消防法に定める屋外石油貯槽の浮屋根応力評価式の検証

<p> During the 2003 Tokachioki earthquake, seven oil storage tanks of floating-roof type located at Tomakomai, Japan were seriously damaged due to liquid sloshing. Immediately after the earthquake, the Fire and Disaster Management Agency of Japan^{2), 3)} has issued the amended notification of the Fire Defense Law (FDL), in which the stress evaluation formulas for a floating roof of oil storage tank under long-period earthquake motion have been newly regulated. However, these are the empirical formulas prioritizing the practical usage, and it is of great practical significance to confirm their validity through comparison with the exact nonlinear solution for the coupled fluid-structure system.</p><p> In the present paper, the hybrid analytical and finite element methood (FEM) proposed by the authors^{11), 12)} is employed for carrying out nonlinear sloshing analysis of coupled liquid-floating roof system. The tank is composed of a rigid cylindrical wall and a flat bottom, while the floating roof is treated as an elastic plate undergoing large deflection. The contained liquid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The method of analysis is based on representation of the liquid motion by superposing the analytical solutions that satisfy the Laplace equation and the rigid wall and bottom conditions. This requires only the discretization of the liquid surface and the floating roof into finite elements (see Fig. 3), thus leading to a computationally very efficient method compared with full numerical analysis. In order to model the pontoon of thin box-shaped cross-section precisely use is made of the eccentric plate and beam elements in this study (see Fig. 1). Numerical results are presented for the case of three oil storage tanks with single-deck type floating roof damaged during the 2003 Tokachioki earthquake (see Table1 and Fig. 2). Comparison is made between the results predicted by the present nonlinear analysis and the evaluation formulas notified in the FDL.</p><p> Conclusions arising from the present study can be summarized as follows:</p><p>・As for liquid surface elevation, the contribution of linear oscillation modes with circumferential wave number 1, especially the contribution of fundamental sloshing mode with radial wave number 1, is dominant (see Figs. 8-10). However, the existence of nonlinear oscillation modes with circumferential wave numbers 0 and 2, caused by finite liquid surface elevation as well as large deformation of the floating roof can never be ignored (see Figs. 11-13).</p><p>・There exist two other sources of nonlinear oscillation modes which are excited by the internal resonant oscillation with the linear second order mode. One is the bi-harmonic resonant oscillation mode at half the fundamental sloshing period, as observed in Model 3A tank of 30,000m³ capacity and Model 4A tank of 40,000m³ capacity (see Figs. 11, 12). The other is the nonlinear oscillation mode with circumferential wave number 3, as recognized in Model 10B tank of 100,000m³ capacity (see Fig. 13).</p><p>・The nonlinear oscillation modes observed in the present study produce excessively large stresses in the pontoon, which are far beyond the evaluation based on the empirical formulas notified in the FDL (see Figs. 14-16).</p><p>・It should be emphasized that the stress evaluation formulas in the amended Notification of the FDL, taking a part of these nonlinear oscillation modes out of consideration, tend to underestimate the pontoon stresses significantly and should be improved (see Fig. 17).</p>