## 5 Conclusions  
In this paper, the influence of SCDI on the motion of the caisson foundation is studied. To this end, a series of 1 g shaking table model tests were conducted on free-field and soil-caisson systems. The test results demonstrate the significant influence of SCDI on the characteristic parameters of the motion of the caisson foundation, the distribution of AMFs along the vertical direction in different test systems, the horizontal acceleration, and the rotational component of the caisson foundation. The main conclusions are summarized as follows:  
(1) The larger the peak acceleration of the shaking table input waves, the greater the influence of SCDI on the motion of the caisson foundation, resulting in a significant decrease in the characteristic frequency and an apparent increase in the characteristic damping ratio of the motion of the caisson foundation.  
(2) The results of the model tests conducted on free-field and soil-caisson systems indicate that the AMFs along the vertical direction exhibit a \"C\"-shaped distribution. Additionally, the SCDI effects exert a considerable influence on the peak acceleration within the caisson embedment depth, significantly attenuating the acceleration response at the ground surface, especially in high peak acceleration cases.  
(3) The horizontal and rotational transfer functions are used to quantify the relationship between the motion of the caisson foundation and the free-field ground motion, while considering the SCDI effects. At lower frequencies, the horizontal transfer function is nearly equal to unity, and although the inertial interaction causes significant fluctuations around the natural frequencies of the system, the horizontal transfer function shows a decreasing trend with increasing frequency, because the effective size of the caisson foundation relative to the seismic wavelength increases as frequency increases, leading to a stronger filtering effect from the caisson foundation. Additionally, the rotational transfer function starts from zero and becomes amplified as frequency increases. In general, the SCDI effects reduce the amplitude of horizontal acceleration of caisson foundation motion, but also introduce a rotational component, which may reduce the maximum absolute acceleration of the tower top and increase the relative displacement between the tower top and tower base for bridge structures, which has been confirmed in the author's subsequent research.  
The results and conclusions of this paper provide preliminary evidence of the influence of SCDI on caisson foundation motions. To further develop analytical expressions for the transfer functions relating the caisson foundation motion to the free-field ground motion, an extensive parametric study based on numerical methods is necessary. The current shaking table tests provide valuable data support for validating analytical expressions and numerical methods. Furthermore, the implementation of this study paves the way for discussing how to modify the free-field ground motion and introduce the rotation component when assessing the seismic performance of long-span bridges with caisson foundations.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
The authors declare no conflicts of interest.