PSI - Issue 84

Domenico Liberatore et al. / Procedia Structural Integrity 84 (2026) 1151–1158

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The recalibrated Young’s moduli are already given in Table 1, while the stiffness of the springs connecting the spandrels to the soil in the normal and tangent direction were increased to 8.4 10 4 kN/m 3 and 1.4 10 5 kN/m 3 , respectively. 5. Pushover analysis Pushover analyses are carried out in the X and Y global directions, corresponding to the longitudinal and transverse out-of-plane directions, respectively, positive and negative. The analyses are performed after the application of the self-weight of the structure, and adopt a mass-proportional loading approach. Due to the high fragility of the parapets, which reached the collapse far before the rest of the structure, these are excluded from the numerical model, in order to avoid premature numerical instability and focus on the global structural performance. The control point is set at the key of the central arch, at the roadway level. Each curve, referring to a Multi-Degree Of Freedom (MDOF) system, is reduced to an equivalent Single-Degree Of Freedom (SDOF) system through participation factors and then linearized to a bi-linear curve (Fig. 5a), according to the Italian Standard Code and the N2 approach. The seismic demand is evaluated considering the elastic spectrum at the Life-Safety Limit State with 5% damping ratio, considering the site of the city of Rome, with soil type D and topographic category T1. The results of the Y (out-of-plane) positive direction only are given in the present article, for the sake of brevity. Figs. 5a and 5b give the results in terms of pushover curve and performance point, while Figs. 6a and 6b show the contour plots of the damage variable at the last step of the analysis before the collapse.

Fig. 5. Pushover capacity curves of the MDOF, SDOF system and bi-linearized (a); performance point and demand-capacity comparison (b); detail of the demand-capacity curve (c).

The capacity curves in Fig. 5a show a high elastic stiffness, as well as a limited plastic branch, highlighting the tendency of the structure to a brittle behavior. The equivalent SDOF curve is then compared to the seismic demand in terms of ADRS, to obtain the performance point. However, as shown in Fig 5c, which zooms the red area in Fig. 5b, the capacity curve and the spectrum do not intersect and T * < T C . In this case, the Italian Standard Code prescribes the evaluation of the maximum displacement as (Figs. 5b,c): ∗ = ∗ , ∗ [1+( ∗ −1) ∗ ]≥ ∗ , (5) Fig. 6. Contour plots of the damage variable; upstream side (a), downstream side (b).