Contributions of Fluid to Rocking–Bulging Interaction of Rectangular Tanks Whose Walls Are Rigid and Bottom Plate Rectilinearly Uplifts

Abstract

At the event of severe earthquakes, the tank rocking response appears subsequent to the tank bulging response. A springmassrigid body combined model was proposed for analyzing the tank response and the required quantities for the model have been rigorously defined based on the mathematical solution of fluid pressure on the tank accompanying the tank response of interest. To date, the apparent density of fluid for the rocking and the bulging responses and the effective mass of those are available for this purpose. However, observations revealed that the interaction between the rocking response and the bulging response is stimulated by the effective mass of fluid for the rocking–bulging interaction that is understood as a part of the effective mass of fluid for the tank bulging response that is also under the action of the rotational inertia. Therefore, regarding a ratio of the apparent density of fluid for the tank rocking response to the original density of fluid as the intensity of a contribution of fluid to the tank rocking response, the apparent density of fluid for the rocking–bulging interaction is defined intuitively and conveniently. The effective mass of fluid for the rocking–bulging interaction is subsequently defined. The distribution of the apparent density of fluid for the rocking–bulging interaction inside the tank is drawn for a combination of the various aspects of tank and the ratios of the uplift width of the tank bottom. The ratios of the effective mass of fluid for the rocking–bulging interaction to the total mass of fluid of the tank as well as the ratios of the arm length to the centroid of the effective mass of that to the tank geometry are also depicted by the same manner.