This section presents the results concerning the set of tests conducted with a buried depth ratio of C/D = 1. It includes 4 tests: a test without the pipe roof and 3 tests conducted with = (0.5, 1.0 and 2.0).
3.1. Excavation Face Support Pressure
Figure 8 shows the variation of the ratio
P/
with the excavation face displacement (
/
D);
P and
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 (
) on the variation of
P/
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.
Table 3 shows the comparison of the minimum load and the final load on the excavation face. In this table,
and
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
, respectively.
is the load at the end of the decrease stage under the effect of the pipe roof, whlie
are the final loads without the pipe roof.
denotes the ratio (
-
)/
, which indicates the excavation face load deviation of the ultimate state, while
designates (
-
)/
, which indicates the excavation face load deviation corresponding to the state of the maximum unloading ratio.
Table 3 shows that with the pipe roof,
/
decreases with increasing pipe stiffness. However, the influence of piles stiffens (
) on
/
is low; the increase of
from 0.5 to 2.0 induces a decrease of approximately 14% in
/
.
As seen by comparing the two working conditions, and increase with increasing pipe roof stiffness. - 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.
3.2. Ground Settlement
Figure 9 shows the variation of the maximum ground settlement with the ratio (
/
D× 1000) for the tests conducted with and without the pipe roof. The maximum settlement was observed at approximately 0.25
D 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, 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, , 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, .
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.
is defined as the excavation face displacement corresponding to the
,
is the excavation face displacement corresponding to the
,
is the excavation face displacement state corresponding to the
, and
is the excavation face displacement corresponding to the
.
For the test without the pipe roof, the displacement of the excavation face corresponding to is smaller than the displacement corresponding to , 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, , is quite large.
When there is no pipe roof, / 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. The / is greater than 1 with the pipe roof, indicating that the monitoring of the excavation face has hysteresis with respect to surface settlement. In conclusion, the pipe roof can effectively limit the environmental disturbance during the construction process.
Figure 10 shows the three-dimensional maps of the ground surface settlement without the pipe roof. The surface settlement area is concentrated on the left side due to the frictional force with the plexiglass. The settlement zone has a spindle shape with a lateral width much greater than the longitudinal length. At the end of the initial development stage, a spindle-shaped settling tank appeared in the ground surface. With the movement of the excavation face, the settlement inside the spindle-shaped settling tank increased, but the range did not change during the experiment.
The white void in
Figure 10f is due to excessive deformation of the ground surface in the final stage. The black stone speckle slipped off, and the adjacent two photographs are not recognized by the corresponding algorithm, which results in a calculation error.
Figure 11 shows the three-dimensional maps of the ground surface settlement with the pipe roof.
Settling was significantly concentrated on the left side of the tank. Regardless of the edge friction, the settling tank is half-elliptic. The length of the elliptical semimajor axis is 1.5L (L is the width of the model box culvert), and the ratio of the semimajor axis to the semiminor axis is approximately 2.5:1. The figure does not show an obvious change in the ground surface from the initial stage to the critical stage. The elliptical settling tank appeared and developed slowly during the development stage. Combined with the results of other working conditions, there is almost no difference in the elliptical settling tank range for different pipe roof stiffness values.
A comparison of
Figure 10 and
Figure 11 shows that the pipe roof increases the range of the longitudinal settling tank and transmits the overburden pressure above the sliding block to the soil on both sides of the sliding block, which effectively reduces the surface settlement.
3.3. Pipe Roof Deformation
The deformation of the pipe roof was monitored by the optical fiber in real time. The marker point of the maximum vertical deformation is at pipe No. 6 approximately 0.25
D in front of the excavation face.
Figure 12 shows the variation of pipe’s maximum deformation with the displacement of the excavation face. The deformation variation includes three stages. In the initial stage, the sliding surface is generated, the pipe roof is almost free from the pressure difference without deformation. Then, the displacement of the sliding block causes the vertical deformation of the pipe roof. With the increase in the excavation face displacement, the sliding block is separated from the upper pipe roof gradually. Finally, the pipe roof supports the overburden pressure and almost no displacement occurs. The vertical deformation increases with decreasing pipe roof stiffness.
Figure 13 shows the shape of pipes with relative stiffness
= 1.0. The maximum point of vertical deformation of the pipe roof is approximately 35 mm in front of the excavation face. The vertical deformation of pipe No. 10 accounts for approximately 60% of that of pipe No. 2 and No. 6 (
Figure 5), indicating that the vertical deformation of the central pipe is significantly larger than that of the edge pipes.
Figure 14 shows the comparative analysis of the vertical deformation of the pipe roof and the corresponding surface settlement.
is defined as the difference between the ground settlement and the pipe deformation. Under the same working conditions, the vertical deformation of the pipe roof is greater than the corresponding ground surface settlement.
decreases with increasing excavation face displacement and is insensitive to the relative pipe stiffness, reflecting the continuous development of the soil arch structure.
Figure 15 shows the comparison between the shape of the pipe roof and the settlement tank of its vertical projection line on the ground surface when the pipe relative stiffness is 1.0 and the buried depth ratio equals 1. The shape of pipe No. 6 and the corresponding surface settlement curve are selected.
Figure 14 shows that the range of ground settlement is larger than that of the pipe roof deformation. The maxima of the soil settlement and pipe roof deformation are located at approximately 0.25
D from the excavation face.
3.4. Soil Pressure
The axis direction of the box culvert is defined as longitudinal direction, and the direction perpendicular to the axis of the box culvert in the horizontal plane is the horizontal direction.
Figure 16 shows the variation of the horizontal earth pressure coefficient (
=
/
) recorded from the four earth pressure cells at the intersection of section
C-
C and section
-
. This test was conducted without the pipe roof. In the initial stage, the horizontal lateral pressure coefficient is equal to the initial lateral pressure coefficient
. It increases first then decreases and finally stabilizes. At high values of the excavation lateral displacement, we observe an increase in the horizontal earth pressure coefficient with a depth up to a maximum (approximately 0.85) and then a decrease with depth down to 0.6.
Figure 17 shows the variation of the longitudinal lateral pressure coefficient (
) during the test. It has the same trend as the horizontal pressure coefficient, but the final value of
in the lower part is smaller than
; it is close to the active earth pressure coefficient
. The change in lateral pressure coefficient in the two directions reflects the formation of the soil arch.
Figure 18 and
Figure 19 show the results obtained with the pipe-roof reinforcement. The variation in the lateral pressure coefficients has similar trends as those observed in the excavation without the pipe roof. The pipe roof stiffness does not influence the distribution of the earth pressure coefficients.
Comparison of
Figure 17 and
Figure 19 shows that the pipe-roof reduces the coefficient of the longitudinal lateral pressure.
3.5. Excavation Face Instability Mode
White sand layers were used in the experimental tests to follow the soil deformation during the excavation process.
Figure 20 shows the instability process development during a test without the pipe roof.
Figure 20b shows the initiation of the shear sliding zone in front of the rectangular excavation face.
Figure 20c–e show the settlement of the soil layer corresponding to the different excavation face displacements. It can be clearly seen that the horizontal white quartz sand line was bent from the bottom to the top and extends to the surface, and the width of the settlement was measured as 0.4
D. Then, the settlement appeared on the ground surface with a settlement width equal to the longitudinal width of the failure zone. In
Figure 20f, the failure zone extended to the ground surface, and the soil arch was completely destroyed.
Figure 21 shows the results of the excavation supported by a pipe roof with
= 1.0. The obvious curvature of the horizontal white quartz is caused by the sand leakage in the gap between the plexiglass panels and the pipe roof. The settlement of the ground surface can be determined by the change of the white line. Similar to the test without the pipe roof,
Figure 21c–e show the settlement of the soil layer corresponding to the different excavation face displacements. The horizontal white quartz sand lines were bent slightly from the bottom to the top but did not extend to the ground surface. The pipe roof blocked the development of the sliding surface and the width of the soil arch was different from the width of the top of the sliding block.
Figure 21f shows the final state with a settlement of 0.6
D. The pipe roof and the overlying soil with the soil arch reached the state of stress balance, and the failure zone does not extend to the surface.
Compared with the condition without the pipe roof, the pipe roof causes an increase of approximately 50% of the longitudinal width of the failure zone. The failure zone does not extend to the ground surface.