## 2 Model Test
### High-Rise Pile Cap Model  
This model experiment takes a coastal offshore wind power project in China as the research background. The prototype pile has a diameter of 1.25 m, a length of 43.75 m, and a burial depth of 35 m. It is obvious that performing prototype tests is not a feasible option. Consequently, the authors intend to conduct an experimental model study and extrapolate prototype experimental outcomes based on the model experimental outcomes. The initial phase of model experimentation necessitates determining the similarity ratio of the experiment. Nonetheless, because of the interdependent effects of intricate factors such as fluid dynamics and pile-soil systems on offshore engineering, employing a unified similarity principle for the comprehensive design of dynamic responses at diverse locations is challenging. Hence, this article solely focuses on similarity design concerning the primary influencing factors of the experiment. The similarity criteria in the equation are called \(\pi\), which involves a set of physical parameters including stress (\(\sigma\)), strain (\(\varepsilon\)), elastic modulus (\(E\)), Poisson's ratio (\(\mu\)), friction angle (\(\varphi\)), cohesion (\(c\)), load (\(p\)), length (\(l\)), and displacement (\(\delta\)). Among these, length and bulk density are regarded as the fundamental quantity group, with their respective units denoted by \(\left[\mathrm{L}\right]\) and \(\left[\mathrm{FL}^{-3}\right]\), and the relationship between the remaining physical quantity, length, and bulk density is in a dimensionless form. The similarity criteria and similarities used in this article are shown in Table 1.  
During the model tests, hollow aluminum alloy was employed as the material for fabricating the model piles. In accordance with [PERSON]'s II similarity theorem and taking into consideration the constraints of the loading equipment and the model slot used in the tests, the geometric similarity ratio of the model pile was set at 1:50. Figure 1 depicts the specifications of the model pile, including a pipe diameter of 25 mm, a thickness of 2 mm, and a length of 875 mm. The elastic modulus of the model pile was measured at 71 GPa. In order to replicate real-world conditions, the model pile was inserted into the soil to a depth of 700 mm, with a suspended section extending 175 mm above the muddy surface. In addition, because of the hollow structure inside the model pile, the bottom of the model pile used in this test was sealed with rubber in order to avoid the formation of a soil plug effect at the end of the pile, so as to meet the stiffness requirement of the model pile. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Physical Quantity** & **Similarity Criteria** & **Similarity Ratio** \\ \hline Stress & \(\pi_{1}=\frac{\sigma}{\mu L}\) & 1:50 \\ Strain & \(\pi_{2}=\varepsilon\) & 1 \\ Elastic modulus & \(\pi_{3}=\frac{\varepsilon}{\mu L}\) & 1:50 \\ Poisson’s ratio & \(\pi_{4}=\mu\) & 1 \\ Friction angle & \(\pi_{5}=\varphi\) & 1 \\ Cohesive force & \(\pi_{6}=\frac{\varepsilon}{\mu L}\) & 1:50 \\ Load & \(\pi_{7}=\frac{\varepsilon}{\mu L^{3}}\) & 1:503 \\ Displacement & \(\pi_{8}=\frac{\varepsilon}{L}\) & 1:50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model test similarity ratio parameters. In order to avoid boundary effects, the distance from the side pile to the edge of the bearing platform was taken as 37.5 mm. The height of the pile embedded in the bearing platform was determined as 50 mm [33]. [PERSON] et al. [18] discovered that the group pile effect became gradually less pronounced as the distance between piles increased, and it was negligible when the spacing exceeded six times the diameter of the piles. Therefore, to delve deeper into the interrelation between pile spacing and the pile group effect, as well as to minimize limitations imposed by testing sites, the pile spacings were set to three, four, and five times the diameter of the piles.