# Seismic Response Effect on Base-Isolated Rigid Structures by Mass Eccentricity in Nuclear Plants
## 4 Simulation Analysis for the Shaking Table Test  
To investigate the effects of the mass eccentricity of the superstructure on the laminated elastomeric bearing (LRB), several cubic steel blocks easy to reform by assembly were fabricated. For the efficiency of the tests, the superstructure was designed for three different configurations: (1) non-eccentric (Non-Ecc, or Con), (2) eccentricity of 12.5% (Ecc1), and (3) Eccentricity of 25% (Ecc2). These configurations were designed to facilitate model changes for on-site reassembly, as shown in Figure 12. The total mass of each model was set to 4 tons, considering support by four 1-ton capacity laminated elastomeric bearings. The actual eccentricities for each model can be calculated as shown in Table 4. Prior to conducting the three-axis shake table tests for these models, seismic response analyses were carried out to simulate the tests.  
Figure 11: 2-D mass eccentricity effect on horizontal max. displacement. (**a**) Effect in the X direction; (**b**) Effect in the Y direction.  
To predict the three-axis shaking table test results, FEM models were created for each test specimen, and seismic analyses were conducted. The same seismic input data from Figure 5 were used as the input for ground motion. To perform response spectrum analysis of the FEM models, the maximum acceleration responses at four corner locations where accelerometers were installed (A2 to A5) were reviewed.  
Tables 5 and 6 show a comparison of the results for maximum acceleration and displacement responses between sensitivity analysis (SA) and FEM simulation analyses for the test, respectively.  
In this comparison, the maximum seismic response differences between the sensitivity analysis and simulation analysis, especially for the mass eccentricities of the base-isolated upper structure, were 0% in the non-eccentric condition, 12.5%, and 25%, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mass Eccentricity**} & \multirow{2}{*}{**Base-Fixed**} & \multicolumn{2}{c}{**Base-Isolated**} \\ \cline{3-4}  & & **Sensitivity Anal.** & **Simulation Anal.** \\ \hline Non-Ecc. (0\%) & 13 cm & 88 & 88 \\ Ec1 (12.5\%) & 13 cm & 55 & 67 \\ Ec2 (25\%) & 12 cm & 82 & 87 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Max. displacement comparison by mass eccentricity in analyses for base conditions.  
Figure 12: Model shapes for simulation analysis for the shaking table test. (**a**) Non-eccentric mass; (**b**) Eccentric mass 1 (Eccl); (**c**) Eccentric mass 2 (Ecc2); (**d**) FEM model for non-eccentric mass for example.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Model Name**} & \multicolumn{1}{c}{**Location [mm]**} & \multicolumn{1}{c}{**Eccentricity [\%]**} \\ \hline Non-Ecc. (Con) & 0 & 0 \\ Ec1 & 77 & 12.5 \\ Ec2 & 154 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mass center location and eccentricity for each model.  
As shown in the tables, the maximum acceleration responses of the three different eccentricity models from both analyses show mostly good matches without remarkable differences. However, the maximum displacements were larger in the FEM simulation analysis compared with the sensitivity analysis. This discrepancy is attributed to the rocking behavior induced by the vertical mass eccentricity of the simulation model, which is not considered in sensitivity analysis. In summary, while the acceleration responses were relatively consistent, the maximum displacements were influenced by eccentricity-induced rocking behavior in the simulation analysis compared with the sensitivity analysis.