PSI - Issue 78

Alessio Bonelli et al. / Procedia Structural Integrity 78 (2026) 505–512

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1. Introduction Industrial plants, particularly those in the chemical, petrochemical, and oil processing sectors, are complex systems made up of numerous interconnected components and equipment. This inherent structural and operational complexity makes such facilities especially vulnerable to seismic events. When natural hazards interact with industrial risks, they can trigger so- called “Na - Tech” (Natural Hazard Triggering Technological Disasters) events, which may lead to a loss of containment, potentially triggering explosions, fires, or the release of toxic clouds, with severe consequences for the environment and human life (Cotton et al. (2016)). Considering these potentially disastrous consequences, the scientific community has devoted significant efforts to advancing the analysis of seismic risk in hazardous industrial plants. This has led to the development of Quantitative Seismic Risk Analysis (QsRA), an adaptation of traditional Quantitative Risk Analysis (QRA) methods applied to industrial facilities (Antonioni et al. (2007)). QsRA specifically accounts for damage caused by natural events, incorporates the inherent randomness of the initial damage scenarios, and considers the propagation of failures due to loss of containment (LoC). The reason is that past earthquakes have demonstrated the high vulnerability of industrial facilities. For example, the 1999 Kocaeli earthquake, where a magnitude 7.4 event caused significant damage to 30% of industrial plants, some of which triggered domino effects due to the release of hazardous materials. Over the years, several similar earthquake-induced industrial accidents have occurred, including the 1964 Alaska earthquake, the 1964 Niigata earthquake, the 1983 Coalinga earthquake, the 1994 Northridge earthquake, the 1995 Kobe earthquake, the 2003 Hokkaido and the 2011 Tohoku earthquake. In most of these cases, storage tanks were among the most affected types of equipment. Their high vulnerability in petrochemical plants is largely attributed to the hazardous materials they store and the significant structural loads they bear. In the case of unanchored tanks, several damage mechanisms can lead to loss of containment. These include pipe detachment caused by tank sliding, shell fractures resulting from buckling or excessive hoop stress, and excessive movement of floating roofs (which can trigger fires if the stored liquid is oil-based). Researchers have adopted various approaches to studying the behavior of such equipment, including analytical methods, numerical simulations, and experimental investigations. Early studies focused on simplified analytical models, such as the spring-mass analogy introduced by Housner (Housner (1957)). On this aim, works such as Paolacci et al. (2018) and Kalemi et al. (2019) provide valuable insights into simplified modelling and probabilistic analysis of unanchored storage tanks, with particular emphasis on sliding behaviour. These studies highlight the critical issues arising from this mechanism, especially when the connected piping systems are buried. Given the practical advantages of such modelling approaches, the present work will assess the seismic vulnerability of a case study based on the results of a lumped mass model developed by using the OpenSees platform. To this end, a parametric fragility analysis will be performed, aiming to illustrate how the probability of damage (interpreted as the likelihood of leakage) varies with parameters such as the fill level and the base friction coefficient. The considered scenario involves a tank subjected to seismic loading which provokes sliding, concretizing in relative displacements between the tank and the connected piping. But while these simplified models offer practical solutions for design, they fall short in capturing the coupled dynamic behaviour of tank-fluid systems under strong seismic excitation, particularly when material and geometric nonlinearities become significant. For this reason, a more advanced modelling approach may be required, one that explicitly accounts for fluid – structure interaction. Accordingly, this work provides the basis for a broader fragility investigation, combining experimental results with both simplified and advanced models. 2. Simplified model of steel storage tanks For practical applications, the dynamic analysis of a liquid-filled tank may be carried out using the generalized single-degree-of freedom (SDOF) approach. It can represent only the first few modes of vibration of the tank-liquid system (1998-4 (2006)). The two principal responses are defined as the “impulsive” motion, represent ing the combination of the structural and the liquid vibration due to the horizontal excitation , and the “convective” motion, associated with liquid free surface sloshing. The two modes can be analysed independently (Fig. 1 ( a)) , given that the natural frequency of