# Experimental Study of the Behavior of Rectangular Excavations Supported by a Pipe Roof
## 3 Results and Analysis
### Excavation Face Support Pressure  
Figure 8 shows the variation of the ratio \(P/P_{0}\) with the excavation face displacement (\(\Delta/D\)); \(P\) and \(P_{0}\) denote the pressure applied to the excavation face and its initial value, respectively. \(D\) is the height of the rectangular excavation face. This shows that the pressure for the test without the pipe roof drops rapidly first; after reaching the minimum value, it increases slowly up to a stabilized value. For tests with the pipe roof, the pressure also drops rapidly to a stabilized value. The influence of pipe stiffness (\(EI\)) on the variation of \(P/P_{0}\) is very low.  
Figure 8 shows also that the relative displacement required for the load stability under the effect of the pipe roof is larger than that without the pipe-roof. The relative displacement required for the load-descending stage with the pipe roof is approximately 3 times that without the pipe roof. In summary, the pipe roof can reduce the load on the excavation face and suppress the load fluctuation.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Monitoring Equipment** & **Monitoring Object** & **Precision** \\ \hline DIC binocular camera & The settlement of the ground surface & 0.01 mm \\ Distributed optical fiber & The deformation of pipes & \(\leq\)1.0\% FS \\ Earth pressure cell & Earth pressure in soil stratum & \(\leq\)0.5\% FS \\ Pull pressure sensor & The axial force of excavation face & \(\leq\)0.5\% FS \\ Displacement sensor & The displacement of excavation face & \(\leq\)0.5\% FS \\ \hline \hline \end{tabular}
\end{table}
Table 2: Monitoring system.  
Table 3 shows the comparison of the minimum load and the final load on the excavation face. In this table, \(P_{min}\) and \(P_{p-U}\) denote the minimum load without the effect of the pipe roof and the load under the effect of the pipe roof corresponding to the same displacement of \(P_{min}\), respectively. \(P_{p-min}\) is the load at the end of the decrease stage under the effect of the pipe roof, while \(P_{f}\) are the final loads without the pipe roof. \(\xi_{U}\) denotes the ratio \((P_{min}\)-\(P_{p-U})/P_{min}\), which indicates the excavation face load deviation of the ultimate state, while \(\xi_{max}\) designates \((P_{min}\)-\(P_{p-min})/P_{min}\), which indicates the excavation face load deviation corresponding to the state of the maximum unloading ratio.  
Table 3 shows that with the pipe roof, \(P_{p-U}/P_{0}\) decreases with increasing pipe stiffness. However, the influence of piles stiffens (\(EI\)) on \(P_{p-U}/P_{0}\) is low; the increase of \(EI\) from 0.5 to 2.0 induces a decrease of approximately 14% in \(P_{p-U}/P_{0}\).  
As seen by comparing the two working conditions, \(\xi_{U}\) and \(\xi_{max}\) increase with increasing pipe roof stiffness. \(\xi_{max}\)-\(\xi_{U}\) describes the reduction of the excavation face load from the limit state to the state of the maximum unloading ratio. It decreases with increasing pipe stiffness, which shows an improvement of the excavation stability with increasing pipe roof stiffness.