## 4 Results and Discussion
### Sloshing Response vs. Spectral Response  
As mentioned above, the tank was subjected to seven near-fault earthquakes under two different conditions. The major horizontal earthquake component acted parallel to the longer wall under the first condition (S1), and the other two components acted in relation to the major component. The ratio of the length for which the major earthquake component and the minor component acted is the ratio of the tank's longer wall to the shorter wall, Rdir_S1, which was equal to 1.29. Under the second condition (S2), the major earthquake component acted parallel to the shorter walls, and the second (minor) horizontal component acted parallel to the longer walls. In this condition, Rdir_S2 was equal to 0.78. Figure 7 shows how these earthquake components acted on the tank in each condition.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Event** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** \\ \hline Chi-Chi-122 & 0.38 & 0.67 & 1.00 & 1.00 & 0.38 \\ Chi-Chi-129 & 0.25 & 0.17 & 0.24 & 0.15 & 0.24 \\ IMV-\#6 & 0.75 & 1.00 & 0.92 & 0.34 & 0.31 \\ IMV-\#7 & 0.53 & 0.82 & 0.96 & 0.37 & 0.47 \\ IMV-EDA & 0.23 & 0.24 & 0.52 & 0.39 & 0.62 \\ Kocai & 1.00 & 0.49 & 0.78 & 0.61 & 1.00 \\ Northridge & 0.19 & 0.40 & 0.59 & 0.36 & 0.28 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Normalized spectral accelerations at the tank’s sloshing periods of vibration along the shorter wall (g).  
Figure 7: The two conditions for applying the seismic loads to the tank.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Event** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** \\ \hline Chi-Chi-122 & 1.00 & 0.45 & 1.00 & 0.80 & 1.00 \\ Chi-Chi-129 & 0.15 & 0.16 & 0.22 & 0.33 & 0.15 \\ IMV-\#6 & 0.50 & 1.00 & 0.58 & 0.96 & 0.34 \\ IMV-\#7 & 0.31 & 0.79 & 0.60 & 1.00 & 0.36 \\ IMV-EDA & 0.23 & 0.15 & 0.25 & 0.63 & 0.39 \\ Kocaeli & 0.46 & 0.71 & 0.49 & 0.80 & 0.60 \\ Northridge & 0.12 & 0.48 & 0.33 & 0.67 & 0.37 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Normalized spectral accelerations at the tank’s sloshing periods of vibration along the longer wall (g).  
In both conditions, the sloshing response was measured in the middle of the tank's shorter and longer walls and the corner, as depicted by points a, b, and c in Figure 7. Table 11 demonstrates the maximum sloshing response of the tank under the considered ground motions in the middle of the shorter wall (a) (under the first loading condition--S1) and the longer wall (b) (under the second loading condition--S2).  
The difference between this response at different locations under both loading conditions is shown in Figure 8.  
Under the considered records, the maximum sloshing response of the tank perpendicular to the major earthquake component was normalized and sorted according to the maximum response for each loading condition. Similarly, this normalization was performed on the value of the spectral accelerations at the first five sloshing periods of vibration (Tables 8 and 9). Table 12 shows the sorted normalized sloshing responses for the shorter and longer walls under the first and second loading conditions.