# Theoretical Analysis on the Effectiveness of Pipe Roofs in Shallow Tunnels
## 5 Discussion  
Based on the above theoretical analysis of the pre-support effects of the pipe shed, we compared the control effects of the pipe shed on formation deformation under different design and construction parameters and proposed general conclusions for controlling formation deformation.  
While keeping other design parameters unchanged, we investigated the distribution curves of the formation loss rate and the distribution curves of maximum surface subsidence for pipe diameters of 89, 108, 152, and 180 mm, as shown in Figure 8. The effect of pipe shed pipe diameter on pre-support was also studied. The equivalent section's moment of inertia and the corresponding elastic modulus of the composite beam composed of a steel pipe and slurry are shown in Table 2.  
Keeping the other design parameters unchanged, Figure 9 presents the distribution curves of the formation loss rate and maximum surface subsidence for pipe-shed design spacing of 40, 60, 80, and 100 cm. We also studied the effects of the circumferential spacing of the pipe shed on pre-support.  
Keeping the other design parameters unchanged, Figure 10 shows the distribution curves of the formation loss rate and maximum surface subsidence for an excavation footage length per cycle of 0.5, 0.75, 1, 1.25, and 1.5 m. The influence of the excavation footage length on the pre-support effect was also analyzed.  
Figures 8-10 show that the ability of the pipe shed to control formation deformation is better when the pipe diameter is larger, the circumferential spacing is smaller, and the footage length of the cyclic excavation is shorter. To further study the correlation between steel pipe diameter, excavation depth, circumferential spacing, and formation deformation control, we investigated the influence of various design parameters on the formation loss rate using the formation loss rate at a distance of 30 m from the tunnel opening.  
Figure 11 shows that, with the other conditions unchanged, a thicker pipe diameter corresponds to a smaller formation loss rate. However, with a continuous increase of the pipe diameter, the influence on the formation loss rate becomes increasingly smaller. This result indicates that when the diameter of the pipe used is small, replacing the steel pipe with one of a larger diameter can effectively improve the ability of the pipe shed to control the formation deformation. If a thicker steel pipe is selected and cannot control formation deformation, it is not economical to consider increasing the diameter of the steel pipe.  
Figure 11: Relationship curve between the pipe diameter and formation loss rate.  
Figure 10: Influence of the excavation footage length on the formation deformation distribution.  
Figure 12 shows that, with the other conditions unchanged, the formation loss rate increases linearly with an increase in the hoop spacing of the tube shed. Reducing the circumferential spacing of the steel pipes can effectively improve the ability to control formation deformation.  
Figure 13 shows that with the other conditions unchanged, the formation loss rate increases linearly with an increase in the footage length of the cyclic excavation. This result indicates that the footage length of cyclic excavation has an obvious influence on the pre-support effect of the pipe shed. During the construction process, the footage length of each cycle should be strictly controlled to ensure the pre-support effect.