# Seismic Analysis of a Large LNG Tank Considering Different Site Conditions
## 5 Summary and Conclusions  
In this study, the modal analysis of large LNG tanks is verified by the basic natural frequency of solid-liquid coupling and the basic natural vibration period of liquid sloshing. A 160,000 m\({}^{3}\) LNG prestressed storage tank subjected to 12 earthquake waves under 4 site classes is analyzed using stress distributions on the outer tank and inner tank as well as tip displacement and base shear. Because the sheer size of the LNG tank eliminates any possibility for direct experiments on a physical prototype, SPH-FEM simulation provides a feasible and efficient method to predict its seismic response. The main conclusions drawn from the numerical simulations can be summarized as follows: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site Class** & **25\% Liquid Level** & **50\% Liquid Level** & **75\% Liquid Level** & **100\% Liquid Level** \\ \hline I & 3.52 & 4.62 & 4.97 & 5.03 \\ II & 4.92 & 5.4 & 6.83 & 7.72 \\ III & 5.36 & 6.8 & 7.97 & 9.41 \\ IV & 6.11 & 7.21 & 7.17 & 8.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Average base shear within each site class for a tank containing different liquid levels. (unit: \(10^{4}\) KN). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site Class** & **25\% Liquid Level** & **50\% Liquid Level** & **75\% Liquid Level** & **100\% Liquid Level** \\ \hline I & 0.91 & 1.01 & 1.25 & 1.31 \\ II & 2.42 & 2.51 & 2.98 & 3.46 \\ III & 2.45 & 2.48 & 3.11 & 3.69 \\ IV & 3.02 & 3.42 & 3.88 & 4.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Average tip displacement under each site condition for an outer tank subjected to different liquid levels (unit: mm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site Class** & **Earthquakes** & **25\% Liquid Level** & **50\% Liquid Level** & **75\% Liquid Level** & **100\% Liquid Level** \\ \hline I & GM1:Tangshan Aftershock & 2.75 & 4.04 & 3.83 & 4.31 \\  & GM2:Imperial Valley & 4.59 & 6.36 & 6.65 & 7.05 \\  & GM3:San Fernando & 3.21 & 3.45 & 3.44 & 3.74 \\ \hline II & GM4:Imperial Valley-01 & 5.33 & 5.49 & 6.22 & 6.62 \\  & GM5:Northridge-01 & 4.14 & 4.93 & 6.65 & 8.55 \\  & GM6:Kern County, California & 5.28 & 5.78 & 7.61 & 7.99 \\ \hline III & GM7:Kobe & 4.76 & 6.44 & 7.17 & 8.62 \\  & GM8:Hollister & 5.20 & 7.22 & 8.14 & 8.44 \\  & GM9:Landers & 6.12 & 6.74 & 8.59 & 11.16 \\ \hline IV & GM10:Tangshan Aftershock & 6.06 & 7.87 & 6.77 & 8.62 \\  & GM11:Cape Mendocino & 6.22 & 7.06 & 6.90 & 7.58 \\  & GM12:Loma Piieta & 6.05 & 6.70 & 7.84 & 9.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Maximum base shear of the tank of different liquid volume under different site conditions (unit: \(10^{4}\) KN). 1. Stress on the outer tank peaks at 52.3 MPa in Class I and diminishes from Class II, Class III, to Class IV, although the numbers do not vary significantly. In addition, stress on the outer tank is minimally affected by the liquid level. 2. The maximum stress of the inner tank is above 500 MPa at 100% liquid levels in all four site classes and creates significant safety hazards. The design optimization and the establishment of an early warning system are imperative to the control of high liquid levels. 3. Under the liquid level 75% and 100%, site class III exhibits the largest base shear, followed by Class IV, Class II, and Class I. Base shear values across four site classes only vary slightly for a liquid level of 25% and 50%, but they vary significantly for a liquid level of 75% and 100%. 4. Under the same liquid level, Class IV exhibits the greatest tip displacement, followed by site Class III, site Class II, and site Class I. This phenomenon indicates that less than ideal site conditions lead to greater tip displacement on the LNG storage tank. In addition, the tip displacements at liquid level of 25% and 50% under site Class IV are on a similar level as the tip displacement at liquid level of 75% and 100% under site Class II. 5.