# Experimental Study on Interface Frictional Characteristics between Sand and Steel Pipe Jacking
## 3 Analysis of Test Results
### Calculation of Mechanical Parameters of Contact Surface
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sandy Soil Type** & \begin{tabular}{c} **Normal Stress** \\ _\(\sigma\)/(kPa)_ \\ \end{tabular} & \
\begin{tabular}{c} **Shear Strength** \\ \(\tau_{p}\)/(kPa)_ \\ \end{tabular} &
\begin{tabular}{c} **Residual Strength** \\ \(\tau_{r}\)/(kPa) \\ \end{tabular} \\ \hline Gravelly sand & 40 & 25 & 18 \\  & 60 & 36.68 & 27.5 \\  & 80 & 45 & 36.5 \\ \hline Coarse sand & 40 & 25.79 & 19 \\ Coarse sand & 60 & 35.34 & 28 \\  & 80 & 45.98 & 38 \\ \hline Medium sand & 40 & 26.59 & 19 \\  & 60 & 35.29 & 28 \\  & 80 & 46.11 & 37 \\ \hline Fine sand & 40 & 27 & 22 \\ Fine sand & 60 & 36.53 & 32 \\  & 80 & 48 & 40 \\ \hline Powdered sand & 40 & 27.5 & 23 \\  & 60 & 38 & 34 \\  & 80 & 49 & 41 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data of shear strength and residual strength of sand–steel interface with different particle sizes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sandy Soil Type** & **Regression Equation** & **Variance R\({}^{2}\)** \\ \hline Gravelly sand & \(\tau_{p}=0.500\sigma+5.560\) & 0.991 \\ Coarse sand & \(\tau_{p}=0.505\sigma+5.418\) & 0.999 \\ Medium sand & \(\tau_{p}=0.488\sigma+6.717\) & 0.996 \\ Fine sand & \(\tau_{p}=0.525\sigma+5.677\) & 0.997 \\ Powdered sand & \(\tau_{p}=0.538\sigma+5.917\) & 0.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Regression equation of shear strength and normal stress of interface. The regression equations of shear strength \(\tau_{p}\) and residual strength \(\tau_{r}\) at the interface between the sand and steel plate, with and without slurry, are shown in Tables 3 and 4, respectively. Combined with the slope and intercept of the regression equation in Tables 3 and 4, we calculated the interface internal friction angle \(\varphi\), the interface cohesion c and the interface sliding friction coefficient \(\mu\), as shown in Table 5.  
From the data in Table 5, it can be obtained that in terms of the interface sliding friction coefficient, \(\mu\) powder sand \(>\mu\) fine sand \(>\mu\) coarse sand \(>\mu\) medium sand \(>\mu\) gravelly sand; in terms of the interface internal friction angle, \(\varphi\) powder sand \(>\varphi\) fine sand \(>\varphi\) coarse sand \(>\varphi\) gravelly sand \(>\varphi\) medium sand; and in terms of the interface cohesion, \(c\) medium sand \(>c\) powder sand \(>c\) fine sand \(>c\) coarse sand \(>c\) gravelly sand. There are differences in the mechanical parameters of the interface between the sand and the steel plate with different particle sizes, which are related to factors such as the sand size, particle gradation and roughness of the pipe itself. In terms of the interface sliding friction coefficient, the friction coefficient of the interface between the sand with smaller particle size and the steel plate is generally greater than that between the sand with larger particle size and the steel plate. In terms of the internal friction angle, the internal friction angle of the interface of the sand and steel pipe with smaller particle size is larger than the internal friction angle of the interface of the sand and steel pipe with larger particle size, while the law is not obvious in the interface cohesion. The reason for the above phenomenon is that the coarse particle content of larger-size sandy soil is greater, the pores between the particles are also larger, the fine particle content is less, and the pores are difficult to completely fill, so the effective interface area between them and the pipe is smaller. The sand with smaller particle size is denser due to a better pore filling effect, so the effective area between the sand and pipe is larger. Therefore, under the same normal stress condition, the shear strength and residual strength of the interface of the sand and pipe are larger, so the interface internal friction angle and sliding friction coefficient are larger.