Unification of the Mechanical Model and Parameter Analysis of the Elastic Foundation Beam of Pipe-Roof

Abstract

Based on the existing model of pipe-roof considering the arching effect, combined with the mechanical model of pipe-roof when the tunnel is excavated to the end, a unified mechanical model of the elastic foundation beam for pipe-roof is established. Deflection and internal force calculation formulas of the model were derived. Combined with actual engineering cases, the model was compared and analyzed, and the parameters affecting the pipe-roof were analyzed by taking the unified model as an example. The results show that the established unified elastic foundation beam model can better represent the actual stress state of a pipe-roof and the model has strong applicability. The stress state of the pipe-roof at the end of excavation can be calculated by changing the boundary conditions of the model. When the diameter of the steel pipe is 108–114 mm, the supporting effect of the pipe-roof is similar. When Ec (elastic modulus of converging) > 40.0Eg (elastic modulus of ground rock), the excavation footage and the diameter of the steel pipe have little effect on the deflection and bending moment of the pipe-roof. Therefore, increasing the elastic modulus of the reinforced area is the most effective method to reduce the deflection and internal force of the pipe-roof. The longer the residual length of the pipe-roof in surrounding rock, the safer the tunnel will be during excavation. The economically reasonable value of the residual length of the pipe-roof in surrounding rock is 2–3 m.