# Understanding the Seismic Resilience of Metallic Cylindrical Tanks Through Parametric Analysis
## 5 Numerical Results Considering a Set of Ten Scaled Record Accelerograms  
To better understand how pressure trends may vary, a series of explicit dynamic nonlinear analyses were performed using a set of different accelerograms as input ground shaking motions. The dynamic response of the case study tanks was assessed by considering a set of ten scaled recorded accelerograms. These records were selected from the PEER NGA database, with magnitudes ranging from 6.2 to 7.6, ensuring compatibility with the EC8 design response spectrum. The reference response spectrum was defined with a peak ground acceleration (PGA) of 0.4 g and a soil category C, according to the European classification. Figure 11 shows the response spectra for the ten accelerograms used in the dynamic response analysis of the case study tanks, and it is complemented by Table 4, which provides details of the seismic input for nonlinear dynamic simulations. More specifically, PEER ID, event, component, moment magnitude (\(M_{W}\)), closest distance from recording site to fault area (\(D_{r}\)), duration (\(t_{tot}\)), and shear wave velocity over the first 30 m (\(V_{s}\)) are shown in Table 4. The matching between the mean response spectrum of the ten unscaled records and the EC8 design spectrum was verified for periods between 0.15 s and 4 s. This range is quite large because sloshing modes and tank impulsive modes have significantly different fundamental periods [45,46]. For the analysis, three case studies were selected to represent squat and slender tanks, specifically with \(H/R\) = 0.75, 1.5, and 4 slenderness ratios. Figure 12a shows the pressure distributions for the squat tank (\(H/R\) = 0.75 and \(R/t\) = 2000) obtained from the FE simulations. A comparison between the results using shaking table excitations and those using the average of the accelerograms indicates that the pressure distributions for the average earthquakes overestimated the trends of pressures observed from the shaking table excitations. The discrepancies were small and are primarily observed at the bottom and upper parts of the tank, which were influenced by the severity of the selected accelerograms, especially for the \"LC9\" earthquake. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Eq. ID** & **PEER ID** & **Event** & **Component** & \(\mathbf{M_{W}}\) [-] & \(\mathbf{D_{r}}\) [km] & \(\mathbf{t_{tot}}\) [s] & \(\mathbf{V_{s}}\) [m/s] \\ \hline
01 & 1233 & Chi-Chi, Taiwan & E & 7.62 & 36 & 90 & 194 \\ \hline
02 & 1153 & Kocaeli & 090 & 7.51 & 127 & 102 & 275 \\ \hline
03 & 851 & Landers & 000 & 7.28 & 157 & 70 & 272 \\ \hline
04 & 1810 & Hector & 090 & 7.13 & 92 & 60 & 345 \\ \hline
05 & 1629 & St Elias, Alaska & 279 & 7.54 & 80 & 83 & 275 \\ \hline
06 & 777 & Loma Prieta & 090 & 6.93 & 28 & 39 & 199 \\ \hline
07 & 1043 & Northridge-01 & 090 & 6.69 & 52 & 48 & 309 \\ \hline
08 & 728 & Superstition Hills-02 & 180 & 6.54 & 13 & 40 & 194 \\ \hline
09 & 172 & Imperial Valley-06 & 140 & 6.53 & 22 & 39 & 237 \\ \hline
10 & 2615 & Chi-Chi, Taiwan-03 & N & 6.20 & 40 & 107 & 273 \\ \hline \end{tabular}
\end{table} 
Table 4: Characteristics of ground motion records for nonlinear dynamic analyses. The same accelerograms were applied to the \(H/R=1.5\) and \(R/t=400\) case study tank. Figure 12b shows the comparison of the total pressure profiles obtained from the shaking  
Figure 11: Comparison of the design acceleration response spectra with the spectra of ten real records selected and uniformly scaled to be spectrum compatible. Figure 12: Horizontal pressure curves for \(H/R=0.75\) and \(R/t=2000\) (**a**), \(H/R=1.5\) and \(R/t=400\) (**b**), and \(H/R=4\) and \(R/t=400\) (**c**) tank considering a set of ten scaled recorded accelerograms and seismic excitations of shaking table. table excitations and the average of the ten accelerograms. Again, the pressures from the average earthquakes overestimated the trend of pressures obtained from the shaking table with the impact of the sloshing wave being mostly negligible.