PSI - Issue 78

Francesco Martini et al. / Procedia Structural Integrity 78 (2026) 2022–2029

2023

height of the silo

H

h 1 , h 2 , h 3 H 1 , H 2 , H 3 i, j mat , s k 1 , k 2 , k 3 k TOT m 1 , m 2 , m 3 N 1 , N 2 , N 3 P h1 , P h2, P h3 P v1 , P v2, P v3 , V 1 , V 2 , V 3 P h , P v n

heights of the contents in the simplified model heights of the walls in the simplified model indexes for the stiffness computation moment of inertia of filling material and steel total stiffness of the silo masses of the simplified model total portions of silo content axial stresses in the simplified model horizontal pressures of the simplified model vertical pressures of the simplified model general definition of horizontal and vertical pressures stiffnesses of the simplified model

external and internal ratios of silo shear stresses in the simplified model

1. Introduction Addressing safety of industrial plants is growing interest among researchers and practitioners, since industrial sites are often characterized by complex structural and non-structural assemblies, which can behave differently under natural or man-made hazardous sources, e.g., earthquakes, floods, explosions. Due to the recent observations in earthquake-prone areas, seismic actions can significantly affect the structural integrity of such installations, leading to relevant direct and indirect losses, e.g., human, economic, environmental, and operational (see for example Paolacci et al. 2012, for the Italian case). Key components of industrial structures are storage systems, among which tanks (for liquids) and silos (for solids or granular-like materials) can be mentioned. Focusing on silos (for tanks, several studies are available, such as Brunesi et al. 2015; Merino et al. 2019), different structural typologies could be considered, but as demonstrated by the recent state-of-the-art (see Khalil et al. 2022), flat-bottom ground-supported steel silos are considered among the most vulnerable ones, especially when considering a near-full storing condition. Over the last years, several works investigated different aspects influencing the behavior of flat-bottom ground supported steel silos under seismic actions, especially for improving the current design practices. Main aspects are following summarized with the main related references: • Geometry, expressed in terms of slenderness (height-to-diameter ratio, H/D), as investigated by Holler and Meskouris (2006), Nateghi and Yakhchalian (2012), Mehretehran and Maleki (2018). • Properties of the stored material, as investigated by Shimamoto et al. (1984), Hardin et al. (1996). • Effective mass under earthquake excitation, as investigated by Sasaki and Yoshimura (1992), Silvestri et al. (2012), Pieraccini et al. (2015). • Additional normal pressure and dynamic overpressure, as investigated Holler and Meskouris (2006), Silvestri et al. (2012), Pieraccini et al. (2015), Butenweg et al. (2017), Khalil et al. (2025). • Compaction of filling material, as investigated by Silvestri et al. (2022). • Soil-structure interaction, as investigated by Butenweg et al. (2017); Holler and Meskouris (2006). • Interaction between steel walls and filling material, as investigated by Holler and Meskouris (2006), Mansour et al. (2022), Khalil et al. (2024). According to this condensed state-of-the-art summary, it is worth observing that the main factors influencing the seismic response of flat-bottom ground-supported steel silos include geometry (height, diameter, wall thickness), filling type and level and, as the main source of uncertainty, the features of the seismic ground motions. Additionally, due to the nature of the structural system, characterized by thin-walled shell structure, silos are extremely vulnerable to different buckling modes during earthquakes, which develop over the height. As reported in Khalil et al. (2024), three main failure modes per buckling can be mentioned: (i) elephant-foot buckling, which develops at the base of the