# Theoretical Analysis on the Effectiveness of Pipe Roofs in Shallow Tunnels
## 2 Establishment of a Pipe Roof Analysis Model  
### The Composition and Effects of the Pipe Roof  
The pre-supported structure of a pipe roof is generally composed of a guide wall (or a set of arches), a guide pipe, a steel pipe, and a grouting reinforcement area. Scholars generally believe that the pre-support protection function of a pipe roof can be achieved by using a composite shell composed of a steel pipe and grouting reinforcement layer to withstand the surrounding rock pressure. Therefore, a composite shell composed of the steel pipes of the pipe roof and the rock mass of the grouting area is the main bearing member of the pre-supported protective structure of the pipe roof. A cross-sectional schematic diagram of the bearing members is shown in Figure 1.  
The purpose of using pipe roof pre-support is to reduce the formation deformation caused by tunnel excavations, improve the stability of the palm surface and the excavation surface, and ensure the safety of construction. Therefore, the effect of pre-support of the pipe roof is mainly measured by deformation of the excavation surface, the stability of the palm surface, and the surface settlement. The tube shed carrying shell can transfer the ground stress that the palm face must bear to the initial support and deeper rock mass, improving the force state of the palm surface and thus also improving the stability of the palm surface. To control formation deformation, a theoretical analysis model of the support effects of the pipe roof based on the construction of force deformation considering the bearing of the pipe roof is established to realize a quantitative descrip  
Figure 1: Schematic diagram of the bearing members of a pipe roof.  
of the surrounding rock of the excavation surface and the settlement of the ground, so as to more accurately guide the design and construction of the pipe roof.  
To study the role of the bearing shell composed of a steel pipe, slurry, and surrounding rock in the grout reinforcement area, the timing and construction conditions of the pipe roof should be considered. First, the steel pipe of the pipe roof and the grouting reinforcement area play specific roles in the pre-support system of the pipe roof. For the grouting reinforcement area, on the one hand, we found that in the grouting process of the pipe roof, due to the unevenness of the joint cracks of the rock mass, the effect of grouting reinforcement on improving the physical properties of the rock is not uniform. On the other hand, for both a pipe roof at the tunnel opening and a pipe roof in the tunnel, although a pulp stop section is reserved at the tail of the steel pipe of the pipe roof, a lack of uniformity often occurs due to the low-lying stress state of the rock mass above the slope of the tunnel opening or the palm. When the grouting pressure reaches a certain level, it will first form a crack in the area that penetrates the surface or palm surface such that the slurry flows out along the crack of this type. These cracks that penetrate the outside world make it difficult for the grouting pressure to meet the design requirements, resulting in a decrease in the reinforcement effects of the rock mass. Therefore, it is difficult for the surrounding rock in the reinforcement area to form a stable holding layer with bearing capacity. The role of this rock is mainly to improve the stiffness of the pre-support boundary and reduce the plastic deformation of the surrounding rock between the steel pipes of the pipe roof, thereby playing a protective role in the support boundary. Therefore, in the mechanical response analysis of the bearing shell, the role of the grouting reinforcement area as a bearing unit is ignored, and the combined beam composed of the steel pipe and slurry is used to withstand the surrounding rock pressure.