# Experimental Study on Interface Frictional Characteristics between Sand and Steel Pipe Jacking
## 3 Analysis of Test Results
### Calculation of Mechanical Parameters of Contact Surface  
Regression analysis of the shear strength \(\tau_{p}\) (the peak shear stress in the \(\tau\)-s curve of the interface) and residual strength \(\tau_{r}\) (the stable value of the shear stress in the \(\tau\)-s curve \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sandy Soil Type**} & \multirow{2}{*}{**Slurry Condition**} & \multirow{2}{*}{\begin{tabular}{c} **Normal Stress** \\ \(\sigma\)**/(kPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Shearing** \\ **Displacement** \\ **s/(mm)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Peak Shear Stress** \\ \(\tau_{\text{max}}\)**/(kPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Stable Value of** \\ **Shear Stress** \\ \(\tau_{\text{stable}}\)**/(kPa)** \\ \end{tabular} } \\ \hline \multirow{2}{*}{Gravally sand} & No slurry lubrication & 60 & 6 & 36.68 & 27.5 \\ \cline{2-5}  & Slurry lubrication & 60 & 4.67 & 27 & 19 \\ \hline \multirow{2}{*}{Coarse sand} & No slurry lubrication & 60 & 6 & 35.34 & 28 \\ \cline{2-5}  & Slurry lubrication & 60 & 4.67 & 26.12 & 19.5 \\ \hline \multirow{2}{*}{Medium sand} & No slurry lubrication & 60 & 6 & 35.29 & 28 \\ \cline{2-5}  & Slurry lubrication & 60 & 4.67 & 27.6 & 20 \\ \hline \multirow{2}{*}{Fine sand} & No slurry lubrication & 60 & 6.66 & 36.53 & 32 \\ \cline{2-5}  & Slurry lubrication & 60 & 4.67 & 27.05 & 23 \\ \hline \multirow{2}{*}{Powdered sand} & No slurry lubrication & 60 & 6 & 38 & 34 \\ \cline{2-5}  & Slurry lubrication & 60 & 4.67 & 29.21 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Shear stress peak and stable value of sand interface under different lubrication conditions. Figure 4: Shear stress-shear displacement curves of different normal stress. of the interface) at the contact surface between sandy soil of different particle sizes and steel plates, with and without slurry, under different normal stresses was completed. To analyze the effect of the sand particle size on mechanical parameters, such as the interface internal friction angle \(\varphi\), interface cohesion c and interface sliding friction coefficient \(\mu\), the interface internal friction angle \(\varphi\) and interface cohesion c are regressed according to Equation (1), and the interface sliding friction coefficient \(\mu\) is regressed according to Equation (2). The shear strength \(\tau_{p}\) and residual strength \(\tau_{r}\) of the interface between sandy soil of different particle sizes and steel plates, with and without slurry, are shown in Table 2, and the regression equations of the shear strength \(\tau_{p}\) and residual strength \(\tau_{r}\) are shown in Tables 3 and 4, respectively. \[\tau_{p}=\sigma\tan\phi+c \tag{1}\]  
\[\mu=\frac{\tau_{r}}{\sigma} \tag{2}\]  
where \(\sigma\)--normal stress, kPa; \(\tau_{p}\)--interface shear strength, kPa; \(\tau_{r}\)--interface residual strength, kPa; \(\varphi\)--interface internal friction angle, \(\circ\); \(c\)--interface cohesion, kPa; and \(\mu\)--interface sliding friction coefficient. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sandy Soil Type** & **Regression Equation** & **Variance R\({}^{2}\)** \\ \hline Gravelly sand & \(\tau_{r}=0.456\sigma\) & 0.999 \\ Coarse sand & \(\tau_{r}=0.472\sigma\) & 0.999 \\ Medium sand & \(\tau_{r}=0.466\sigma\) & 0.998 \\ Fine sand & \(\tau_{r}=0.518\sigma\) & 0.972 \\ Powdered sand & \(\tau_{r}=0.538\sigma\) & 0.944 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression equation of residual strength and normal stress of interface.