## 3 Test Design
### Design of Scale Factors  
The prototype caisson foundation in the model test is from the middle tower of the Taizhou Yangtze River Highway Bridge. The dimensions of the prototype caisson foundation are 56.2 m in length, 44.1 m in width, and 76 m in height, with an embedment depth of 55 m. According to similarity theory [20; 23], the simulation of SCDI effects should  
Figure 1: Physical view of the model soil container: (**a**) Inside view; (**b**) Outside view. mainly consider three aspects: geometric similarity, physical similarity, and mechanical similarity. Considering the large geometric dimensions of the caisson foundation, the design of the length scale factor incorporates considerations such as the size and bearing capacity of the shaking table, the dimensions of the model soil container, the boundary effect, the model manufacturing process, and other factors, ultimately leading to the determination of the length scale factor for the model test, which is set at \(S_{l}=1/80\). The results of the dynamic triaxial and resonant column tests of model soil conducted by [PERSON] et al. (2014, 2015) showed that adding sawdust to sand soil reduced both the density and dynamic shear modulus. This finding is consistent with the requirement of similarity. Thus, a mixture of sawdust and dry sand was chosen as the model soil, with a mass ratio of 1:2.5. This ratio was then used to calculate the scale factors for both the modulus of elasticity (\(S_{E}=1/32\)) and the density (\(S_{\rho}=1/2\)). Once the scale factors of length, modulus of elasticity, and density are determined, the remaining physical quantities can be deduced according to the Buckingham \(\pi\) law. The scale factors of the model soil are listed in Table 1.  
The use of organic glass in the fabrication of model structures is common due to its favorable characteristics, such as low density, homogeneous composition, high strength, low modulus of elasticity, and ease of processing and fabrication. In the design of the model structure, the following basic physical quantities are chosen: \(S_{l}=1/80\), \(S_{\rho}=1/2\), and \(S_{a}=5\). According to the material properties of organic glass, the elastic modulus scale factor \(S_{E}\) and the density scale factor \(S_{\rho}\) can be determined as \(1/10\) and \(1/2\), respectively. However, the elastic modulus scale factor \(S_{E}\) does not fully satisfy the similarity theory. Preliminary finite element analysis indicates that the elastic modulus scale factor \(S_{E}\) is approximately \(1/10\) or \(1/32\), which has minimal impact on the dynamic response of displacement and acceleration of the caisson foundation and the soil, primarily due to the significant stiffness discrepancy between the caisson foundation and the soil. The stiffness difference between the caisson foundation and the soil means that the caisson foundation can be considered a rigid body in the soil, regardless of whether the elastic modulus scale factor \(S_{E}\) of the model structural material is \(1/10\) or \(1/32\). Therefore, the elastic modulus scale factor of the model structure, \(S_{E}\), is set to \(1/10\) for this experiment. Once the length, elastic modulus, and density scale factors are determined, the remaining scale factors can be calculated using the Buckingham \(\pi\) law. The scale factors of the model structure are also presented in Table 1.