## Appendix A  
To investigate the accuracy of the assumption of a distribution of the deck mass of continuous bridges based on the tributary loading area of the piers, the actual mass distribution of a continuous deck with four spans of the same length was calculated, taking account of the stiffness of its structural elements.  
Finite element models of four bridges were formulated in SAP2000 v.19 software [33] using elastic beam elements for the deck and the piers, replicating the pier layouts (5-5-5 m; 10-10-10 m; 20-20-20 m; 5-10-5 m) examined in the parametric study. The geometric and material properties defined in Table 1 (for the deck) and Tables 2-4 (for the piers) were assigned to the bridge elements in order to reproduce the characteristics of the bridges considered in Table 1. The elements were modeled without mass, and a distributed load on the deck was assigned according to Table 1. The lower end of the piers had fixed restraints; the abutments were modeled as hinges, and pinned connections were assumed between the piers and the deck.  
The results of the analyses are shown in Figure A1 for the 20 m long RC slab deck with lightening tubes and in Figure A2 for the 35 m long RC box girder deck, respectively. The panels shown in the Figures report, for each pier type and pier layout, the ratio between the vertical reaction on the pier calculated by the finite element model and the vertical reaction according to the tributary area. Regardless of the type of deck and piers, the analyses reveal that the simplified mass distribution overestimates the vertical reactions on the abutments and underestimates the reactions on the two external piers. The accuracy of the simplified approach depends on the characteristics of the deck and of the piers, but the relative deviation in the vertical reactions for the two external piers P1 and P3 is, on average, between 5% and 15%. It is also interesting to note that the effect of piers of different heights, and therefore different stiffnesses, is evident only for continuous deck resting on circular cross-section piers.  
The effectiveness of deck isolation for the continuous deck bridges was assessed again by considering the vertical loads on the piers resulting from the actual mass distribution, providing the results shown in Figure A3. For the bridge with a 20 m RC slab deck the results are equivalent to those shown in Figure 14. For the bridge with a 35 m RC box girder deck the only difference concerns the case of the 10 m high pier with a circular section in zone 1: the deck isolation is found to be not effective if the simplified deck mass distribution is assumed but turns out to be effective by considering the more accurate vertical reactions, which give a 4% increase in the vertical load on every pier. As highlighted in the study, increasing the axial load on the piers has a beneficial effect, as it increases the capacity of the RC section. It is worth noting that in the only case where the accurate mass distribution provided a different result than the simplified distribution, the \(a_{EL}/a_{ES}\) ratio was very close to unity (0.988 for the simplified approach; 1.013 for the accurate approach).