## 3 Seismic Input, Load Scenarios and Analyses
### Nonlinear-Static Analysis (NLSA--Multimodal Pushover Analysis or MMPO)  
In the framework of the NLSA, two principal horizontal seismic motion input corresponding to two load cases were introduced: n. 1 based on the Italian National code [41] non-site-specific spectrum (NSS) approach, and n. 2 using a site-specific spectrum (SSS) approach. Considering the first input seismic motion, it is quite important to highlight that the viaduct is entirely an infrastructure pertaining to the then-administrative department of the municipality of Terenzo (Parma). The Italian update of the seismic classification of the Emilia-Romagna region relocates the territory of the municipality of Terenzo to seismic zone 3 following the most recent classification of seismic hazard. This corresponds to a maximum acceleration expected on the ground (with a probability of exceeding 10% in 50 years) between 0.05 g and 0.15 g: the viaduct seismic ground acceleration is \(a_{gSLV}\) (T\({}_{\rm r}\) = 50 years) = 0.069 g.  
To define the design spectrum, it is necessary to investigate the soil on which the viaduct is located. Official documentation, made available by the Emilia-Romagna region, indicate that the main stratigraphic characteristics of the soils of the municipality are remarkably heterogeneous, with \(V_{sH}\) (shear wave velocity) ranging between 202 m/s and 559 m/s. However, this research additionally benefitted from some MASW (multichannel analysis of surface waves) seismic tests carried out, one of which was performed in the vicinity of the A15 motorway in a section adjacent to the viaduct. A value of the shear velocity \(V_{sH}\) = 225 m/s was reported which suggests characterising the site as a type C subsoil as per the Italian design code [41]. To be on the conservative side of this approach, the topographical effects of the site were also considered, observing that the motorway viaduct is located along the ridge of a slope that ends in the bed of the Taro River. For this reason, a \(S_{T}\) value of 1.2 (topographic category \(T_{2}\), \(h/H\) = 0.5) was assumed. Table 2 outlines the spectral parameters of the elastic response spectrum, and Figure 2 illustrates a comparison between the elastic response spectrum of soil type A and the elastic response spectrum of the Terenzo site for ULS according to the Italian design code [41]. With regards to horizontal load case n. 2 corresponding to the SSS approach, the Emilia-Romagna Region, generally, and the municipality of Terenzo (i.e., the territory within which the viaduct is located), specifically, have consistently remained within a level 2 seismic zone following a regional seismic micro-zonation study conducted in 2017 [42]. In particular, 36 single-station seismic tests (HVSR--Horizontal to Vertical Spectral Ratio Analysis) and 14 geophysical surveys of the MASW + HVSR type were performed and \(11\) geo-mechanical surveys were also carried out on outcrops belonging to the various formations present in the municipal area. Figure 2: Comparison between elastic response spectrum for soil A and elastic response spectrum for the Terenzo site for ULS, according to Italian the design code. Table 3 and Figure 3[42] illustrate the velocity of the shear waves \(\beta\) at various depths and the thickness of the layer \(H\) with homogenous shear wave velocities, measured with an HVSR test near the viaduct in Selva Bocchetto zone (Terenzo, PR--Parma). According to the measurements of the HVRS test and based on a simplified Italian National Code approach [41], the stratigraphic profile of the Selva Bocchetto site can be associated with an \"E\" type subsoil, characterized by very low shear wave velocities and a maximum bedrock depth of 30 m (in this case, 8 m). Hence, it seems fully justified to proceed with an evaluation of the amplification of the seismic signal from the bedrock to the surface and, therefore, build a site-specific spectrum. To do this, a soil model was defined using Deepsoil\({}^{\circledotimes}\) software [43] by implementing the aforementioned stratigraphy.