## 5 Finite Element Analysis of Post-Grouted Piles  
### Model Building  
Due to the limited computational capabilities of computers in the past, numerical simulations in traditional post-grouted pile engineering primarily relied on simplified 2D models [19; 20]. However, this approach resulted in a lack of refinement in the models and neglected the three-dimensional geometric shapes of actual objects. With advancements in computer technology, constructing more detailed and accurate 3D models has become the preferred method to conduct numerical simulation tests on post-grouted piles [21]. Compared to 2D models, 3D models can more comprehensively represent the geometric shapes of actual individual piles and lay the foundation for future, even more refined numerical simulation tests of post-grouted piles. Research has indicated that numerical simulation analysis using PLAXIS 3D V22 to evaluate the bearing capacity of pile foundations can yield effective and regular conclusions [21; 22]. Therefore, a three-dimensional full-scale finite element model was developed in PLAXIS 3D V22 software using the field-tested pile TP1 as the foundational blueprint. In this model, the soil and additional solids are simulated utilizing the Moore-Cullen model, while the pile is defined as a linear elastic material. Since the bored piles were symmetric cylinders, and the setup of the combined post-grouting device was relatively uniform in the horizontal direction, the monopile models before and after grouting were considered symmetric bodies. The test pile possesses a diameter of 1.5 m and a length of 56.5 m. The dimensions for pile end grout consolidation are established with reference to the coring test results [23], with the diameter and height set to 1.9 times the pile radius. Additionally, the height of the grout's upward return is designated as 12 m, in accordance with the JTG 3363-2019 \"Code for Design of Highway Bridge and Culvert Foundations and Fundamentals\" [24]. The grout on the pile side is represented as an interface unit, with a virtual thickness factor of 0.2. To simulate the force exerted by the self-balancing load box in the pile at a distance of 28.5 m from the pile end, a pair of vertically opposed forces is implemented in the model. The calculation domain for the soil extends 20 times the pile diameter (\(D\)) horizontally and 1.5 times the pile length (\(L\)  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pile No.** & **Stage** & **Side Resistance** & **Side Resistance as a Proportion of the Ultimate Load** & **End Resistance (kN)** & **End Resistance as a Proportion of the Ultimate Load** & **Ultimate** \\ \hline \multirow{3}{*}{TP1} & Before grouting & 24,191 & 87.51\% & 3453 & 12.49\% & 27,644 \\  & After grouting & 29,907 & 81.35\% & 6858 & 18.65\% & 36,765 \\ \cline{1-1}  & Before grouting & 23,110 & 87.01\% & 3450 & 12.99\% & 26,560 \\ \cline{1-1}  & After grouting & 29,972 & 81.52\% & 6793 & 18.48\% & 36,765 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The ratio of pile resistance to pile top load under ultimate bearing capacity.  
vertically from the pile's tip. PLAXIS 3D automatically meshes the pile by configuring the appropriate parameters. The granularity of mesh delineation has a direct impact on both calculation accuracy and speed; thus, 15-node cells are employed for mesh delineation. After comprehensive consideration, the piles and soil within a specific range are refined and encrypted. Figure 6 illustrates the mesh division of the calculation model. The blue area in the figure is the encrypted area of the mesh division, which improves calculation efficiency while ensuring calculation accuracy. Table 6 shows the specific parameters of each material in the model.