## 5 Finite Element Analysis of Post-Grouted Piles
### Analysis of Calculation Results  
To validate the rationality of the model, a comparative analysis was conducted between the load-displacement curves of the test piles, as calculated through numerical simulation prior to grouting, and the corresponding curves measured during field testing. The comparison is depicted in Figure 7. Observing Figure 7, it is evident that the load-displacement curves derived from the numerical simulation align well with those recorded in the field, despite the presence of minor discrepancies. Overall, the results from both the numerical simulation and field testing exhibit a consistent trend, indicating that the established calculation model and parameter selection are reasonably accurate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material Name** & **Stage** & \(\mathbf{E}\) **(MPa)** & \(\mathbf{\
u}\) & \(\mathbf{c}\) **(kPa)** & \(\mathbf{\varphi}\) **(\({}^{\circ}\))** \\ \hline \hline \begin{tabular}{c} Pile \\ soil \\ \end{tabular} & \multicolumn{2}{c}{\(3.15\times 10^{4}\)} & 0.2 & \\ \begin{tabular}{c} 30 \\ \end{tabular} & \multicolumn{2}{c}{\(0.3\)} & 4 & 30 \\ \begin{tabular}{c} Grout \\ consolidation \\ \end{tabular} & \begin{tabular}{c} Before grouting \\ After grouting \\ \end{tabular} & \begin{tabular}{c} 30 \\ \end{tabular} & \begin{tabular}{c} 0.3 \\ \end{tabular} & \
\begin{tabular}{c} 3.2 \\ \end{tabular} &
\begin{tabular}{c} 24 \\ 35 \\ \end{tabular} \\ \hline \hline \end{tabular}  
* Note: \(\mathbf{E}\), modulus of elasticity of the material; \(\mathbf{\
u}\), [PERSON]’s ratio of the material; \(\mathbf{c}\), the cohesion of each soil; \(\mathbf{\varphi}\), the internal friction angle of each soil.  
\end{table} 
Table 6: Specific parameters of material. Figure 6: Computational modeling and mesh segmentation. Furthermore, this analysis underscores the feasibility of utilizing PLAXIS 3D software to analyze the force characteristics of pile foundations prior to grout injection. Numerical simulation serves as an efficient tool for investigating issues related to the post-grouting of pile foundations. As illustrated in Figure 8, load-displacement curves for the self-balancing tests of pile foundations, both before and after grouting, have been computed. Upon examining Figure 8, it is apparent that, after grouting, under identical loading conditions, the displacements of both the upper and lower pile sections are significantly reduced compared to before grouting. Prior to grouting, the upper pile section bears the entire load primarily through pile side resistance. However, post-grouting, this resistance is substantially enhanced due to soil reinforcement surrounding the pile and improved pile-soil interface mechanical properties. Both before and after grouting, the pile side resistance exhibits a notable steep decline as the load increases, eventually reaching a limit value where the upper pile section can no longer sustain additional load, leading to pile-soil displacement and significant relative movement. Differently, the lower pile section supports the load from the load box through a combination of pile side resistance and pile tip resistance. Comparing the load-displacement curves of the lower pile before and after grouting reveals a significant reduction in displacement under the same load following combined grouting, indicating a substantial improvement in the single-pile bearing capacity. Furthermore, Figure 8 demonstrates that the curves for the lower pile section, both pre- and post-grouting, do not exhibit a steep decline. Upon reaching the maximum resistance of the upper pile segment's lateral surface, the lower pile segment's bearing capacity remains unmaximized, indicating that the pile tip resistance has yet to be fully utilized and is still in a phase of gradual growth. This observation indicates that pile tip resistance and pile lateral resistance develop asynchronously, and the capacity of a single pile to support heavier loads is predominantly influenced by the extent of pile tip resistance mobilization.