Numerical Investigation on Accuracy of Mass Spring Models for Cylindrical Tanks under Seismic Excitation

The main objective of this article is evaluation of the simplified models which have been developed for analysis and design of liquid storage tanks. The empirical formulas of these models for predicting Maximum Sloshing Wave Height (MSWH) are obtained from Mass Spring Models (MSM). A Finite Element Modeling (FEM) tool is used for investigating the behavior the some selected liquid storage tanks under available earthquake excitations. First, the results of FEM tool are verified by analyzing a liquid storage tank for which theoretical solution and experimental measurements are readily available. Then, numerical investigations are performed on three vertical, cylindrical tanks with different ratios of Height to Radius (H/R=2.6, 1.0 and 0.3). The behaviors of the tanks are initially evaluated using modal under some available earthquake excitations with various vibration frequency characteristics. The FEM results of modal analysis, in terms of natural periods of sloshing and impulsive modes period, are compared with those obtained from the simplified MSM formulas. Using the time history of utilized earthquake excitations, the results of response-history FEM analysis (including base shear force, global overturning moment and maximum wave height) are compared with those calculated using simplified MSM formulations. For most of the cases, the MSWH results computed from the time history FEM analysis demonstrate good agreements with the simplified MSM. However, the simplified MSM doesn't always provide accurate results for conventionally constructed tanks. In some cases, up to 30%, 35% and 70% average differences between the results of FEM and corresponding MSM are calculated for the base shear force, overturning moment and MSWH, respectively.