# Numerical Investigations of Pile Group Foundations under Different Pile Length Conditions
## 8 Conclusions  
By utilizing numerical simulation methods and considering the engineering reality and geological conditions of large bridges, the bearing capacity characteristics of group pile foundations with different pile lengths were studied, leading to the following conclusions:  
Finite element models were established to simulate static load tests on pile foundations with varying pile lengths. Analysis of the vertical load-bearing characteristics of a single pile revealed displacement and settlement curves that align with the load transfer mechanism between the pile and soil. Comparison with a group pile foundation model consisting of piles of the same length demonstrated that the displacement curves were largely similar. This suggests that group pile foundations with different pile lengths and those with the same length exhibit comparable bearing performance. The modeling approach and selected parameters can serve as a reference for similar engineering projects. Under the axial uniform load, settlement at the pile base varies depending on the location. The middle pile row experiences minimal settlement, while the rear pile row undergoes greater settlement compared to the front pile row. Uneven settlement of the cap is observed, particularly in areas without backfilled soil. In contrast, the cap in the backfilled soil region tends to move upward. To prevent cap tilting, it is recommended to fill the entire bottom area of the cap with soil. Analysis of the pile group indicates that the location of the maximum bending moment of the pile body is in the region of the gravel soil layer. With small loads, the maximum bending moment is distributed along the soil layer interface. As the load gradually increases, the bending moment direction of the pile body gradually changes, and the maximum bending moment location of the front pile row gradually shifts to the surface of the gravel soil layer. The distribution revealed by the finite element numerical simulation software of the entire plastic zone confirms that the presence of a group pile foundation disrupts the continuous state of the plastic zone in the uppermost soil layer. This interruption contributes to the stabilization of the upper slope. The factor of safety provides a quantitative method for evaluating the stability of slopes. By comparing the resisting force against sliding to the driving force causing sliding, a numerical value is obtained to assess the stability of the slope under specific conditions. A higher factor of safety implies that the slope's resistance to sliding is relatively greater than the external driving forces. Therefore, when facing external loads or other unfavorable factors, the slope is more likely to remain stable, avoiding sliding or collapse. The obtained Factor of Safety (FOS) of 2.4 further indicates the overall stability of the slope. However, as the load increases, the FOS continues to decrease. \begin{table}
\begin{tabular}{c c c c c c c c} \hline Load (kN) & 100 & 150 & 200 & 250 & 300 & 350 & 400 & 450 \\ \hline Factor of safety & 2.4 & 2.32 & 2.09 & 1.78 & 1.46 & 1.27 & 1.14 & 1.06 \\ \hline \end{tabular}
\end{table} 
Table 3: The factor of safety under different loads. In summary, this study provides insights into the bearing performance of group pile foundations with different pile lengths under vertical loads using finite element numerical simulation methods. The conclusions drawn from this analysis can serve as a reference for related engineering design, yielding cost savings and significant economic benefits while ensuring safety. Conceptualization, C.Z. ; methodology, C.Z. ; software, C.Z., Z.C. and J.Z. ; formal analysis, Z.C. ; investigation, C.Z. ; writing--original draft preparation, C.Z. ; writing--review and editing, J.Z. ; supervision, C.Z. All authors have read and agreed to the published version of the manuscript.