Discrete Models for Seismic Analysis of Liquid Storage Tanks of Arbitrary Shape and Fill Height

A finite element method (FEM)-based formulation is developed for an effective computation of the eigenmode frequencies, the decomposition of total liquid mass into impulsive and convective parts, and the distribution of wall pressures due to sloshing in liquid storage tanks of arbitrary shape and fill height. The fluid motion is considered to be inviscid (slip wall condition) and linear (small free-surface steepness). The natural modal frequencies and shapes of the sloshing modes are computed, as a function of the tank fill height, on the basis of a conventional FEM modeling. These results form the basis for a convective-impulsive decomposition of the total liquid mass, at any fill height, for the first few (two or three at most) sloshing modes, which are by far the most important ones in comparison to all other higher modes. This results into a simple yet accurate and robust model of discrete masses and springs for the sloshing behavior. The methodology is validated through comparison studies involving vertical cylindrical tanks. Additionally, the application of the proposed methodology to conical tanks and to the seismic analysis of spherical tanks on a rigid or flexible supporting system is demonstrated and the results are compared to those obtained by rigorous FEM analyses.