Theoretical study on earth pressure on shallow tunnel considering principal stress rotation

The traditional analytical methods for calculating the earth pressure on shallow tunnel are irrespective of the principal stress rotation, and do not reveal the real stress state of soils, and thus result in inaccurate values. A new quantitative method is proposed to acquire the earth pressure on shallow tunnel in sandy soil considering the principal stress rotation. The rotation process and the stress state are firstly analyzed based on the generalized collapse mode for surrounding soil. To obtain the vertical pressure on overlying soil, the equilibrium equation for the horizontal differential layer is established, considering the corresponding relationship among the lateral interlaminar stress, average interlaminar stress and average vertical stress. Eventually the earth pressure is derived by the equilibrium equation for the lateral soils of tunnel. The results show that the ratio of vertical to major principal stress decreases with the increase of the distance to center line, and it presents a decreasing-to-increasing trend with the increase of the internal friction angle. The values of earth pressure calculated by the proposed method fit well with the experimental results when the tunnel is shallow. The new method is even superior to the method irrespective of the principal stress rotation and Terzaghi’s semi-empirical method. The accuracy of the proposed method is validated. It may provide a theoretical basis for the design of shallow tunnel.