Response and failure of fluid-filled tanks under base excitation

Abstract

An analytical model is developed that leads to better understanding of the response of fluid-filled tanks whose bottom may separate from and lift off the foundation, during base excitation. First, the hydrodynamic problem is solved in closed form, for the most general motion of the structure. This eliminates the fluid response unknowns and therefore only the structural degrees-of-freedom need to be considered. Then, application of Hamilton's Principle in the structural domain sets up the system equations of motion. During this procedure, the uplifting behavior is modeled by an appropriate rotational spring, placed between the foundation and the bottom of the tank. Equivalent springs are also used for modeling the ground/structure interaction. Moreover, shell flexibility and liquid sloshing effects are also incorporated and investigated. Using this model, results are obtained and compared with experimental data. This comparison reveals some interesting effects of the base uplift on the system response. Ground flexibility is found to reduce the effective beam-type stiffness of the structure, but this reduction is much smaller than the substantial stiffness reduction induced by the possibility of uplifting. For the cases examined, the stiffness reduction due to the base uplift changes dramatically the dynamics of the system, which in turn alters the developed hydrodynamic loads, through the fluid/structure coupling process. Also, the shell flexibility effects - which can be important for the anchored tank case - are found to be negligible for an unanchored tank. Knowledge of the structural response leads to direct calculation of the hydrodynamic loads and consequently to prediction of failure. Buckling phenomena observed experimentally at the top and the bottom of scale model tanks are studied and explained.