## 2 Materials and Methods  
### The Structure and Analysis Models  
The structure used in the study is a newly constructed 242 m-long bridge located in Romania (Figure 2). The design has been completed according to Eurocode, which became mandatory a couple of years before the bridge's construction. Figure 2 contains a photo of the bridge. Figure 3 shows a cross-section of the superstructure with a view of the central pier, which is composed of two circular columns, connected at the top by a rectangular pier cap. The bridge has deep foundations, with 16 m-long bored piles, tied together just below the surface by a 1.75 m-thick pile cap. Figure 1: Overview of a complete probabilistic SSI analysis. Figure 2: Fartec bridge in Brasov, Romania. As part of the geotechnical study at the design stage, multiple boreholes were drilled near the future bridge's foundations. The soil profile at the bridge site is typical for the Brasov basin, with a relatively thin top layer of sand above a thick layer of gravel. Figure 4 contains the soil profile with its main dynamic characteristics as follows: S-wave and P-wave velocity. The study focuses mainly on the comparison of the results obtained through a typical design approach versus a sophisticated SSI analysis. The typical design approach uses industry-standard modelling approaches and the well-known software package CSiBridge. The piles, piers and superstructure girders are modelled as beam elements and the pile cap and superstructure slab as shell elements. The soil-structure interaction along the length of the piles is accounted for by springs of varying stiffness, which increases along with depth. Figure 5 shows a general view of the design model. Figure 4: Soil profile. S-wave and P-wave velocities. Figure 3: Superstructure cross section and pier front view [49]. Regarding the modelling of the seismic action, typical design approaches include the application of an equal acceleration across the whole model, irrespective of the size of the structure. Additionally, for bridges longer than 200 m, the following simplified approach for the introduction of an equivalent effect to ground motion spatial variability is presented in Eurocode 8: the introduction of varying static displacements on infrastructure foundations. As highlighted by Figure 6, these displacements can increase in a single direction (Set A) or have sign variations, giving a saw-like result (Set B). The sophisticated SSI analysis is carried out in ACS SASSI, a highly specialized finite element software, that performs soil-structure interaction analysis for structures in contact with the ground (shallow, embedded, deeply embedded or buried). Originally, the software was created for the specific use on nuclear structures, but lately it has also been used for bridges, high-rise buildings, tunnels, etc. Because of the limited computational capabilities, a single pier has been included, with its corresponding foundation. The corresponding superstructure mass has been concentrated at the top, in its center of gravity. The finite element model is composed of the following 2 parts: the pier structure itself and the near-field soil volume (Figure 7). For the structural part, the piles and the pile cap are modelled as solid elements and the rest of the structure (that is above the ground) as  
Figure 5: Typical design finite element model in CSiBridge. Figure 6: Simplified models for the ground motion spatial variation effect, as per Eurocode 8 (**a**) Set A; (**b**) Set B [6]. beam elements. The equivalent mass of the superstructure has been concentrated at the top of the pier, in its center of gravity. Previous studies [49; 51; 52] highlighted the need include the soil that is in direct contact with the foundation in the model, as solid elements. The characteristics of the soil solid elements are the same as for the layers of free-field soil, at the corresponding depth.