PSI - Issue 78

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

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sloshing is significantly lower than that of impulsive motion. In most of tanks (0.3 < H/R < 3), the first impulsive and convective modes excite 85 – 98% of the total liquid mass. For this reason, considering only these modes is generally sufficient to produce reliable results. 2.1. Seismic response mechanism and modeling approaches

Fig. 1. (a) simplified model for the seismic analysis of liquid storage tanks; (b) uplifting mechanism model; (c) sliding simplified model

Unanchored steel storage tanks are widely used in industrial facilities for storing large volumes of hazardous or flammable substances. This type of equipment is particularly vulnerable to several mechanisms that can occur during strong seismic events, as cracking for buckling phenomena, detachment of pipes from tank’s wall, friction (triggering fires) between floating roof and inside wall (Salimbeni et al., 2023) … Even though they differ in terms of the physics of the event, they can be traced back to base motion involving sliding and uplifting. The first one can led to pipeline detachment and nozzle failure, whereas uplifting may trigger local buckling of the shell near the base (affecting the pipe too). Understanding and accurately modelling these mechanisms is crucial for assessing the seismic vulnerability of unanchored tanks and preventing loss of containment. Focusing on the two, uplifting in unanchored steel storage tanks is triggered when the overturning moment induced by lateral seismic forces exceeds the stabilizing moment provided by the tank’s self -weight and the hydrostatic pressure of the stored liquid (Vathi and Karamanos (2015)). Once the uplift moment surpasses the resisting moment, local separation occurs between the tank bottom and the foundation. This partial detachment does not involve the entire base but can progress dynamically in cycles. Such mechanism can be simulated by introducing a nonlinear rotational spring at the tank base (Fig. 1(b)) within a simplified model where the equipment is represented as a single lumped-mass cantilever. The spring is designed to reproduce the nonlinear relationship between the overturning moment and the corresponding base rotation. The best way to define a simplified system which can reproduce the sliding mechanism is in Fig. 1(c). It consists of a “Two mass model”, composed by cantilevers (representing the impulsive and convective modes), which activate the base slider when the horizontal seismic force exceeds the frictional resistance. At the top of each cantilever are assigned the impulsive and convective mass, representing the stored liquid mass involved in each mode (Kalemi et al. (2019)).