## 3 Friction Force Variation Characteristics
### Field Monitoring Results  
The actual jacking forces during construction were obtained (see Figure 9). As shown in Figure 9a, during the initial 0-17 m of jacking length in Case A, no lubricant was injected, and the jacking force increased linearly with the jacking length. The jacking force decreased gradually after a jacking length of 17-80 m due to the significant friction reduction effect after lubricant injection. From 80 m to 240 m, the jacking force increased linearly again, but the slope was significantly smaller than that from 0-17 m. As shown in Figure 9b, the measured jacking force in Case B also showed the same variation pattern. The cutterhead resistance is typically kept constant, and the slope of the jacking force curve can reflect the change in friction forces [10; 14; 15]. It was observed that the construction process includes three conditions: without lubrication, lubrication gradually coming into play, and lubrication fully in play, which should be divided into zones when calculating the friction force. (1) Without lubrication zone (WL). During the hoisting and installation of the box pipe, the hydrocylinder will be contracted, removing the jacking force acting on the already jacked box. After the soil in front of the excavation face loses the jacking force support, active earth pressure will be generated, which will cause the cutterhead and the already jacked box to have a tendency to retreat towards the launching shaft, and the acting direction of the friction force will be reversed. If the friction force cannot balance the active earth pressure, the slight retreat will induce instability of the excavation face and may even cause accidents such as collapse and ground subsidence. Therefore, without injecting lubricant in the initial stage of jacking, a significant friction force can be achieved to prevent the instability of the excavation face when the hydrocylinder contracts. This is a characteristic method for long-distance box jacking. (2) Lubrication gradually coming into play zone (GP). After the first injection of lubricant, free water in the lubricant filters into the surrounding soil, causing a rapid decrease in lubricant pressure, and it is difficult to maintain \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Code** & **Stratum** & **Thickness (m)** & **Density (g/cm\({}^{3}\))** & **Cohesion (kPa)** & **Friction Angle (\({}^{\circ}\))** \\ \hline \hline
1.5 & Plain fill & 4.3 & 1.92 & 27.9 & 16.8 \\
4 & Clay & 2.0 & 1.99 & 41.4 & 15.7 \\
5 & Silty clay with silt & 1.3 & 1.92 & 16.8 & 22.7 \\
6.1 & Silty sand with silt & 4.4 & 1.91 & 4.6 & 31.4 \\
6.2 & Silty sand & 4.0 & 1.94 & 3.8 & 33.4 \\
7 & Silty clay & 5.7 & 1.93 & 25.7 & 17.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Soil properties in Case A. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Code** & **Stratum** & **Thickness (m)** & **Density (g/cm\({}^{3}\))** & **Cohesion (kPa)** & **Friction Angle (\({}^{\circ}\))** \\ \hline
2.3 & Silty sand & 18.5 & 1.85 & 6 & 30.5 \\
4 & Mucky clay & 7 & 1.69 & 14 & 11.5 \\
5 & Silty clay & 3.2 & 1.82 & 16 & 20.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Soil properties in Case B.  
stability in the soil around the tunnel. As the solid particles of the bentonite fill the soil pores via flocculation and bridging, a mud cake is formed in the over-cutting space, reducing the box-soil friction coefficient. Since the complete filling of soil pores and the continuous stability of the surrounding soil require repeated actions of the lubricant, the box-soil contact state can not be changed from full box-soil interaction to one-side box-soil interaction immediately; instead, it gradually transitions to a state where three sides or two sides of the pipe are in contact. (3) Lubrication fully in play zone (FP). After multiple injections of lubricant, a complete mud cake is formed around most box sections, stabilizing the surrounding soil. The contact state develops into a one-side box-soil interaction, and the unit area friction force significantly decreases.