The problem of soil-tank-fluid interaction was addressed by many investigators. Haroun and Abdel Hafiz [92] considered soil-tank interaction effects and showed that it substantially reduced the amplified tank response. Haroun and Abou-Izzeddine ([83], [84]) performed parametric study on the dynamic soil-tank interaction under horizontal seismic excitations. Hori [109] presented the effects of soil on the dynamic response of liquid-tank systems. Fisher et al [65] presented a dynamic response analysis of vertically excited liquid storage tanks including both the liquid-tank and the liquid-soil interaction. The system considered was a thin-walled elastic cylindrical shell entirely filled with an incompressible and inviscid fluid, resting on a flexible foundation over an elastic halfspace with frequency dependent stiffness and damping parameters.
Zaman et al [296] developed an analytical formulation to examine the flexural behavior of rectangular foundations resting on elastic half space and supporting cylindrical tanks. The formulation was based on the principle of minimum potential energy and was applicable to problems having geometric and loading symmetry with respect to the x and y axes. The deflected shape of the foundation was approximated by a polynomial in terms of the even powers of x and y, and the contact stress distribution was assumed to be a function of the foundation deflection. The wall-foundation interaction was included by modifying the wall deflection function and satisfying the compatibility conditions applicable to the junction between the foundation and the tank wall.
Shimizu [254] presented a study which investigated the seismic design of cylindrical liquid storage tanks with a rigid foundation slab resting on elastic soil subjected to sway and rocking motions. This study concerned with the derivation of a vibration for a cylindrical tank as a super-structure. In a following work [253], he presented a study that concerns the seismic design of a cylindrical liquid storage tank with rigid foundation resting on elastic soil subjected to earthquake ground motions. He showed a procedure of a whole vibration model of the tank-foundation-soil system and proposed a conventional seismic design procedure for the tank. Furthermore, Shimizu [252] presented a seismic design method of cylindrical liquid storage tanks resting on elastic soils that are subjected to horizontal ground motions. He derived equations of motion of a lumped-mass model for describing the coupled motion of the tank-liquid-foundation system.
Zaman and Mahmood [297] examined the response of a cylindrical storage tank foundation system using the finite element technique which considered the interaction between the tank wall foundation and supporting soil medium. Emphasis was given to modeling of nonlinear deformation characteristics of the interface between the foundation and the soil medium using a joint element. He presented parametric studies to assess the effects of depth of foundation embedment, interface roughness, soil nonhomogeneity, nonlinearity, and relative rigidities of the tank wall-foundation and soil systems.
Seeber et al [244] presented three dimensional analysis of the dynamic behavior of liquid filled elastic cylindrical tanks based on flexible grounds, undergoing horizontal and vertical earthquake excitation. The interaction of the ideal fluid with the elastic shell and with the flexible ground yielded a problem of linear potential theory which was solved together with the equations of motion of the shell and of the ground. With the unknown nodal shapes of vibration developed in Fourier and in Fourier Bessel series, the partial differential equations were transformed into coupled generalized equations of vibration by a weighted residual approach. The results showed the strong influence of the flexible ground characterized by a remarkable shifting of natural frequencies, by the existence of additional natural frequencies and by high damping ratios.
Veletsos et al [278] made a study of the effects of soil-structure interaction on the response of liquid containing upright circular cylindrical tanks subjected to a horizontal component of ground shaking. He generalized the mechanical model for laterally excited rigid tanks supported on a nondeformable medium to permit consideration of the effects of tank and ground flexibilities, and base rocking. Responses were evaluated for harmonic and seismic excitations over a range of tank proportions and soil stiffnesses, and the results were presented in a form convenient for use in practical applications.
Hangai and Ohmori [78] investigated a soil-structure interaction problem which dealt with the nonlinear contact vibration of a rigid as well as a flexible bar rested on uniformly distributed Winkler type springs and considered uplift of a portion of the bar. Bars were subjected to both vertical dead load and time varying moment around the center of gravity to model the external excitation from the superstructure. The finite difference method was used in order to discretize the equilibrium equations of motion, derived under small deflection theory, and the Runge-Kutta method was applied to the numerical analysis. Hangai and Ohmori concluded that, for a flexible structure, soil reaction took complicated modes along the time history and vertical displacement components of the center of gravity played an important role in the nonlinear soil-structure interaction problem considering uplift.
Ishida et al ([126], [127]) presented a dynamic mechanical model of a four degree of freedom mass-spring system for the rocking response analysis of unanchored tanks by considering the partial uplift of the bottom plate as a rotational spring of bilinear type. The finite element method was used to analyze the deflection of the bottom plate by replacing it with an elastic-plastic beam model. Also, they proposed a calculation method for the bottom plate uplift based on the small deflection theory and assuming a rigid foundation. They performed a shaking table experiment and a static tilt test on a stainless steel model tank, provided with a rubber mat in order to simulate the actual soil foundation effect, and test results were compared with those obtained from the four degrees of freedom system.
D'Orazio [47] simulated the uplift behavior with model tests and measured both the amount of uplift and the radial displacements. He gave an interpretation of the measurements, and illustrated a method for estimating radial displacements based primarily on deformations at the foundation level. Both flexible and rigid foundations were considered. Radial displacements of uplifted and anchored tanks were compared. He concluded that the foundation deformation and uplifting control the radial displacements.
The settlement of soil due to the large pressure exerted from liquid storage tanks was also investigated. Ma et al [164] presented analysis of such a system. The analysis includes the effect of sloshing of liquid in the tank and the associated hydrodynamic pressure, and the effect of coupling between liquid, tank and soil foundation. The effect of tank settlement on its response was also presented in ([23], [46], [48], [59], [60], [110], [260], [263], [264]). In addition, analysis and design of the tank foundation was discussed ([201], [275], [287]).