PSI - Issue 78

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

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As visual results of the dynamic analysis are proposed a sliding time history, Fig. 4(a), and a sliding path, Fig. 4(b). For both the cases, it is considered the earthquake that generated the highest excitation on the equipment (Loma Prieta, USA, 1989). By paying attention on the two images, it is possible to observe that the maximum displacement in both directions in Fig. 4(a) can be seen by looking at the x and y axes in Fig. 4(b) too. If the product between the tank mass and the impulsive component of the spectral acceleration (Sa(Ti)) does not exceed the friction force, the displacements will be confined to the elastic domain of the friction model, hence it will be practically imperceptible (and the sliding path will be a point).

Fig. 4. (a) sliding time history; (b) sliding path.

4.3. Computation of the fragility curves and parametric analysis The final step of the study consists of parametric fragility analysis. Specifically, the computation of fragility curve came from the approach defined in the previous section. From this, parameter as filled level height and friction coefficient were varied, specifically 0.2,0.3,0.4 for μ ( Fig. 5(a)) and 80%, 50%, 25% of the total height (H) for the fill level (Fig. 5(b)). The results highlight that higher friction coefficients lead to a more conservative response, as they require greater base shear (i.e. a bigger acceleration) for the sliding beginning. Conversely, for lower filling heights, the damage in term of LoC occurs for bigger acceleration due to the reduction of the spectral component involved in the response. The reason of this latter point is linked to the range of spectral acceleration for this type of equipment, which is defined around the tenths of a second, so a reduction of the mass (coming from the lower liquid level) produces a reduction of the acceleration (coming from the spectrum). By observing both illustrations in the picture below is possible to deduct that the probability of damage, in term of leakage, is equal to 50% for a spectral acceleration of about 0.3, 0.4 and 0.6g considering the filling level variation (respectively 80%, 50% and 25% of the structural height of the equipment). Instead, for the same LoC probability, the intensity measure values are 0.2, 0.3 and 0.5g for the friction coefficient variation (μ equal respectively to 0.2, 0.3 and 0.4).

Fig. 5. (a) fragility curve for different filling level; (b) f ragility curves for different μ .