# Model Experiment Study on Vertical Bearing Characteristics of Large-Diameter Ring Piles
## 4 Numerical Simulations for Verification  
To verify the accuracy of the model experiments, three sets of numerical simulation experiments were designed and implemented. In the numerical simulation experiment scheme, the solid pile; Ring Pile No. 3; and the most unfavorable ring pile, Ring Pile No. 5, were selected as references and designed according to the original project size. The specific experimental scheme is shown in Table 8.  
Numerical simulations were performed by using Midas GTX NX finite element numerical simulation software, according to pile diameter and pile length. To avoid the boundary effect, a soil model with 10 times the pile diameter, that is, with a size of 100 m \(\times\) 100 m \(\times\) 100 m, was established ([PERSON], 2017) [14]. According to the original engineering geological survey, the model constituted seven soil layers, and finite element calculations were carried out by using the Mohr-Coulomb soil constitutive model. Model piles are elastic constitutive models. Figure 16 shows the results of the numerical simulations conducted on the model. Except for the top surface, which was free, the remaining surfaces were not allowed to produce displacement. The material of the model piles is the same as the original project and is regarded as an elastic \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Project**} & **Elastic Modulus** & \multirow{2}{*}{**Poisson’s Ratio**} & **Standard Value of** & **Design Value of** \\  & **E/MPa** & & \
\begin{tabular}{c} **Compressive Strength** \\ _f\({}_{\text{ck}}\)_/MPa** \\ \end{tabular} &
\begin{tabular}{c} **Compressive Strength** \\ _f\({}_{\text{c}}\)_/MPa** \\ \end{tabular} \\ \hline Concrete & 3.0 \(\times\) 10\({}^{4}\) & 0.3 & 23.5 & 14.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Related parameters of C30 concrete. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pile Type** & **Solid Pile No. 1** & **Ring Pile No. 2** & **Ring Pile No. 3** & **Ring Pile No. 4** & **Ring Pile No. 5** \\ \hline Maximum strain & \(-\)40 & \(-\)65 & \(-\)35 & \(-\)175 & \(-\)254 \\ Maximum stress & 1.2 MPa & 1.95 MPa & 1.05 MPa & 5.15 MPa & 7.62 MPa \\ Concrete strength & & \(f_{\text{ck}}\) = 23.5 MPa & & \(f_{\text{c}}\) = 14.3 MPa & \\ \(K\) & 1 & 0.6 & 0.4 & 0.28 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Stresses corresponding to the peak strain of the piles. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Project**} & **Outer** & \multirow{2}{*}{**Inner**} & **Wall** & \multirow{2}{*}{**K**} & **Concrete** \\  & **Diameter** & & & **Diameter/m** & & **T/m** & \\ \hline Solid Pile No. 1 & 10 & 0 & 5 & 1 & 0\% \\ Ring Pile No. 3 & 10 & 6 & 2 & 0.4 & 36\% \\ Ring Pile No. 5 & 10 & 8 & 1 & 0.2 & 64\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Input parameters for the numerical simulations. constitutive model. In the meshing process, using a small volume grid yields more accurate and detailed calculation results. However, refining the grid of the entire model was not necessary. Therefore, the grid sizes of the pile body and boundary were in the ratio 1.5. ([PERSON], 2016; [PERSON], 2022) [15,16]. The experimental load and settlement results of the model experiment were projected onto the original project according to the similarity coefficient and compared with the numerical simulation results. Figure 17 shows a comparison of pile top settlements. The pile-top settlement results of the numerical simulations show a flat line without any obvious inflection point. The load corresponding to the settlement of 40 mm was taken as the ultimate load of the pile. The ultimate load was concentrated in the range of 280-367 MN. The ultimate bearing capacity of the model test pile was in the range of 320-440 MN, and the difference was approximately 15%. Even though the numerical simulation experiment process is too ideal and only serves as a guide for the regularity conclusion, the specific results of the model test shall prevail. Figure 16: Numerical model.