## 3 Numerical Simulation of Uplift Capacity in Composite-Anchor Piles
### Numerical Simulation Based on Finite Element Method
Two common diameters, namely 21.8 mm and 15.2 mm, were selected for the study. These diameters are widely used in practical engineering projects and can cover most scenarios. By examining these two common steel strand diameters, a better understanding of the influence of the diameter on the bearing capacity of composite piles can be obtained. Furthermore, the interface between different components within composite-anchor piles plays a crucial role in influencing their behavior. Thus, during the creation of the model, distinct contact surfaces are established for steel strands, grout materials, steel pipes, and pile concrete. To define these contact surfaces and solid element parameters, relevant information from previous research is utilized. The Coulomb shear model is employed to simulate the contact effect, with penalty functions utilized to incorporate tangential behavior. The friction coefficient is determined based on empirical formulas sourced from the existing literature [28]. Moreover, throughout the simulation process, it is assumed that only tangential relative slip occurs once the pile-soil contact is established. Once the physical model is created, vertical and horizontal displacement constraints are applied at the bottom of the model, while normal horizontal constraints are established around the model. A gravity load is then applied to replicate the in situ stress conditions. Next, the displacements of the entire model are set to zero, and the vertical load is incrementally applied at the top of the pile. The incremental loading process mimics the field load \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Density \(\rho\) (kg/m\({}^{3}\))** & **Elastic Modulus E (MPa)** & **Poisson’s Ratio \(\
u\)** \\ \hline Grout & 1.80 \(\times\) 10\({}^{3}\) & 2.50 \(\times\) 10\({}^{4}\) & 0.20 \\ High-strength steel pipe & 7.85 \(\times\) 10\({}^{3}\) & 2.10 \(\times\) 10\({}^{5}\) & 0.30 \\ Steel strand & 7.85 \(\times\) 10\({}^{3}\) & 1.95 \(\times\) 10\({}^{5}\) & 0.28 \\ C35 Concrete & 2.30 \(\times\) 10\({}^{3}\) & 3.15 \(\times\) 10\({}^{4}\) & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physical parameters of the composite-anchor uplift pile [20]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Soil Layer** & **Thickness** & **Density** & **Cohesion** & **Friction** & **Elastic Modulus E** & **Poisson’s** & **Pile-Side Ultimate Friction q (MPa)** \\ \hline
1 & 1.81 & 1.9 \(\times\) 10\({}^{3}\) & 0.01 & 10 & 6.2 & 0.33 & 0.03 \\
2 & 2.5 & 1.94 \(\times\) 10\({}^{3}\) & 0.015 & 23.6 & 7.6 & 0.33 & 0.045 \\
3 & 1.7 & 1.95 \(\times\) 10\({}^{3}\) & 0 & 25 & 20 & 0.33 & 0.04 \\
4 & 6.5 & 2.0 \(\times\) 10\({}^{3}\) & 0 & 28 & 30 & 0.33 & 0.06 \\
5 & 7.5 & 2.05 \(\times\) 10\({}^{3}\) & 0 & 32 & 45 & 0.33 & 0.065 \\
6 & 1.99 & 2.05 \(\times\) 10\({}^{3}\) & 0 & 32 & 55 & 0.33 & 0.070 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physical parameters of the soil layers [20]. testing procedure to ensure accuracy in the simulation results. This approach helps avoid potential errors that may arise from loading inconsistencies and enables a more precise analysis of the pile's behavior under different loading conditions. By following a loading process similar to the field load testing process [20], the simulation results can better reflect the real-world conditions and provide more reliable insights into the performance of the composite pile.