## 4 Test Results and Discussion
### Distribution of Acceleration Magnification Factors
#### 4.2.2 Distribution of AMFs of the Soil-Caisson System Model Test  
Upon examining the test results of the soil-caisson system presented in Figure 6, it is evident that the AMFs still show a \"C\"-shaped distribution pattern under Chichi and Kobe waves. However, the AMFs at the surface measurement point within the soil-caisson system are generally smaller than those observed in the free-field system, indicating that the presence of the caisson foundation has an attenuating effect on the peak acceleration at the surface of the soil. Furthermore, the results in Figure 6 illustrate that the AMFs of the soil-caisson system subjected to the Chichi wave are typically greater than those under the Kobe wave. This is because the Chichi wave is richer in low-frequency content, as illustrated in Figure 5, and the soft soil, such as sand, amplifies low-frequency waves more effectively.  
In addition, it has been noted that the soil-caisson system subjected to the Chichi wave exhibits larger AMFs at the ground surface with smaller table input acceleration, indicating a more significant amplification effect of the system on the input excitation in this scenario. The mechanism behind this phenomenon is consistent with that observed in the free-field system tests, where an increase in table input acceleration leads to a decrease in AMFs at the ground surface. However, under the Kobe wave, the amplification effect of the system to the input excitations initially increases and then subsequently decreases with the increase in the table input acceleration. This behavior occurs because the soil remains essentially elastic in the Kobe 0.1 g-Kobe 0.5 g cases, as reflected in the displacement amplitude and characteristic frequency data in Table 3, where the energy dissipation of the soil undergoes minimal changes, resulting in an increase in the AMFs at the surface with the increase in the input energy to the system. In contrast, under the Kobe 0.75 g-Kobe 1.0 g cases, the soil-caisson system exhibits significant plastic behavior, as evidenced by the characteristic frequencies of the motion response of the caisson foundation and substantial changes in displacement amplitudes, illustrated in Table 3. Consequently, as the table input  
\begin{table}
\begin{tabular}{c c c c} \hline
**Loading Case** & **Characteristic Frequency (Hz)** & **Characteristic Damping Ratio (\%)** & **Displacement Amplitude (mm)** \\ \hline WN1 & 6.33 & 3.06 & 3.85 \\ Chichi 0.1 g & 6.52 & 8.33 & 0.87 \\ Chichi 0.25 g & 6.29 & 9.1 & 2.32 \\ Chichi 0.5 g & 5.50 & 11.1 & 5.2 \\ WN2 & 6.35 & 2.04 & 3.33 \\ Kobe 0.1 g & 6.58 & 8.33 & 0.43 \\ Kobe 0.25 g & 6.74 & 8.33 & 0.58 \\ Kobe 0.5 g & 6.50 & 9.09 & 0.63 \\ WN3 & 6.37 & 2.04 & 3.82 \\ \hline \end{tabular}
\end{table}
Table 4: Characteristic parameters of the free-field ground motion under different loading cases.  
acceleration increases, the dynamic shear modulus of the soil decreases, the damping ratio increases, and the energy dissipated by the soil increases, leading to a reduction in AMFs at the surface.  
In this section, a comparative analysis of the distributions of AMFs in the free-field system and the soil-caisson system is presented. The findings demonstrate that the SCDI effects exert a considerable influence on the peak acceleration within the caisson embedment depth and significantly attenuate the peak value of the surface acceleration response.