## 4 Base-Isolated Liquid Storage Tank
### Numerical Modeling and Selected Records
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SAC Reference** & **Record** &
\begin{tabular}{c} **Moment** \\ **Magnitude** \\ \end{tabular} & **Distance (km)** & **PGA (g)** & **PGV (m/s)** \\ \hline NF01 & Tabas, 1978 & 7.4 & 1.2 & 0.90 & 1.13 \\ NF03 & Loma Prieta, 1989, Los Gatos & 7 & 3.5 & 0.72 & 1.36 \\ NF05 & Loma Prieta, 1989, Lex. Dam & 7 & 6.3 & 0.69 & 1.54 \\ NF07 & C. Mendonco, 1992, Petrolia & 7.1 & 8.5 & 0.64 & 1.41 \\ NF09 & Erzincan, 1992 & 6.7 & 2 & 0.43 & 0.85 \\ NF11 & Landers, 1992 & 7.3 & 1.1 & 0.71 & 0.95 \\ NF13 & Northridge, 1994, Rinaldi & 6.7 & 7.5 & 0.89 & 1.38 \\ NF15 & Northridge, 1994, Olive View & 6.7 & 6.4 & 0.73 & 1.01 \\ NF17 & Kobe, 1995 & 6.9 & 3.4 & 1.09 & 1.68 \\ NF19 & Kobe, 1995, Takatori & 6.9 & 4.3 & 0.79 & 1.70 \\ NF21 & Elysian Park 1 & 7.1 & 17.5 & 0.86 & 1.01 \\ NF23 & Elysian Park 2 & 7.1 & 10.7 & 1.80 & 3.16 \\ NF25 & Elysian Park 3 & 7.1 & 11.2 & 1.01 & 1.93 \\ NF27 & Elysian Park 4 & 7.1 & 13.2 & 0.92 & 2.40 \\ NF29 & Elysian Park 5 & 7.1 & 13.7 & 1.16 & 3.11 \\ NF31 & Palos Verdes 1 & 7.1 & 1.5 & 0.97 & 2.71 \\ NF33 & Palos Verdes 2 & 7.1 & 1.5 & 0.97 & 2.64 \\ NF35 & Palos Verdes 3 & 7.1 & 1.5 & 0.87 & 2.15 \\ NF37 & Palos Verdes 4 & 7.1 & 1.5 & 0.79 & 1.71 \\ NF39 & Palos Verdes 5 & 7.1 & 1.5 & 0.92 & 2.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected near-fault excitations. Figure 4: Predominant periods of the selected accelerograms compared to liquid content component periods (Reprinted from Computers and Structures, Volume 243, [PERSON] and [PERSON], Optimizing the seismic response of base-isolated liquid storage tanks using swarm intelligence algorithms, Pages No. 106407, Copyright (2022), with permission from Elsevier). Fast Non-linear Analysis (FNA) is adopted for the dynamic analyses, as it is suitable for structural systems in which the non-linear behavior is observed at the isolation system, while the superstructure response remains elastic [39]. Lastly, the global damping of the structural system is 5% for the ultimate limit state [31], while for the impulsive liquid component, it is 2% [44]. Regarding the SFPB isolators, the \"Friction isolator\" non-linear link element available in SAP2000 is used. This is a biaxial isolator, in which the two shear displacements as well as the friction parameters constitute a coupled system. A distinctive property of this link element is its post-slip stiffness along the horizontal directions due to the radius of curvature of the sliding surface. Moreover, it exhibits a gap behavior along the axial direction, while linear-effective stiffness is used for the three moment deformations. In addition, there is a proportional relationship between the compressive axial force and both friction and pendulum forces [39]. Accordingly, the following parameters need to be defined in the \"Friction isolator\" link element in SAP2000 for each SFPB isolator: effective stiffness and damping, non-linear stiffness, friction coefficient (slow/fast), rate parameter and the radius of curvature. The \"Triple-pendulum isolator\" element is suitable for the accurate representation of TFPB [39]. It is modeled as a biaxial SFPB isolator, consisting of four concave sliding surfaces, i.e., two outer and two inner surfaces. The motion of the two inner surfaces can be considered as coupled due to kinematic conditions; this is represented as a series of three \"Friction isolators\". The shear force-displacement curve can be adjusted by choosing different friction coefficients and radii of curvature. For this reason, different responses can be provided for various excitation levels, which are suitable when implementing a performance-based design (PBD) approach [12].