Initial analytical studies dealt with the hydrodynamics of liquids in rigid tanks resting on rigid foundations. It was shown that a part of the liquid moves in long-period sloshing motion, while the rest moves rigidly with the tank wall. The latter part of the liquid – also known as the impulsive liquid – experiences the same acceleration as the ground and contributes predominantly to the base shear and overturning moment. The sloshing liquid determines the height of the free-surface waves, and hence the freeboard requirement. It was shown later that the flexibility of the tank wall may cause the impulsive liquid to experience accelerations that are several times greater than the peak ground acceleration. Thus, the base shear and overturning moment calculated by assuming the tank to be rigid can be nonconservative. Tanks supported on flexible foundations, through rigid base mats, experience base translation and rocking, resulting in longer impulsive periods and generally greater effective damping. These changes may affect the impulsive response significantly. The convective (or sloshing) response is practically insensitive to both the tank wall and the foundation flexibility due to its long period of oscillation.
Tanks analysed in the above studies were assumed to be completely anchored at their base. In practice, complete base anchorage is not always feasible or economical. As a result, many tanks are either unanchored or only partially anchored at their base. The effects of base uplifting on the seismic response of partially anchored and unanchored tanks supported on rigid foundations were therefore studied. It was shown that base uplifting reduces the hydrodynamic forces in the tank, but increases significantly the axial compressive stress in the tank wall.
Further studies showed that base uplifting in tanks supported directly on flexible soil foundations does not lead to a significant increase in the axial compressive stress in the tank wall, but may lead to large foundation penetrations and several cycles of large plastic rotations at the plate boundary. Flexibly supported unanchored tanks are therefore less prone to elephant-foot buckling damage, but more prone to uneven settlement of the foundation and fatigue rupture at the plate-shell junction.