A finite element program was developed to analyze the complexities associated with the nonlinear dynamic response of unanchored liquid storage tanks. The program is capable of modeling curved shells with material and geometric nonlinearities, nonlinear sloshing behavior of fluids, nonlinear fluid-structure interaction and a general class of contact problems. It was observed that the overturning moment exerted on an unanchored tank may be smaller than that exerted on a similar anchored tank due to the longer-period characteristic of the rocking motion, which dominates the behavior of unanchored tanks. However, due to the nature of the boundaries associated with unanchored tanks at their base, the axial and hoop stresses at the bottom of an unanchored tank shell may be larger than those of a similar anchored tank subjected to the same ground motion. The response of unanchored tanks was dominated by the uplift mechanism that varied nonlinearly with the intensity and frequency of the input motion. The coupling of the uplift mechanism with out-of-round distortions resulted in high compressive axial membrane stresses developed over a narrow contact zone. This effect is reflected by the sharp peaks on the compression side of the time histories of axial stresses, which occurred simultaneously with large uplifting displacements. The cases on which axial stresses at the bottom of an anchored tank shell were larger than those of a similar unanchored tank are attributed to the large difference between the overturning moments in the two tanks. Yet, sharp peaks appear on the compression side of the axial stress time history of these tanks.
Many factors that affect the seismic response of unanchored tanks were investigated. It was found that unanchored tanks supported on flexible foundations exhibit lower compressive stresses and higher uplift displacements than those supported over more rigid foundations. This was attributed to flexible foundations, where the contact zone is larger and the pressure distribution on the soil is more uniform than those of rigid foundations. In addition, foundation softness lengthens the rocking period of the tank resulting in less hydrodynamic forces. Membrane forces induced due to large deflections were found to reduce uplift displacements and consequently axial stresses. Formations of a plastic hinge in the connection between the tank shell and base plate increase uplift displacements. Reducing the thickness of the base plate causes the tank to uplift more and consequently more axial stresses are developed at the bottom of the tank shell. In addition, decreasing the base plate thickness reduces the rocking stiffness and consequently lengthens the rocking period. Thus, the developed hydrodynamic forces were less than those for tanks with thicker base plates. Vertical ground motions were found to alter the hydrodynamic forces exerted on unanchored tanks. If the peak response to the vertical component of an earthquake occurred simultaneously and in the same direction with the peak response to the horizontal component, the exerted hydrodynamic forces on the tank may significantly increase.