Table2_Unification of the Mechanical Model and Parameter Analysis of the Elastic Foundation Beam of Pipe-Roof.XLSX

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.

基于考虑拱效应的现有管棚（pipe-roof）模型，结合隧道掘进至终点时的管棚力学模型，建立了统一的管棚弹性地基梁（elastic foundation beam）力学模型，并推导了该模型的挠度与内力计算公式；结合实际工程案例对该模型进行对比分析，并以该统一模型为范例，对影响管棚的各类参数展开分析。研究结果表明，所建立的统一弹性地基梁模型能够更精准地反映管棚的实际受力状态，且具备较强的工程适用性，通过调整模型的边界条件，即可计算隧道掘进终点处管棚的受力状态；当钢管直径处于108~114 mm区间时，管棚的支护效果相近，当Ec（收敛弹性模量，elastic modulus of converging）大于40.0倍的Eg（围岩弹性模量，elastic modulus of ground rock）时，隧道掘进进尺与钢管直径对管棚的挠度及弯矩影响微乎其微，因此提升加固区域的弹性模量是降低管棚挠度与内力的最有效手段；管棚在围岩中的残余长度越长，隧道掘进过程中的安全性越高，管棚在围岩中的残余长度的经济合理取值区间为2~3 m。