## 1 Introduction
However, the above studies are subject to one or more of the following issues: (1) the soil is usually assumed to be linearly elastic, homogeneous, and isotropic, and the influence of confining pressure and soil nonlinearity on the soil parameters is not considered; (2) the contact between the soil and the structure is usually assumed to be perfect, and the effects of separation and slip between the soil and the foundation are not considered; (3) the above studies are usually conducted in the plane strain conditions or using two-dimensional numerical models, and it has been demonstrated that a three-dimensional model is more accurate and real for examining the dynamic interaction between soil and foundations; and (4) the embedment of the foundation in the aforementioned study is relatively shallow, with the maximum embedment depth of 12 m. However, the embedment depth of the caisson foundation employed for long-span bridges is typically greater than 40 m, and the influence of the embedment depth on the motion of caisson foundations is more significant. Therefore, it is necessary to verify the applicability of the above research results on the effect of dynamic interaction between soil and foundations on the motion of shallow embedded foundations to the deep embedded caisson foundations of long-span bridges in real situations. Adopting the experimental method to study the influence of SCDI effects on the motion of caisson foundations can address the issues mentioned above in a more satisfactory manner. The experimental research on the SCDI effects has not yet been fully conducted. [PERSON] et al. [17; 18; 19] employed the centrifuge model test, which can simulate stress levels equal or similar to those of the prototype, and effectively reproduce the physical properties of the prototype, to analyze the seismic performance of the bridge pier with the caisson foundation. However, they paid more attention to the SCDI effects on the seismic performance indexes such as maximum acceleration, maximum displacement at the top of the pier, and maximum bending moment at the bottom of the pier, etc., without focusingon the SCDI effects on the motion of the caisson foundation. In addition, the prototype embedment depth of the caisson foundation in their test was only 11 m, which is much smaller than the embedment depth of the caisson foundation for the long-span bridge. Therefore, it is difficult to use the centrifuge model test to study the SCDI effects on the motion of the large-size caisson foundation, due to the limitation of the capacity and size of the centrifuge. The 1 g shaking table model tests, with larger geometry and higher bearing capacity than centrifuge model tests, allow precise loading, control, and observation [20; 21], and are more suitable for the study of large-size caisson foundations. Additionally, the 1 g shaking table model test method can realistically reproduce the whole process of seismic loading action and serves as the most direct approach for studying the characteristics of the SCDI and its impact on the caisson foundation motion. Therefore, this paper adopts the method of 1 g shaking table model test to study the influence of SCDI, and the novelty is shown: By carefully designing the model dimensions, and configuring the model soil to meet the specific similarity relationship according to the similarity theory, the 1 g three-dimensional shaking table model test for the deeply embedded caisson foundation of the long-span bridge can simultaneously consider the influence of the nonlinear soil, the complex three-dimensional contact relationship between the soil and the caisson, the ultra-large embedment of the long-span bridge foundation, and other factors. Thus, the influence of SCDI on the motion of the caisson can be evaluated more truly and accurately. A series of 1 g shaking table model tests were conducted in this study, including a free-field system model test and a soil-caisson system model test, in which the free-field system model test consisted of soil only and no structure included.