PSI - Issue 78

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

510

displacements as outcomes of the dynamic analysis. It will take part in fragility analysis as EDP, while the LS is represented by the results of Bursi et al. (2012), represented in Fig. 3(b). Thus, LS is assumed equal to the opening displacement of the flanged joint (0.6 mm) registered during the campaign. The reason came from the assumption that the underground entry point of the pipe can be considered as an embedding constraint and the tank shell non deformable, as the two pipe segments (due to their reduced local length). All these aspects contribute to making the flange open the only mechanism able to take part as a form of strain. 4.2. Structural modeling Dynamic analysis of a liquid-filled tank is carried out using the concept of generalized single-degree-of-freedom (SDOF) systems, which represent the impulsive and convective vibration modes of the tank-liquid system, as illustrated in Fig. 1(c). A three-dimensional numerical model is implemented using the finite element platform OpenSees. The mass, height, natural period, and stiffness used in the model are derived from existing methodologies (Malhotra et al. (2000)):

Table 1. Dynamic characteristic of the tank.

Liquid component

impulsive

convective

Mass [kg] Height [m]

m i = 4.26 * 10 6

m

c = 7.66 * 10 6

h i = 4,48 ξ i = 2% T i = 0.21

h c = 6.24 ξ c = 0.5%

Damping ratio [-]

Period [s]

T c = 7.3

Stiffness [N/m]

k i = 3.77 * 10 9

k c = 5.56 * 10 6

The considered equipment is free to slip on the ground surface but only when the seismic base shear force is greater than the friction resistance. So, a Coulomb friction model is introduced using a flat slider bearing element with a friction coefficient equal to 0.3, Fig. 3(a).

Fig. 3. (a) Coulomb friction model; (b) experimental curve for limit state compute.

The tank model was subjected to seismic action using 300 ground motion records (two set of 150 records), selected from acquisition stations located near Priolo Gargallo (Latitude 37.17°, Longitude 15.17°, within a radius of 100 km) obtained from ITACA, “Italian Accelerometric Archive”. It is a national database of strong -motion recordings developed and maintained in collaboration between the “Italian National Institute of Geophysics and Volcanology” - INGV, and the “Italian Department of Civil Protection” -DPC.