# Model Experiment Study on Vertical Bearing Characteristics of Large-Diameter Ring Piles
## 2 Model Experiment Design  
The model parameters are based on the project of the Tsinghua Experimental Base in Beijing, China, which intends to build an LDRP with a diameter of 10 m and a length of 33 m. The size similarity coefficient of the model test was determined to be 20:1. A new parameter, \(K\), was introduced as the classification basis for ring piles. \(K\) is defined as the ratio of the wall thickness (\(T\)) of an LDRP to the pile radius (\(R\)). The specific formula is given in (1). Figure 1 shows the cross-section of a pile body, such as an LDRP. This parameter can directly represent the proportion of the hollow part of the ring pile. For a solid pile, \(K=1\), and the smaller the \(K\) value, the smaller the wall thickness and the larger the proportion of the hollow part. \[K=T/R \tag{1}\]  
In this experiment, \(K\) was taken as the main reference and concrete savings as the secondary reference. A total of 5 groups of model pile tests were set up (as shown in Table 1). Concrete with the same specifications as the original project was selected as the material for the model pile, with an elastic modulus of E = 3.0 \(\times\) 10\({}^{4}\) MPa and a reinforcement cage of uniform size. The bottom of the model pile was a 300 mm concrete seal. The pile strength measured 28 days after pouring and curing was 30 MPa. The only difference in the model piles was the difference in the hollow ranges, i.e., the difference in \(K\). Figure 2 shows the cross-section of the pile model. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Project**} & **Outer** & \multirow{2}{*}{**Inner Diameter**} & \multirow{2}{*}{**Wall Thickness**} & **Pile** & \multirow{2}{*}{**Diameter Ratio**} & **Concrete** \\  & **D/mm** & & & & & \(K\) \\ \hline Solid Pile No. 1 & 500 & 0 & 250 & & 1 & 0\% \\ Ring Pile No. 2 & 500 & 200 & 150 & & 0.6 & 16\% \\ Ring Pile No. 3 & 500 & 300 & 100 & 1670 & 0.4 & 36\% \\ Ring Pile No. 4 & 500 & 360 & 70 & & 0.28 & 52\% \\ Ring Pile No. 5 & 500 & 400 & 50 & & 0.2 & 64\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model pile’s specifications. Figure 1: Cross-section of pile body. The model box was designed as a steel tube (2200 mm in height and 1000 mm in diameter) formed by bending a steel plate. The tubular model box can better maintain the stress field in the soil and prevent the dissipation of the Chow ring stress in the pile during the experiment. According to geological exploration data, at the original project site, within a 36 m depth range, the soil type was a gravel layer mixed with sand. Therefore, in the experiment, we used a soil layer with 10-20 mm of gravel and fine sand, mixed in the ratio of 2:3 (Figure 3). The relationship between relative density and the free fall of sand particles, as mentioned in [PERSON] (2020) [12], is shown in Figure 4, where sand particles falling from a height of 520 mm resulted in a soil bed with a relative density of 70%. The height of the model box for this experiment was 2200 mm. First, soil was poured into the box, using the sand-pouring method. At every 200 mm in depth, the soil was compacted by using artificial vibrations. By following this procedure, soils in the model box with relative densities greater than 90% can be obtained, and the uniformity of the relative densities of the soils can be ensured. Figure 4: Variation of relative density of sand with the height of free fall ([PERSON], 2020) [12]. Figure 3: Model soil. Figure 2: Cross-section of pile model (from left to right: No.1, No. 2, No. 3, No. 4, No. 5). The bottom of the model box was first paved with 500 mm of soil, which was the bearing soil at the end of the pile. Then the model pile was placed and filled with soil. The model piles were rearranged in the same way after every replacement. The ultimate bearing capacity of the prototype pile is 389,169 kN. According to the dimension similarity coefficient, \(\mathrm{C_{L}}\) = 20:1, the estimated load of the model pile is 48 kN.