## 4 Results and Discussion  
### Dynamic Properties of the Tank  
In the literature, several dynamic models have been proposed to simulate the dynamic behavior of liquid storage tanks. Procedures suggested by guidelines, such as [43; 73; 74; 75], utilize the spring-mass model, which assumes two different vibration modes (impulsive and convective), as proposed by [76]. The procedure suggested by [73] was used to calculate the first natural period of vibration of the convective mass (sloshing period). The natural sloshing periods of vibration for the longer and shorter tank walls were 6.17 s and 4.99 s,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \# & **Event** & **Station** & \(\mathbf{M_{w}}\) & \(\mathbf{R_{rup}}\) (km) & **PGA (g)** & **PGV (cm/s)** & **PGD (cm)** & \(\mathbf{T_{P}}\) \\ \hline
1 & Chi-Chi & TCU122 & 7.62 & 9.34 & 0.26 & 34.05 & 36.1 & - \\
2 & Chi-Chi & TCU129 & 7.62 & 1.83 & 1 & 59.6 & 50.07 & - \\
3 & Imperial Valley06 & El Centro Array \#6 & 6.53 & 1.35 & 0.44 & 109.8 & 65.83 & 3.77 \\
4 & Imperial Valley06 & El Centro Array \#7 & 6.53 & 0.56 & 0.46 & 109.3 & 44.72 & 4.38 \\
5 & Imperial Valley06 & El Centro Differential Array & 6.53 & 5.09 & 0.48 & 40.81 & 14.03 & 6.27 \\
6 & Kocaeli & Yarimca & 7.51 & 4.83 & 0.35 & 62.18 & 51 & 4.95 \\
7 & Northridge & Sylmar-Converter Sta East & 6.69 & 5.19 & 0.83 & 117.5 & 34.45 & 3.53 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The major horizontal components of the selected near-fault ground motions and their properties.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Major Horizontal**} & \multicolumn{2}{c}{**Minor Horizontal**} & \multicolumn{2}{c}{**Vertical Component**} \\ \cline{3-8}
**Event** & **Station** & \multicolumn{2}{c}{**Component**} & \multicolumn{2}{c}{**Component**} & \multicolumn{2}{c}{**Component**} & \multicolumn{2}{c}{**Vertical Component**} \\ \cline{3-8}  & & **PGA** & **PGV** & **PGA** & **PGV** & **PGA** & **PGV** \\ \hline Chi-Chi & TCU122 & 0.4 & 52 & 0.34 & 65 & 0.37 & 64 \\ Chi-Chi & TCU129 & 0.4 & 24 & 0.25 & 14 & 0.13 & 14 \\ Imperial Valley & El Centro Array \#6 & 0.4 & 100 & 0.37 & 59 & 1.5 & 52 \\ Imperial Valley & El Centro Array \#7 & 0.4 & 94 & 0.29 & 40 & 0.47 & 23 \\ Imperial Valley & El Centro Differential & & & & & & \\  & Array (EDA) & 0.4 & 34 & 0.29 & 60 & 0.59 & 17 \\ Kocaeli & Yarimca & 0.4 & 71 & 0.31 & 75 & 0.28 & 36 \\ Northridge & Sylmar-Converter Sta East & 0.4 & 57 & 0.24 & 36 & 0.18 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 5: PGA and PGV of the horizontal and vertical components of the selected earthquakes after being scaled.  
The free vibration analysis was carried out using the finite element package ANSYS to calculate the natural frequencies and mode shapes of tanks using the reduced method, which determines all frequencies and mode shapes within a limited range of frequencies. In this method, the eigenvalues and eigenvectors are derived using the HBI algorithm (Householder-bisection-inverse iteration) for the calculation of the mass and stiffness matrices for the system. The method uses a reduced number of degrees of freedom, called the master degree of freedom. The system analysis was performed with a frequency range of 0-100 Hz. The lower frequencies in the Z direction provide the sloshing modes, and the higher frequencies in the X and Y directions provide the modes of the tank walls.  
The contours, shown in Figure 5, demonstrate the displacement response of the water under free vibration analysis, where the red and blue colors show the maximum and minimum displacements, respectively. The first three sloshing frequencies of the water are also shown in the upper left of Figure 5.