## 2 Shaking Table Test of LNG Storage Tank Model
### Design of Lead-Core Rubber Bearing  
Using MATLAB software to analyze the frequency spectrum of the seismic wave after compression time, the predominant periods of the El Centro wave, Taft wave, Wolong wave and Artificial wave were 0.125 s, 0.134 s, 0.078 s and 0.067 s, respectively. In order to avoid the resonance phenomenon of the test tank, the isolation period should be far from the seismic predominant period. A lead-core rubber bearing is arranged between the test tank and the pile foundation, and the parameters of them are shown in Table 2.  
The calculation formula of the isolation period is as follows [27]:  
\[T_{iso}=2\pi\sqrt{\frac{M_{i}+M_{s}}{K_{iso}}} \tag{1}\]  
Total stiffness of horizontal isolation layer \(K_{iso}\) is:  
\[K_{iso}=nk_{iso} \tag{2}\]  
\[M_{i}=\frac{\tanh[0.866(D/h_{w})]}{0.866(D/h_{w})}M_{l} \tag{3}\]  
where: \(T_{iso}\) is the isolation period; \(K_{iso}\) is the horizontal stiffness of the isolation layer; \(M_{i}\) is the mass of the liquid that moves with the tank; \(M_{s}\) is the mass of the tank; \(k_{iso}\) is the equivalent stiffness of a single lead-core rubber bearing; \(D\) is the diameter of the inner tank; \(h_{w}\) is the height liquid storage, its value is 0.75 m; and \(M_{l}\) is the total mass of the liquid.  
Taking the equivalent stiffness of a single isolation bearing in Table 2 into Equation (2), and then from Equation (1), the isolation period can be obtained as 0.967 s, which is distant from the predominant period of the input seismic wave. This preliminarily indicates that it is reasonable to choose lead rubber bearing.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Condition Number** & **Test Condition** & **Excitation** & **Peak** \\  & & **Direction** & **Acceleration (g)** \\ \hline
1 & White noise & X, Y, Z & 0.05 \\
2–5 & Wolong, Artificial & X, Z; X, Y, Z & 0.1 \\
6 & White noise & X, Y, Z & 0.05 \\
7–10 & Wolong, Artificial & X, Z; X, Y, Z & 0.25 \\
11 & White noise & X, Y, Z & 0.05 \\
12–21 & El Centro, Taft, Wolong, Artificial & X; X, Z; X, Y, Z & 0.50 \\
22 & White noise & X, Y, Z & 0.05 \\
23–34 & El Centro, Taft, Wolong, Artificial & X; X, Z, X, Y, Z & 0.75 \\
35 & White noise & X, Y, Z & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Arrangement of test conditions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Parameter** & **Item** & **Parameter** \\ \hline type & LRB300 & height & 150 mm \\ effective outer diameter & 300 mm & shear modulus & 0.392 MPa \\ outer diameter of bearing & 320 mm & rubber standard elastic modulus & 1.5 MPa \\ lead diameter & 60 mm & second shape factor & 5.77 \\ side length of sealing plate & 400 mm & effective area & 70,685.8 mm\({}^{2}\) \\ sealing plate thickness & 11 mm & bearing area & 160,000 mm\({}^{2}\) \\ rubber layers & 26 layer & hardness correction coefficient & 0.9 \\ layers of sheet steel & 25 layer & vertical stiffness & 887 kN/mm \\ thickness of rubber layer & 3 mm & equivalent horizontal stiffness & 821 kN/m \\ thickness of steel plate & 3 mm & yield force & 22.6 kN \\ total thickness of rubber & 78 mm & post yield stiffness & 469 kN/m \\ total thickness of steel plate & 50 mm & equivalent damping ratio & 30.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lead-core rubber bearing parameters.