## 5 Interpretation and Discussion  
### Frequency Response of the Model  
To evaluate the effect of the interchange station on soil response, a transfer function (TF) was used to obtain the Fourier amplitude ratio of the acceleration response at the ground surface as a function of the frequency of the input motion at the base. For a free field homogeneous damped soil on a rigid base, the analytical formulation of the transfer function can be expressed as [36]  
\[|\text{TF}(\omega)|=1/\sqrt{\cos^{2}\!\left(\frac{\omega H}{V_{s}}\right)+\left[ \xi\!\left(\frac{\omega H}{V_{s}}\right)\right]^{2}} \tag{3}\]  
where \(\omega\) is the frequency, \(\xi\) is the damping ratio and \(H\) and \(V_{s}\) are the height and shear wave velocity of the soil, respectively. The analytical solution is based on the assumption of the viscoelastic behavior of the soil. Thus, low-intensity white noise (PGA = 0.02 g) was adopted in order to minimize the effect of nonlinear degradation of the shear modulus of the model soil. Figure 13a compares the transfer function of the model ground recorded in the cases of WN-0 and WN-3, along with the analytical solution at the SA-ff array. Similar comparisons are shown in Figure 13b for the SA-4 array out of the cross interchange station.  
The good comparison of the experimental TF in the two white noise cases, WN-0 and WN-1, confirmed the consistency of the dynamic characteristics of the model ground throughout the tests, indicating the repeatability of the test results. The fundamental frequencies (\(f_{1}\)) of the ground at both arrays were observed to be 7.4 Hz. The analytical fitting was then calculated through Equation (3), associated with the target parameters of the fundamental frequencies \(f_{1}=7.4\) Hz and the damping ratio \(\xi=7\%\). As shown in Figure 13a, the comparison between the analytical TF and experimental TF recorded  
Figure 12: Comparison of dynamic strain recorded on columns in the two-story part of the interchange station (_section 3_ and _section 5_) and the single station (_section iii_) at **(a)** the top end of the upper column, (**b**) the top end of the lower column and (**c**) the bottom end of the lower column during the sinusoidal excitation with a dominant frequency of 10 Hz.  
from the SA-ff array was generally good, in terms of the first three harmonic frequencies (denoted in order as \(f_{1}\), \(f_{2}\) and \(f_{3}\), respectively). It confirmed that the soil response recorded at the SA-ff array (out of the single station) was close to the analytical assumption as a free field condition. The slight discrepancy around the frequency of 10 Hz could apply to the influence of the single station structure [20]. In the SA-4 array, which was \(1.1W\) from the interchange station structure (Figure 13b), the fundamental frequency followed the far field soil. However, for the second and third fundamental frequencies (\(f_{2}=16.9\) Hz and \(f_{3}=24.7\) Hz), the TF of the SA-4 array differed from the analytical solution, which indicated the influence of the underground structures on the high-order frequency of the free field response. It should be noted that both the SA-ff and SA-4 arrays were \(1.1W\) away from the two-story structure. However, SA-4 was further affected by the conjunction and the three-story section, which led to spatial effects of the interchange station on the soil.