An Analysis of Deformations and Internal Forces of the Pipe-roof by Double-parameter Elastic Foundation Beam Models

Pipe-proof supporting method has been widely applied in mining shallow tunnels.Mechanical characteristics of the pipe-proof are analyzed theoretically in order to be helpful to the design and construction of the pipe-roof supporting.Taking Xidan station engineering on Line 4^# of Beijing Subway as an example, the double-parameter elastic foundation beam models for the pipe-roof are put forward.Differential equations of the corresponding deformations,turning angles and bending moments are deduced and the solutions of these models are given.The deformation and internal force characteristics of the pipe-roof are analyzed based on the supporting conditions of the pipe-roof ends.The analysis results show that the maximum deformation and the maximum shear of the pipe-roof are presented near the working surface at the excavated and non-supported section and the surrounding rock are loosened and deformed in the area of 1.5 to 2 times of the excavated height ahead the working surface.