Calculation of earth pressure distribution on the deep circular tunnel considering stress-transfer mechanisms in different zones

• A multi-arch model for predicting the distribution of the vertical earth pressure on a deep tunnel was proposed. • A formula for calculating the height of the loosened zone was deduced. • The verification of the proposed model was checked by comparison with the centrifuge model tests and numerical simulations. It is of great significance for ensuring the lining safety to reasonably determine the earth pressure on the tunnel, especially the deep-buried tunnel. In this study, the stress-transfer mechanisms of soils in different zones above the tunnel were analyzed firstly. A multi-arch model for calculating the distribution of the vertical earth pressure on a deep tunnel in dry sand was then proposed based on the limit equilibrium method. The model is composed of three parts: the upper end-bearing arch, the stability zone and the lower friction arch. The key parameters (i.e., width and height of friction arch zone, thickness of end-bearing arch zone and lateral stress ratio in friction arch zone) in the proposed model were suggested according to the existing literature, and a formula for predicting the height of the friction arch zone was deduced. The experimental and numerical results and Terzaghi’s solution were adopted to assess the validity of the proposed model, which indicates that the proposed model not only coincide with the test results of average vertical earth pressures on the tunnel, but also describe the nonuniform distribution characteristics of vertical stress on the circular tunnel, namely, the minimum vertical earth pressure is located at the centreline of the tunnel, and then gradually increases as it moves away from the centreline. Finally, the impacts of geotechnical and geometrical parameters on the earth pressure were discussed.