# Numerical Analysis of Friction Reduction of Grouting in Long-Distance Pipe Jacking
## 4 Conclusions  
This paper introduces the grouting materials, grouting process, and grouting-friction-reduction mechanism. To evaluate the effect of friction reduction on the jacking force, the different interface reduction coefficients are simulated via FEM. The improved theoretical method is developed based on the numerical results to achieve relatively more precise  
Figure 13: Contrast among three methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(R_{inter}\) & \(f_{k}\) /kN - m\({}^{-2}\) & **Friction Resistance/kN** & **Total Jacking Force/kN** \\ \hline
0.2 & 9.6 & 67,600 & 72,400 \\
0.24 & 11.5 & 81,100 & 85,900 \\
0.28 & 13.4 & 94,600 & 99,400 \\
0.32 & 15.4 & 108,000 & 112,800 \\
0.36 & 17.3 & 121,700 & 126,500 \\
0.40 & 19.2 & 135,200 & 140,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the improved theoretical methods. outcomes compared to the previous results presented in Section 2. The findings provide valuable references for engineering design. The main conclusions are as follows:  
1. Grouting-friction-reduction technology can significantly reduce the jacking force. Optimizing the grouting process and preparing a suitable thixotropic slurry can effectively decrease the jacking force for long-distance pipe jacking. * In long-distance cases, the frictional resistance around the pipe is the main source of jacking force. As the interface reduction coefficient increases, the total jacking force increases approximately linearly, and the distribution of the stress around the pipe becomes more uneven. Thus, if the interface friction angle is sufficiently large, the variation in shear stress across the same section should be considered. 2. The simulated jacking force is significantly larger than the theoretical value presented in Section 2, especially when the pipe is buried at a greater depth. Therefore, alternative methods, like the improved theoretical method, should be used in such cases, as the previous theoretical approach may not accurately reflect these conditions. 3. In previous theoretical methods, the average unit frictional resistance between the pipe's outer surface and the soil cannot be precisely selected, leaving only an imprecise range for engineers from which to select. The improved theoretical methods address this issue by providing formulae to estimate the value more accurately. * There are some limitations in the improved theoretical method, such as its inability to account for the uneven distribution of shear stress across the section, and the unclear correlation between the interface reduction coefficient, and the effect of the grouting. It is recommended that future studies investigate the effect of the shear stress distribution on the friction resistance and a more precise calculation method to assess the friction reduction of the grout. [PERSON]: conducted a comprehensive literature review for the Sections 1 and 2, summarizing existing theories and methods. He also carried out finite element simulations in Section 3. [PERSON]: supervised the overall research process and provided critical guidance for the study. He offered tuition into Sections 1 and 2 and advised on the development of the new method in Section 3. [PERSON] also reviewed and revised the manuscript, managed correspondence with the journal, and ensured the scientific accuracy of the paper. [PERSON]: contributed to Section 3 by assisting with the finite element simulations, and he interpreted the resulting data and proposed a new theory based on the simulation outcomes. [PERSON]: participated in literature review for Sections 1 and 2. And she assisted [PERSON] with summarizing existing theories and methods. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China under grant No. 51738010, the Shanghai Natural Science Foundation (no. 22 ZR1464600). The institutional review board has no dissenting opinions. All authors consent to the manuscript. All the data needed are presented in the manuscript.