# Experimental Study of the Behavior of Rectangular Excavations Supported by a Pipe Roof
## 3 Results and Analysis
### Ground Settlement  
Figure 9 shows the variation of the maximum ground settlement with the ratio (\(\Delta/D\times 1000\)) for the tests conducted with and without the pipe roof. The maximum settlement was observed at approximately \(0.25D\) in front of the excavation. The presence of the pipe roof induces an important decrease in the ground settlement. Increasing pipe stiffness reduces the soil settlement; however,  
Figure 8: Variation of the normalized pressure on the excavation face \((P/P_{0})\) with the face displacement. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Load**} & \multicolumn{2}{c}{**The Relative Stiffness**} & \multicolumn{2}{c}{**Load**} & \multicolumn{2}{c}{**Load Deviation**} \\ \hline \(P_{min}\)/\(P_{0}\) & \(P_{f}\)/\(P_{0}\) & **of the Pipe Roof** & \(P_{p-U}\)/\(P_{0}\) & \(P_{p-min}\)/\(P_{0}\) & \(\xi\)/\(\
u\)\% & \(\xi_{max}\)/\(\
u\)\% \\ \hline \multirow{3}{*}{0.151} & \multirow{3}{*}{0.253} & 0.5 & 0.128 & 0.109 & 15.23 & 27.85 & 12.62 \\  & & 1.0 & 0.118 & 0.102 & 21.85 & 32.45 & 10.60 \\ \cline{1-1}  & & 2.0 & 0.110 & 0.097 & 27.15 & 35.76 & 8.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Influence of the pipe roof on the key pressure parameters. this influence is weak. The initial stage corresponds to the fast reduction in the load. The sliding block moves, the pipe roof deforms, the soil arch is generated and a small settlement occurs when the surface settlement enters the development stage. The displacement of the excavation face continues to increase until the pipe roof is balanced with the upper soil arch and supports the overburden pressure. Finally, the sliding block is separated from the upper pipe roof and the surface settlement becomes stable. The settlement curves with and without the pipe roof begin to separate rapidly in the settlement development stage. The pipe roof is effective in limiting the development of surface settlement during the settlement development stage. The surface settlement without the pipe roof at the point where the gradient of the settlement begins to increase significantly is defined as the critical settlement, \(S_{cr}\), and the corresponding state is defined as the critical state. Under the effect of the pipe roof, considering the disturbance requirements of the surrounding environment, the surface settlement at the end of the initial nonsedimentation stage is defined as the surface critical settlement, \(S_{p-cr}\). Table 4 shows the comparison of the excavation face displacement corresponding to the limit support pressure and the surface critical settlement, respectively. The displacement values are taken as the corresponding normalized parameters. \(\Delta_{PU}\) is defined as the excavation face displacement corresponding to the \(P_{U}\), \(\Delta_{SCR}\) is the excavation face displacement corresponding to the \(S_{cr}\), \(\Delta_{p-PU}\) is the excavation face displacement state corresponding to the \(P_{p-U}\), and \(\Delta_{p-SCR}\) is the excavation face displacement corresponding to the \(S_{p-cr}\). For the test without the pipe roof, the displacement of the excavation face corresponding to \(P_{U}\) is smaller than the displacement corresponding to \(S_{cr}\), indicating that the surface settlement has hysteresis with respect to the displacement of the excavation surface. At the ultimate state, the displacement of the excavation face is small, with a quasi-zero surface. The displacement of the excavation face required to generate the surface critical settlement, \(S_{cr}\), is quite large. When there is no pipe roof, \(\Delta_{PU}/\Delta_{SCR}\) is less than 1, indicating that the ground settlement monitoring during tunnel construction to judge the stability of the excavation face is insufficient due to hysteresis. Consequently, it is necessary to monitor and control the excavation face pressure simultaneously to ensure the stability.