## 5 Discussion and Conclusions
The parametric study also shows that the vulnerability of the piers is reduced as the dead load of the deck increases, thanks to the increase in the resistance of the RC section induced by the axial compression. This effect is evident when the frame pier is considered. In the simply supported scheme in zone 2, isolation is not effective for 10 m and 20 m high piers supporting 20 m long decks but becomes effective when the same piers support the 35 m long deck, whose dead load is approximately two times greater. Similarly, for the continuous deck scheme in seismic zone 1, the frame pier remains vulnerable after deck isolation when it is combined with the 20 m RC slab deck, but it is protected when it supports the 35 m box girder deck. In the parametric study, for bridges with a continuous deck on multiple supports, for simplicity, a distribution of the deck mass on the piers based on the tributary loading area was used. This approach was validated, for the considered case studies, by comparing the results with those provided by a rigorous calculation of the vertical reactions based on the stiffness of the piers. The results of the comparison, reported in Appendix A, show that, for the examined bridge prototypes, the tributary area approach leads to underestimating--in general, by an amount between 5% and 15%--the axial load on the piers, which is conservative, since the elastic capacity of the RC sections of the piers increases with the increase in compression. Furthermore, the assessment was repeated considering the accurate reactions on the piers, obtaining a matrix of effectiveness practically equivalent to the one shown in Figure 14. Only in one case, where the \(a_{EL}/a_{ES}\) ratio was very close to unity, was a different outcome observed. However, in cases of continuous deck schemes with a more complex geometry than those considered in the study (which, it is worth recalling, represent common typologies of Italian bridges), when the \"\(a_{EL}/a_{ES}\)\" ratio is close to unity, the assumption of uniform deck mass distribution may affect the result, providing a false positive or a false negative. To avoid this situation, in the application of the procedure, it is recommended, when the simplified mass distribution provides an \"\(a_{EL}/a_{ES}\)\" ratio between 0.95 and 1.05, to proceed according to the more rigorous approach that takes into account the stiffness of the structural elements. As a final comment, it should be emphasized that, although some general conclusions of the parametric study can be extended to other types of bridges (in particular, bridges with short piers or with very tall piers with a long vibration period are expected to perform better during an earthquake), the results are not applicable to piers with different sections. Even for the RC piers examined in the study, the results depend on the steel reinforcement and therefore cannot be generalized, as the characteristics of the reinforcement strongly depend on the historical period of construction of the bridge. The collection of the geometric and material characteristics of the bridge components is therefore a fundamental step for the correct implementation of the procedure. Although in the examples shown in the paper, the assessment procedure has been applied to some prototypes of RC bridges, in principle, it can be applied to any type of bridge that meets the requirement of having a deck totally supported by bridge bearings, regardless of the static scheme (simply supported spans or continuous deck) and the geometry and materials of the deck and the piers. It is therefore suitable for RC bridges, steel bridges, and composite bridges. In the opinion of the Authors, the proposed method can represent a practical tool for the assessment of bridges at the network scale. The criterion allows for performing an initial evaluation of the effectiveness of the deck isolation in a simple and fast way, avoiding in the preliminary phase time-consuming analyses which require the formulation of complex numerical models of the bridges.