# Model Experiment Study on Vertical Bearing Characteristics of Large-Diameter Ring Piles
## 3 Analysis of Model Experimental Results  
### Analysis of Settlement Law of Pile Top and Pile Bottom in Model Experiment  
The Q\({}_{\text{top}}\)-s curve of the pile top and Q\({}_{\text{bottom}}\)-s curve of the pile bottom are shown in Figures 7 and 8, respectively. Two methods to determine the ultimate bearing capacity of a single pile are stipulated in China's _GB50007-2011 Code for the Design of Building Foundations_[13]:  
1. When the load-settlement curve suddenly changes from a slow drop at the beginning to a steep drop, the load corresponding to the initial point of the curve's steep drop can be considered the ultimate bearing capacity of the pile. Figure 8: The settlement of pile bottom. Figure 7: The settlement of pile top. 2. If no obvious change in the load-settlement curve is observed and the overall trend is a slow decline, then the load corresponding to the settlement of 40 mm can be regarded as the ultimate bearing capacity of the pile. In this experiment, obvious inflection points were observed in the settlement curves of the pile top and pile bottom of the five model piles. The inflection points are concentrated in the load range of 40-55 kN. In this range, the settlement of the pile body changed from a gentle increase to a steep increase. Therefore, the load at the inflection point is the ultimate bearing capacity of the pile body. Because pile top settlement directly affects the superstructure, it is taken as the main reference index. As shown in Figure 7, from the beginning of the loading to 20 kN, the settlement of the pile body was small and had no obvious change. The settlement of the pile tops of the five piles was approximately 0.5 mm. The settlement increased gradually when the load increased to 40 kN. An inflection point appeared between 40 and 55 kN, at which point we considered the pile foundation to be destroyed. When the upper load continues to increase, the settlement after the inflection point begins to increase significantly. The maximum settlement amount of the pile body was 10 mm at 100 kN. A comparison of pile settlements for different model piles is shown in Table 2.  
Combining the data in Table 2 with those in Figure 7, when the outer diameter of the pile is the same and the bottom of the pile is covered, a small difference is observed in the ultimate bearing capacity of LDRPs and LDSPs, with \(K=0.2\)-1, set in this test. For Ring Pile No. 5, with the least favorable \(K=0.2\), only 36% of the concrete content of the solid pile can attain 80% of the ultimate bearing capacity of the solid pile. In addition, pile safety is clearly stipulated in \"_GB50007-2011 Code for Design of Building Foundation_\" [13], approved and issued by the Ministry of Construction of the People's Republic of China. The vertical ultimate bearing capacity of a single pile is divided by a safety factor of 2, which is the characteristic value \(\rm{R_{a}}\) of the vertical bearing capacity of a single pile. This characteristic value will be used as the actual engineering design standard. The characteristic values of the bearing capacities of Solid Pile No. 1 and Ring Pile No. 5 are shown in Table 3. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Model Pile**} & **Outer** & \multirow{2}{*}{**Wall Thickness**} & \multirow{2}{*}{\(K\)} & **Ultimate** & \multicolumn{2}{c}{**Settlement under Ultimate**} \\  & **Diameter** & & & **Bearing** & \multicolumn{2}{c}{**Bearing Capacity**} \\  & **D/mm** & & & **Capacity/kN** & **Pile Top** & **Pile Bottom** \\ \hline Solid Pile No. 1 & 500 & 250 & 1 & 50 & \(-\)2.2 & \(-\)2 \\ Ring Pile No. 2 & 500 & 150 & 0.6 & 50 & \(-\)2.4 & \(-\)2.02 \\ Ring Pile No. 3 & 500 & 100 & 0.4 & 50 & \(-\)2.4 & \(-\)1.7 \\ Ring Pile No. 4 & 500 & 70 & 0.28 & 40 & \(-\)1.2 & \(-\)1.5 \\ Ring Pile No. 5 & 500 & 50 & 0.2 & 40 & \(-\)0.9 & \(-\)1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of settlement of model piles.