Effect of Wall Flexibility and Damping Ratio on Dynamic Response of Rectangular Liquid Storage Tanks

1. The dynamic response of liquid containers to the underground excitation has been studied intensively in recent years. In early investigations, the fluid response in rectangular liquid storage tanks was represented by impulsive and convective components [1]. The fluid was assumed to be incompressible and the container was assumed to have rigid walls. The Housner’s model [1] has been adopted in most of the current codes and standards for calculating the hydrodynamic pressures in concrete tanks. Very strong earthquakes in the United States and Japan caused heavy damage to many liquid storage tanks. It has become perfectly clear that the concept of a rigid wall could not be retained for further modeling, since the real tanks deform significantly under earthquake loads. Including the wall flexibility in a dynamic analysis requires a systematic knowledge and understanding of the fluid–structure free-vibrational characteristics. As a direct result, new models have been developed and different experiments have been conducted, taking into account the flexibility of the tank walls [2]. Studies on the seismic response of rectangular tanks are not adequate, while those concerning cylindrical tanks are numerous. The time-history analytical method has been used to obtain the dynamic response of fluid storage tank subjected to earthquakes [3]. 2. In this study, the procedure for computing hydrodynamic pressures in rectangular tanks is described. This procedure considers the effect of tank wall flexibility in determining the hydrodynamic pressures produced by the impulsive response. Based on a two-dimensional model of the tank wall, a dynamic time-history analysis is carried out to study the effect of wall’s thickness and damping ratio on the response. Six different models for the tank wall with different thicknesses and the same height are considered. The wall section in models 1 to 4 does not change along the wall height, while it varies in model 5. Model 6 is based on the lumped mass approach assumption adopted by current codes. 3. The results of the analyses are compared with those obtained based on current design practice codes and standards which use a lumped mass approach. The effect of wall flexibility and damping ratio on wall displacements and base shears are also discussed. Fig. 1 shows the hydrostatic pressure versus tank height relationship for models 1 to 4 when the maximum base shear is reached. Fig. 2 compares the hydrostatic pressures of model 3 with model 5. Table 1 presents the maximum base shear due to the hydrostatic pressures, and the elevation of the resultant force for all models.Table 1. Base shear forces and the elevation of resultant forces for different models6 5 4 3 2 1 Model412.2 256.44 307.26 280.35 230.34 221.58 FB hyd (kN)4.2 4.73 5.31 5.06 5.19 5.22 hi(m)4. This study considers the wall flexibility of liquid tanks in the dynamic analysis. The results of the analysis are compared with those obtained from the lumped mass approach adopted by current codes. The comparison shows that in most cases, the lumped mass approach overestimates the base shear. The effect of wall flexibility and damping ratio on wall displacements and base shears are also discussed. The results show that the wall flexibility has a major effect on the hydrodynamic pressure and the seismic behavior of liquid tanks and should be considered in design criteria of tanks.