## 4 Test Results and Discussion
### The Effect of Soil-Caisson Kinematic Interaction
#### 4.3.1 Effect on the Horizontal Acceleration Motion  
Firstly, the influence of the kinematic interaction on the horizontal acceleration motion of the caisson foundation is investigated by comparing the acceleration response of the free-field surface measurement point with that of the corresponding elevation measurement point on the caisson. The results are presented in Figure 8.  
As illustrated in Figure 8a,b, in the case of Chichi 0.1 g, the horizontal acceleration of the caisson foundation is virtually identical to that of the free-field ground motion in terms of waveform and amplitude, indicating that the influence of the kinematic interaction is negligible. However, as the acceleration peak increases, although the horizontal acceleration waveform remains similar between the caisson foundation motion and free-field ground motion, there is a noteworthy reduction in the amplitude of the horizontal acceleration of the caisson foundation compared to that of the free-field ground motion. Specifically, the horizontal acceleration amplitude of the caisson foundation is reduced by 2.38%, 34.57%, and 26.24% for the Chichi 0.1 g, Chichi 0.25 g, and Chichi 0.5 g cases, respectively, compared to the amplitude of the free-field ground motion in the corresponding cases. To better understand the impact of the kinematic interaction on the horizontal acceleration of the caisson foundation motion, a transfer function (TF) between the acceleration response of the free-field ground motion (FFM) and the caisson foundation motion (CFM) at the same elevation is computed. In this analysis, the FFM serves as the input signal, while the CFM serves as the output signal. In practice, the transmissibility function [31; 32] Equation (3) and the coherence function [9] Equation (4) are employed to estimate the TF and evaluate the influence of noise on the signals, respectively. The coherence function close to unity indicates minimal noise effect and a strong correlation between the two signals. Reliable transfer function estimates are considered at frequencies of \(\gamma^{2}\geq 0.8\)[9; 32]. \[\left|H_{gf}(\omega)\right|=\sqrt{\frac{S_{gg}}{S_{ff}}} \tag{3}\]\[\gamma^{2}(\omega)=\frac{\left|S_{gf}(\omega)\right|^{2}}{S_{gg}(\omega)S_{ff}( \omega)} \tag{4}\]  
where \(S_{gg}\) and \(S_{ff}\) are the power spectral density functions of the acceleration response of the CFM (\(A_{gg}\)) and the acceleration response of the FFM (\(A_{ff}\)) at the ground surface, respectively, and \(S_{gf}\) is the cross-power spectral density function. Results of the transfer function \(\left|H_{gf}(\omega)\right|\) between \(A_{gg}\) and \(A_{ff}\) under Chichi and Kobe waves are presented in Figure 8c,d, where the results of \(\left|H_{gf}(\omega)\right|\) with a high coherency are also demonstrated with dots at the same time. From the results in Figure 8, it can be seen that: (1) The influence of noise on the signals in the tests is negligible; (2) When the frequency is less than 15 Hz, the transfer function approaches unity. As frequency increases, the transfer function shows a decreasing trend, indicating that the caisson foundation filters high-frequency components of the incident seismic waves; (3) The first three orders of natural frequencies of the soil-cainsson system are 6.4 Hz, 19 Hz, and 29.5 Hz, respectively, and close to the natural frequency of the system, the transfer function demonstrates distinct fluctuations, attributed to inertial interaction [29; 31; 32]. (4) The transfer function exhibits clear frequency dependence, with the dominant frequency and peak acceleration of the table input wave significantly influencing the deviation of \(A_{gg}\) and \(A_{ff}\).