PSI - Issue 81

Mykhailo Hud et al. / Procedia Structural Integrity 81 (2026) 434–438

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particularly in the lower modes where global deformation dominates. Similarly, Hashemi et al. (2013) demonstrated that even partial filling induces notable changes in modal shapes due to the redistribution of mass and internal forces. Virella et al. (2008) contributed detailed insights into the evolution of local vibration modes, showing that structural stiffness is the primary driver of high-frequency spectral patterns. Although large-scale industrial tanks are well studied, fewer works address the modal behaviour of small reinforced concrete pool structures. This gap underscores the relevance of examining hydrostatic pressure effects in compact reservoirs. 2. Modelling The model of the pool tank was created using the LIRA finite element analysis environment. This ensured an accurate representation of the spatial behaviour of engineering structures. It also took into account geometric nonlinearity, the real physico-mechanical properties of materials, and applied loads. The computational scheme was constructed using three dimensional finite elements with a mesh size of 10 × 10 cm, which provided a sufficient level of detail and ensured an appropriate approximation of the actual geometry of the pool tank. The structural dimensions are 3 × 6 m, with a depth of 1.6 m. These characteristics correspond to those of compact reservoirs intended for water retention under sustained internal pressure. Reinforced concrete of class C20/25 was selected as the structural material, whose physico-mechanical properties are typical for constructions of this type. This ensures the required strength, stiffness, and durability during operation.

Fig 1. 3D model of the pool bowl

The developed finite element model (Fig 1.) accounts for the stiffness of the walls and the bottom slab, thereby reproducing the realistic distribution of stresses and deformations within the shell of the pool tank. Furthermore, the model incorporates the action of hydrostatic water pressure, which is applied to the internal surfaces of the structure in accordance with the depth dependent distribution of loads. The study examined the behaviour of the basin under three characteristic filling conditions, which made it possible to assess the influence of water mass and hydrostatic pressure on natural vibration frequencies. In particular, the following scenarios were analysed: a fully filled reservoir representing nominal operating conditions with maximum internal pressure; a partially filled reservoir (half full), simulating intermediate operating conditions with uneven distribution of hydrostatic load along the wall height; and an empty reservoir, corresponding to the absence of internal fluid pressure and allowing the assessment of the inherent stiffness of the reinforced concrete structure of the reservoir. 3. Result and discussion The frequency spectrum was analysed using a dataset obtained from numerical modelling in order to ascertain how it changes under different loading conditions. The particular focus was on those conditions influenced by variations in hydrostatic pressure and water mass in the tank. This facilitated the observation of trends in the natural frequencies and the characteristics of vibration modes, thereby providing insight into the dynamic behaviour of open reservoir structures. These observations are of paramount importance for comprehending the manner in which the structure responds to divergent operational scenarios and for providing a framework for further stability assessments.