## 6 Parameter Analysis
### The Effect of Soil  
The first five convective frequencies, horizontal impulsive frequency and rotational impulsive frequency are calculated for \(V_{s}\) in Table 4. The parameters are selected from the utilized parameters in Figures 11-14 which depict the effects of baffles to further analyze the effects of soil for the same soil-tank coupling system: \(M=2\), \(\beta_{1}=0.3\), \(\beta_{2}=0.6\), \(\beta_{3}=1.0\), \(\gamma=0.8\) and \(R_{2}=10\) m. It can be observed that the shear wave velocity of soil \(V_{s}\) has little effect on convective frequencies. The greater the shear wave velocity the soil is, the closer the results under flexible soil are to those under rigid soil, implying that the convective characteristics of the sloshing in tanks resting on flexible soil are similar to those on rigid  
Figure 14: The maximum of the hydrodynamic response for the baffle inner radius \(\gamma\): (**a**) the shear force \(F_{\text{max}}\); (**b**) the overturning moment \(M_{\text{max}}\).  
soil. Nevertheless, the impulsive frequencies remain almost the linearized growth with increase in \(V_{\rm s}\).  
For the NF and FF seismic excitation, the ratios \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\) are investigated in Figures 15-17 with different vs. for \(M=2\) and \(R_{2}=10\) m. It is observed that the amplitudes of the seismic responses do not vary monotonically with the increase in \(V_{\rm s}\). The values of \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\) at lower shear wave velocities (representative of more flexible soils) are relatively larger than those at greater shear wave velocities (stiffer soils), showing that soil-tank interaction magnifies the tank response. For Kobe wave excitation, the maximum values of \(\alpha_{1}\) and \(\alpha_{2}\) occur at \(V_{\rm s}\) equal to 320 m/s and \(\beta_{3}=3.0\); for Coyote Lake wave excitation, the maximum values of \(\alpha_{1}\) and \(\alpha_{2}\) appear at \(V_{\rm s}\) equal to 400 m/s and \(\beta_{3}=3.0\). The phenomenon that the peak values pertaining to the shear wave velocity of the soil deviate under the two excitations may be attributed to the fact that the predominant frequencies of NF and FF seismic motions are different. Then, by further increasing the shear wave velocity of the soil, the values of \(\alpha_{1}\) and \(\alpha_{2}\) for \(\beta_{3}=3.0\) both decline typically. The peak values of \(\alpha_{1}\) and \(\alpha_{2}\) both increase as the fluid height increases from \(\beta_{3}=2.0\) to \(\beta_{3}=3.0\). The magnification is a factor of both the shear wave velocity of soils (greater magnification for flexible soils) and the geometry characteristic of tanks (greater magnification for tall tanks). With an increase in soil stiffness, the values of \(\alpha_{1}\) and \(\alpha_{2}\) approach 1.0, indicating that the responses with respect to soils vanish.  
In Figure 18, the impulsive displacement characteristically declines with the increase in \(V_{\rm s}\). The greater the fluid height is, the greater the horizontal impulsive displacement becomes typically if the shear velocity of the soil is held constant. It can be also seen from Figures 15-18 that with increase in the soil stiffness, \(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\) approach 1.0 and the impulsive displacement reaches zero gradually, indicating that corresponding seismic responses with respect to soil vanish.