Calculation model for vertical stress of shallowly buried pipe-roofing tunnels and its engineering application

The traditional horizontal differential element method used to characterize the soil arching effect neglects the contribution of inter-layer shear forces to vertical stress transfer, leading to conservative calculation results. In view of this, the pipe-roofing tunnel was first simplified into a "trapdoor" model. A finite element limit analysis (FELA) method was adopted to systematically investigate the variation of the slip angle of the shallow trapdoor under different depth-to-width ratios and soil internal friction angles. Accordingly, based on the trajectory of the major principal stress, a vertical stress calculation model of an arched differential element was established, and the vertical stress solution for the shallow trapdoor was derived. Furthermore, the influences of soil internal friction angle, dilation angle, and surface surcharge on the normalized vertical stress of the trapdoor were clarified. Finally, the proposed model was applied to a pipe-roofing tunnel project to explore its engineering applicability. Research results indicate that the calculation results of the proposed model show good agreement with existing solutions, FELA solutions, and laboratory model test results; compared with the classical Terzaghi theory and code methods, the proposed model reduces the normalized vertical stress by 30.7% and 45.3%, respectively, and it reduces carbon emissions by 9.1% and 16.6%, respectively.