## 7 Results and Discussions  
### Effect of MetaFoundation  
To evaluate the influence of the proposed MetaFoundation in the time domain, the time transient analysis is performed under selected ground motions. The seismic responses of liquid storage tanks mounted on MF are compared with the corresponding responses in fixed base condition. The parameters of the MF are described in the previous section. Figure 8: Verification of the obtained responses subjected to the Friuli, A-TMZ270 earthquake. Figure 7: (**a**) Pseudo-acceleration and (**b**) response displacement spectra of considered earthquake ground motions. Figure 9 shows the time history of seismic responses of considered tanks under ABBAR--L, Manjil earthquake. The seismic responses are depicted for both squat and slender tanks in fixed base condition and mounted on MF, respectively. The performance index of seismic responses of the selected liquid storage tank tanks subjected to various ground motions is depicted in Figure 10. According to the obtained responses, two different trends were observed for the performance of the MF on the seismic responses of squat and slender tanks. First, in the squat tanks, it is observed that the displacement of the impulsive mass, overturning moment on top of the foundation, and base shear have been reduced in most cases due to the implementation of the MF. The mean performance index of the displacement of impulsive mass, overturning moment on the foundation, and base shear are 0.551, 0.551, and 0.551, illustrating that the MF reduces the input excitation. Therefore, the use of the MF in the squat tank is an effective solution to improve its dynamic behaviour. The best performance of the MF was observed when the system was subjected to G03000, Loma Prieta ground motion in which the PI of the displacement of the impulsive mass, overturning moment on the MF, and base shear equalled 0.091, 0.09, and 0.091, respectively. However, a performance index of more than one is seen in some cases. For example, a PI equal to 1.491, 1.480, and 1.476 for the displacement of impulsive mass, the overturning moment on the foundation and base shear was observed when the system was excited by HEC090, showing that the MF increases the responses compared to fixed base condition. This is attributed to the fact that the performance of MF highly depends on the frequency content of input earthquake ground motion as well as the stop band. According to Figure 11, it is seen that in some frequency ranges, the TR is magnified. This illustrates that the amplitude of the input wave will be intensified, and therefore, the responses of liquid storage tanks are increased compared to the fixed base condition. The reduction of the  
Figure 9: Time history of responses of squat and slender tank subjected to ABBAR—L, Manjil ground motion for w/o and w MF. overturning moment leads to a decrease in the axial demand in the tank wall, which is the main reason for the buckling of the tank wall. Hence, the more economical and reliable design of the tank is achievable by the use of MF. Figure 11: TR of the displacement above the MF. Figure 10: Performance index (PI) of various seismic responses of squat and slender tanks. Conversely, it is seen that the MF increases the vertical displacement of the free surface of the liquid. The mean performance index of the vertical free surface displacement is 1.5. Therefore, it is vital to consider a more freeboard to avoid the disrupting consequences corresponding to vertical displacement of the free surface. Second, with reference to Figure 10, one can conclude that the displacement of impulsive mass, overturning moment on the foundation, and base shear in the slender tank are magnified in most cases. The mean PI of the impulsive displacement, overturning moment, and base shear in the slender tank are 1.315, 1.315, and 1.35, respectively. Therefore, it can be concluded that the MF has an adverse effect on the seismic responses of the slender liquid storage tank.