PSI - Issue 84

Gianluca Quinci et al. / Procedia Structural Integrity 84 (2026) 199–206

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longitudinal primary girders—either precast or cast in situ—resting on elastomeric or steel bearings. The deck system includes reinforced concrete slabs, cross-beams, bearing plinths, edge curbs, and additional secondary components. A detailed geometric survey was carried out for each bridge in order to collect the essential information required for modeling and subsequent analyses. The survey campaign focused on: • total bridge and individual span lengths, • dimensions of piers (height, width, cross-section), • deck width, • quantity and dimensions of main and transverse beams, • geometry of curbs and bearing plinths. All measurements were compiled into a structured digital database designed to consistently represent the geometric attributes of every asset. In addition to field data, original design drawings and reports were retrieved and examined to reconstruct the mechanical characterization of construction materials. In particular, the following information was extracted: • concrete compressive strength, elastic modulus, and ultimate strain, • steel yield and tensile strengths, and Young’s modulus, • layout and thickness of the longitudinal and transverse reinforcement. Combining archival documentation with geometric surveys enabled a reliable representation of the as-built configuration, providing a robust basis for the numerical idealization and seismic performance evaluation. To reproduce the seismic response of the bridge set, nonlinear static analyses were adopted following the N2 method, Fajfar 2000. This choice allows the structural capacity under earthquake loading to be estimated while explicitly accounting for inelastic mechanisms that cannot be captured through linear analysis procedures. To keep the overall computational burden manageable at portfolio scale, each bridge was reduced to an equivalent single-degree-of-freedom (SDOF) system. The equivalent mass was defined to represent the deck portion associated with a representative pier. The lateral stiffness was obtained from the ratio between yield shear force and yield displacement, where these quantities were identified through moment–curvature analyses of the pier sections. The moment–curvature results, constructed using the concrete and steel mechanical properties, provided the key response points needed to define yield and ultimate displacements, as well as shear capacities. For each bridge, the pushover-based workflow included the construction of the Acceleration–Displacement Response Spectrum (ADRS) and the derivation of a bilinear capacity curve. The seismic demand spectrum was then intersected with the capacity curve to identify the Performance Point, interpreted as the expected displacement demand for the considered seismic input. Overall, 3750 nonlinear static analyses were performed (25 bridges × 150 spectra). The demand spectra were obtained from a set of 150 accelerograms selected to be consistent with the regional seismic hazard, based on probabilistic hazard curves for Sicily. All simulations were executed through a custom MATLAB implementation, specifically developed to streamline the workflow and to enable large-scale runs by splitting the calculations into computational blocks. For each analysis, the key response quantity was the maximum deck displacement induced by the seismic action. These displacement demands were treated as Engineering Demand Parameters (EDPs) for fragility derivation. Following the Cloud Analysis procedure, each bridge was described by 150 PGA–EDP pairs, forming a statistical “cloud” capturing the response over a wide intensity range. The median relationship between demand and PGA was obtained via log-linear regression in the natural logarithmic domain, while the dispersion around the fitted trend was quantified through the logarithmic standard deviation, under the usual lognormal assumption (i.e., normally distributed logarithm of displacement). Exceedance probabilities were then computed at each PGA level through the standard cumulative distribution function. In this study, the adopted threshold was the ultimate displacement capacity d_u derived from pushover analysis, corresponding to a collapse-level performance condition. Accordingly, each fragility curve represents the probability that the displacement demand exceeds d_u as seismic intensity increases. From each curve, the parameters μ (median demand) and β (dispersion) were extracted and used as target outputs for the supervised ML stage. The corresponding input variables for learning consisted of the geometric and mechanical descriptors previously collected for each bridge.