone 1, only for the low pier (5 m high), the bending moment caused by the seismic force does not exceed the sectional resistance, and deck isolation is effective. On the contrary, in moderately high-seismicity zones, the isolation of the deck is always effective in protecting the piers.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Property** & **Symbol** & **Value** & **Unit** \\ \hline Pier axial load & \(N\) & 5046 & kN \\ Pier shear strength & \(V_{RD}\) & 3151 & kN \\ Pier yielding moment & \(M_{y}\) & 5833 & kNm \\ Effective mass & \(m_{off}\) & 515.8 & ton \\ Elastic Limit acceleration & \(a_{EL}\) & 2.26 & m/s\({}^{2}\) \\ Pier bending stiffness & \(K\) & 593,305 & kN/m \\ As-Built period & \(T_{As\,Built}\) & 0.19 & s \\ As-Built acceleration & \(a_{As\,Built}\) & 9.14 & m/s\({}^{2}\) \\ Substructure mass & \(m_{sub}\) & 114.9 & ton \\ Substructure acceleration & \(a_{sub}\) & 6.45 & m/s\({}^{2}\) \\ Equivalent Substructure acceleration & \(a_{ES}\) & 1.44 & m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Example of suitability assessment.  
The frame pier is evaluated separately in the two horizontal directions of the bridge, since the pier has higher flexibility and lower strength in the longitudinal direction and higher stiffness and strength in the transverse direction. In this regard, the analyses highlight the intrinsic vulnerability of the pier due to its low capacity in the longitudinal direction. Bridge retrofit is always needed (at least in the weakest longitudinal direction), even in cases of moderately low seismicity. In the zones of high and moderately high seismicity, deck isolation is not effective for piers higher than 5 m but is effective for piers supporting the heavy RC deck with V beams in zone 2. The reduced vulnerability of the pier in this situation is an effect of the weight of the deck (the loads of the three simply supported decks are reported for reference in Table 1): heavy decks increase the axial compression of the pier and hence the bending capacity of the RC section.  
The pier with a hollow rectangular cross-section was also evaluated separately in two principal horizontal directions due to its different inertial characteristics. It was found that seismic rehabilitation is necessary (at least in the weakest longitudinal direction) for all bridges and pier heights in high and moderately high seismicity zones, and in some cases in zone 3 (low or tall piers). Deck isolation is always effective except for tall (20 m) piers in seismic zone 1, thanks to the high elastic capacity of the hollow cross-section.