PSI - Issue 78

Yazdan Almasi et al. / Procedia Structural Integrity 78 (2026) 433–440

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3. Structural vulnerability and fragility methodology The assessment of structural vulnerability and the derivation of fragility functions are central to the risk analysis of industrial equipment exposed to sequential earthquake-tsunami scenarios. A large body of literature focuses on evaluating the seismic and tsunami fragility of components such as atmospheric storage tanks (ASTs), pressure vessels, pipelines, and horizontal vessels—elements that are often critical for process continuity and hazard containment in industrial facilities. In the seismic domain, vulnerability assessment typically begins with the development of numerical models to simulate the nonlinear behavior of components under ground shaking (Phan et al., 2018, 2020; Phan & Paolacci, 2018). Nonlinear time-history (NLTH) analysis (Phan et al., 2020; Quinci et al., 2025) and multiple-stripe analysis (MSA) (Phan et al., 2020; Quinci et al., 2025; Zhu et al., 2025) are among the most widely used approaches, allowing researchers to capture the response variability across a range of seismic intensity measures. Limit states are defined according to observable failure mechanisms, such as anchorage failure (Paolacci et al., 2015; Phan et al., 2019), shell buckling (Caprinozzi et al., 2020; Phan et al., 2020), roof sloshing (Caprinozzi et al., 2021), nozzle tearing, or pipe joint separation (Alessandri et al., 2018; Bursi et al., 2025). For storage tanks, fragility analysis has focused on limit states as elephant-foot buckling (Phan et al., 2019, 2020), sloshing-induced roof damage (Caprinozzi et al., 2020, 2021), and uplift under vertical acceleration (Phan et al., 2019, 2020), with the tank fill level, roof mass, and base playing key roles in anchorage (Caprinozzi et al., 2020; Phan et al., 2019, 2020). Studies often adopt simplified beam-shell finite element models with soil-structure interaction components to capture the dynamic amplification introduced by soft foundations or reclaimed soils (Bursi et al., 2025; Caprinozzi et al., 2020, 2021; Phan et al., 2019, 2020). Pipelines and pressure vessels have been evaluated using segment-based models or pseudo-static force assumptions, with fragility defined in terms of strain thresholds or rupture limits (Alessandri et al., 2018; Bursi et al., 2025; Caputo et al., 2019; Corritore et al., 2021; Phan et al., 2019). These models incorporate uncertainties in material properties, connection detailing, and geometric configurations(Caputo et al., 2019; Phan et al., 2020), and fragility functions are typically derived using lognormal cumulative distribution fits (Paolacci et al., 2015; Phan et al., 2018, 2019, 2020; Pitilakis et al., 2024).

Fig. 1. (a) Elephant foot buckling of a tank; (b) Sloshing buckling of a tank; (c) LPG tank failure during the 2011 Tōhoku Earthquake; (d) Damages to tanks with floating roof due to Tokachi-Oki earthquakes; (e) LPG tank failure during the 2011 Tōhoku Earthquake. (Source: Caputo et al. (2019)) Tsunami vulnerability analysis introduces a different set of challenges, primarily due to the complex nature of hydrodynamic loads and the limited availability of high-fidelity structural data post-event. Industrial fragility studies for tsunami loads commonly rely on empirical (Basco & Salzano, 2017; Goda & De Risi, 2023; Nishino et al., 2024; Rahimi et al., 2025), analytical (Basco & Salzano, 2017), or hybrid approaches (Vitale, Ricci, et al., 2024). Empirical fragility curves are developed using post-tsunami damage data and relate damage probabilities to flow depth, velocity,