## 3 Results
### Dynamic Characteristics of Fluid Surface According to the Ratio of Fluid Height and Structure Width  
The h/B was set at 200, 250, 300, 350, and 400 mm (h/B: 0.4, 0.5, 0.6, 0.7, and 0.8) in order to estimate the dynamic characteristics of the fluid surface according to the ratio of the width of the fluid storage structure to the initial fluid height. The specifics of the structure applied to the analysis are shown in Figure 9, and the analysis was performed by applying the seismic load shown in Figure 6a. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** \\ \hline Time (s) & 6.460 & 7.750 & 4.370 & 3.765 & 5.080 \\ \hline Max. (mm) & 363.0 & 363.0 & 369.0 & 368.0 & 369.0 \\ \hline Min. (mm) & 180.0 & 183.0 & 183.0 & 184.0 & 182.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of slushing heights generated by earthquakes of different shapes. Figure 8: Comparison of fluid surface shape by earthquakes of different shapes. Figure 9: Analytical model for evaluating the influence of fluid height and structure width. Figure 10 shows the shape of the fluid surface at 7.300, 6.790, 8.050, 12.930, and 12.910 s, which are the times when the maximum sloshing height of the fluid surface occurs. As shown in Table 5, as the ratio h/B of the fluid height and the width of the structure increased from 0.4 to 0.8 by 0.1, the maximum sloshing height was measured as 287, 338, 398, 471, and 500 mm, and the minimum sloshing height was measured as 156, 206, 240, 287, and 338 mm. However, when h/B was 0.8, the maximum sloshing height could not be accurately measured because the fluid surface was in contact with the upper slab. Table 6 shows the fluid height to structure width ratio (h/B) and the initial fluid height to maximum sloshing height ratio (h\({}^{\prime}\)/h) based on the results shown in Table 5 and Figure 10. It can be seen that as the h/B decreases, that is, as the ratio of the fluid height to width of the fluid storage structure decreases, the maximum sloshing height of the fluid increases. Through regression analysis of the fluid height to structure width ratio (h/B) and the initial fluid height to maximum sloshing height ratio (h\({}^{\prime}\)/h), it was confirmed that there is a relationship between Equation (2) and that the correlation coefficient R\({}^{2}\) was 0.811. \[\frac{h^{\prime}}{h}=-0.376\left(\frac{h}{B}\right)+1.568 \tag{2}\]  
where \(B\) is the width of the fluid storage structure, \(h\) is the initial fluid height, and \(h^{\prime}\) is maximum sloshing height. Table 7 shows the relationship between h/B and the ratio of the initial fluid height and the minimum sloshing height (h\({}^{\prime}\)/h). It can be seen that the smaller the h/B, that is, the lower the ratio of the fluid height and the width of the fluid storage structure, the lower the minimum sloshing height of the fluid. Through regression analysis of the fluid height to structure width ratio (h/B) and the initial \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**h/B** & **0.4** & **0.5** & **0.6** & **0.7** & **0.8** \\ \hline Time (s) & 7.300 & 6.790 & 8.050 & 12.930 & 12.910 \\ \hline Min. (mm) & 156.0 & 206.0 & 240.0 & 287.0 & 338.0 \\ \hline Max. (mm) & 287.0 & 338.0 & 398.0 & 453.0 & 500.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum and minimum sloshing height according to h/B. Figure 10: Comparison of fluid surface shape from ratio of initial fluid height to structure width. fluid height to maximum sloshing height ratio (h\({}^{\prime\prime}\)/h), it was confirmed that there was a relationship between Equation (3) and the correlation coefficient R\({}^{2}\) of 0.848. \[\frac{h^{\prime}}{h}=0.126\left(\frac{h}{B}\right)+0.738 \tag{3}\]  
In this study, the shape of the fluid surface during a seismic load was assumed to be a straight line (the most simplified form) and can be represented as Equation (4).