## 2 Factors Controlling Friction Forces
### Box-Soil Friction Coefficient  
As shown in Table 2, the friction coefficient (\(\mu\)) can be calculated using back analysis based on field monitoring data, a method that has been adopted in various friction solutions [19; 20]. Additionally, some standards reduce the friction coefficient based on the internal friction angle of the soil, which fails to reflect the lubricant effect. In practical engineering, the friction coefficient (\(\mu\)) is related to soil type and lubricant properties, making it challenging to accurately evaluate using the mentioned methods. Therefore, conducting contact shear tests for box-soil-lubricant interactions is a more feasible method for obtaining the friction coefficient [21; 22]. In this study, shear friction tests on box-soil interactions were conducted, measuring the friction coefficient under different lubrication conditions and soil particle sizes. As shown in Figure 5, the upper shear box was filled with soil, and the lower shear box was placed with concrete blocks simulating the outer surface of the box. Constant normal stress is applied to the soil-concrete interface by a vertical motor, and simultaneously, the upper shear box was fixed while the lower shear box was driven horizontally along a straight guide rail at a constant speed using a horizontal motor. The friction force exerted on the driven lower shear box was measured. In addition, the test considered the lubrication \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Soil Type**} & \multicolumn{2}{c}{**Friction Coefficient**} \\ \cline{3-4}  & & **Without Lubricant** & **With Lubricant** \\ \hline \multirow{2}{*}{Stein [19]} & Sand & 0.3–0.4 & \multirow{2}{*}{0.1–0.3} \\  & Clay & 0.2–0.3 & \\ \multirow{2}{*}{Pellet-beaucour [20]} & Sand & 0.2–0.4 & \multirow{2}{*}{0.07–0.1} \\  & Clay & 0.1–0.3 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Friction coefficients \(\mu\) proposed in existing studies. conditions at the soil-concrete interface. As the over-cutting space in practical engineering can accommodate a 2 cm thick layer of lubricant, a 2 cm thick layer of bentonite lubricant was poured onto the concrete block. The average surface roughness of the concrete block was 20.23 \(\upmu\)m, while the actual box jacking pipe section had an average surface roughness of 15.45 \(\upmu\)m. The surface roughness difference of within 5 \(\upmu\)m meets the test requirements. The experimental lubricant used a material and ratio commonly employed in sand-layered box jacking projects (bentonite:water = 0.06:1). The funnel viscosity was 69 s, and the fluid loss was 12 mL/30 min, meeting the pumping capacity and anti-filtration requirements of practical engineering. As shown in Table 3, the friction coefficients for various soils were obtained using shear tests. Compared with Table 2, the classification of soil types and lubrication conditions is more detailed, providing a reference for other studies. It can be observed that the friction coefficients under saturated and dry soil conditions were relatively close, indicating limited lubrication effects from pore water. Under lubrication conditions, the friction coefficient of sand decreased by 66.6-73.4%, and that of clay even decreased by 92.1%. Field data also show that the friction force can be reduced by 70-90% using a large amount of lubricant, and the friction coefficient no longer depends on the soil type but on the liquid limit of the lubricant [23; 24]. Figure 5: The shear test for friction coefficient.