## 4 Case Study: The Grottalunga Viaduct  
### Bridge Structural Scheme and FEM Model  
The structure chosen for the case study is the Grottalunga viaduct, designed by [PERSON] in 1962 and located on the A3-Salerno-Reggio Calabria highway, where the seismic action is represented by the elastic response spectrum corresponding to subsoil class \"B\" of Eurocode 8 [36], with a peak ground acceleration of 0.333 g.  
The viaduct is a framed girder extending approximately 221 m in length and 49 m in height, built by segments through cantileering technology. It is composed of two side spans of 53 m and a central span of 115 m (Figure 3(a)). A drop-in span of 19 m length finds a place between the two tips of the cantilevers through Gerber saddles. Figure 3: Bending moment on the bridge with continuous girder for gravity load and seismic actions (**a**) moment M\({}_{y}\) for seismic action in longitudinal direction x; (**b**) moment M\({}_{x}\) for seismic action in transverse direction y. For local needs, the abutments were designed as frames; this led to the following study considering the abutments as fixed points without considering the approach spans but focusing only on the three main spans of the viaduct. The cantilevered spans are made from prestressed reinforced concrete segments 3.5 m long, with the exception of the segments corresponding to the piers, which measure 2.25 m. The section of each segment (Figure 4b) is box-shaped with 0.4 m thick webs, 0.25 m top slab, and a variable bottom slab, with section heights ranging from 7 m in the connection section to the piers up to 2.2 m at the ends. The concrete grade is C40/50, and steel bars have a characteristic yielding strength of \(\mathrm{f_{yk}}\) = 450 MPa. The piers have the same cross-section and reinforcement as those described in Section 3 of this paper; nonlinear behavior was modeled through fiber elements, adopting the Mander model for the confined concrete [37] and the Menegotto-Pinto model [38] for the steel of the reinforcing bars. A more refined model of the restraints was developed. More precisely, in order to model the vertical and torsional resistance of the bearing and the chance of uplifting, a two-dimensional restraint was modeled by rigid elements. In Figure 5a, the restraint on abutments is shown, while in Figure 5b, the connection between the tip of the cantilever and the drop-in span is shown. Both models have the length of rigid elements equal to the width of the deck. For each deck end, two elastomeric pot bearing types are considered, one having the strength to transverse force of 500 KN and the other allowing transverse displacement, both having a vertical tensile strength of 800 kN and free longitudinal displacement in the range of \(\pm\)100 mm. Similar bearings are considered at the Left end of the Drop-in Span (LEDIS), while at the right end, each bearing restrains the longitudinal displacement with the strength of 500 kN each. Thus, for the longitudinal and transverse directions, the operational limit of performance of the restraint that allows movements (Figure 5d) is \(\mathrm{d_{OLS}}\) = \(\pm\)100 mm. Once \(\mathrm{d_{OLS}}\) is overcome, the deck is placed directly on the abutment or the Gerber saddle, and then an additional displacement of \(\pm\)50 mm is permitted with a horizontal passive reaction force due to the friction of concrete elements (deck cross-section, saddle, or abutment). The friction coefficient \(\mathrm{\mu_{c}}\) = 0.25 was assumed, thus a displacement at the damage limit state \(\mathrm{d_{DLS}}\) = \(\pm\)150 mm is assumed. When the \(\mathrm{d_{DLS}}\) is overcome, either the bounding or the unseating can occur. For restraints that prevent displacements, the yielding displacement of \(\mathrm{d_{y}}\) = \(\pm\) 1 mm and a subsequent plastic displacement of \(\mathrm{d_{p}}\) = \(\pm\)25 mm are modeled, and then the same limits for the unrestrained displacement are assumed (Figure 5e): \(\mathrm{d_{OLS}}\) = \(\pm\)100 mm and \(\mathrm{d_{DLS}}\) = \(\pm\)150 mm.