PSI - Issue 78

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

508

3. A fragility analysis of storage tanks in terms of LoC Understanding the most common damage mechanisms which can trigger leakage is fundamental for the seismic vulnerability assessment and for probabilistic approaches, as the fragility analysis, of such equipment. The latter provide a solid procedure that can led to the evaluation of the probability of damage, concretized into the fragility function. They are obtained combining, by a lognormal distribution, the Engineering Demand Parameter (EDP) and an Intensity Measure (IM). But while the EDP is inherently tied to the model and its internal behaviour, the IM can be selected from a wide range of parameters describing the seismic event. In this regard, a significant contribution was made by Phan et al. (2021), who, through a regression-based analysis of residuals for various IMs, demonstrated that the most efficient intensity measure for fragility analysis is the so- called “Average Spectral Acceleration” (SaAV). Once the dataset composed by demand and intensity is established, the next step is the selection of the damage threshold, the Limit State (LS). Accordingly, for this work, the focus will be paid on the detachment of pipes from tank’s wall (due to the asses sment of the sliding mechanism reported in the case study). 3.1. Selection of the limit state The substances stored inside the tanks are carried through pipelines connected to the equipment, where flow is regulated by means of valves and joints. Thus, the seismic interaction between the piping system and the tank represents one of the main structural vulnerabilities due to the different behaviour of the two apparatus. Such interaction can give rise to three distinct kinematic mechanisms, during which the connected pipelines are subjected to tensile and bending stresses; such mechanisms are sliding, uplifting, and buckling. Experimental observations as La Salandra et al. (2016), Wieschollek et al. (2013), Karamanos et al. (2003), have shown that loss of containment following such events is mainly caused by the failure of specific piping components. These include rupture of the nozzle, Fig. 2(a), (the pipe segment welded directly to the tank wall), opening of elbows, Fig. 2(b) (solution used either to provide flexibility to the system or to accommodate spatial constraints), and opening of the flanged joints, Fig. 2(c), (which connect the tank nozzle to the pipeline).

Fig. 2. (a) experimental collapses of nozzles; (b) experimental damage of elbows; (c) experimental setup of bolted flange joints.

Thus, by monitoring the development of the leakage, it is possible to define the limit state. It represents the stress value to which the sample is subjected when the fault occurs. While the most accurate process is composed by a laboratory campaign, whose results can be evaluated and exploited for fragility analysis, the easiest way to compute a limit state is usually trough nonlinear modelling. Next section provides a short summary of one of the most used tools, based on linear regression, for fragility function computation.