PSI - Issue 84

Marianna Crognale et al. / Procedia Structural Integrity 84 (2026) 898–905

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Fig. 2. Baseline pushover curves obtained from the fiber-based distributed plasticity FEM model.

2.3. Offline Fiber–Section Dataset Generation A section-level nonlinear analysis was conducted to generate the training dataset for the proposed machine-learning surrogate. Reinforced-concrete pier sections were modeled using fiber discretization in OpenSees and subjected to monotonic moment–curvature (M – κ) loading under constant axial force. The reference section corresponds to the main bridge pier ( P1 ), with geometry and reinforcement layout derived from the structural model. Concrete and steel fibers were modeled using the so-called “Concrete02” and “Steel02” constitutive laws, respectively, where Concrete02 (Kent-Scott-Park model) simulates concrete with linear tension softening, while Steel02 (Giuffré-Menegotto-Pinto model) provides isotropic strain hardening. To isolate section behavior from member- and system-level effects, a short cantilever element with unit length was adopted as a numerical section tester, allowing curvature to be directly evaluated from the imposed rotation. Geometric nonlinearities (i.e., P– Δ effects) were intentionally excluded. The reference axial load ( = −16.8 ) was obtained from gravity-load combinations of the global model; two additional axial levels ( = −15.0 and = −18.5 ) were also considered to represent plausible gravity-load variability. Bending was imposed about the weak axis of the pier section, which governs the seismic response for the considered geometry and direction (the longitudinal one). The M – κ response was obtained through incremental moment-controlled loading while monitoring curvature and resisting moment. Material degradation was introduced in a controlled and uniform manner by scaling the mechanical properties of concrete and reinforcing steel. Three degradation levels were considered for concrete and two for steel, resulting in six degradation scenarios. For each scenario, the complete M – κ curve was generated. A stiffness-based termination criterion was adopted to halt the analysis once a marked reduction in secant stiffness was observed, preventing nonphysical curvature growth beyond section failure. The resulting dataset consists of degradation-dependent M– κ curves, providing a consistent and physically grounded basis for training data-driven surrogates of section stiffness and strength degradation. Table 1 summarizes the scenarios, whose results are shown in Fig. 3 (for reasons of brevity, only the case of axial force of 15 MN is reported). From these curves, it clearly emerges that the effect of the deterioration of the reinforcing steel is marginal, whereas the effect of concrete reduction is significant.

Table 1. Degradation scenarios and reduction factors for concrete (cover and core) and reinforcing steel. Concrete level Cover Core Steel Reduction factor C0 1.00 1.00 S0 1.00 C1 0.80 0.90 S1 0.75 C2 0.60 0.80 S2 0.60