Loosening zone and earth pressure around tunnels based on modified ellipsoid theory

The prediction of loosening zone around tunnels is crucial for the calculation of loosening earth pressure. Therefore, in order to accurately and easily predict the limit loosening zone around tunnels under different geological characteristics and working conditions, the ellipsoid theory is firstly modified from the perspective of ground loss. Then, the modified ellipsoid theory is verified by using the self-designed test device and the PIV technique. Finally, the equation for the loosening earth pressure around tunnels is modified by combining the ellipsoid theory and the rotation of the principal stress axis of the soils inside the loosening zone. The study shows that: (1) With the generation and increase of ground loss, the ground outflow area and the limit loosening area above tunnels resemble the shape of an ellipse, and their long and short semi-axes are gradually expanded. The modified ellipsoid theory is more consistent with the experimental results than the existing theories through comparison. (2) The modified formula for the loosening earth pressure integrates the range of loosening zone and the soil arching effect, and the rationality of the modified formula for calculating the loosening earth pressure is verified by comparing with the experimental results in the related literatures. So the proposed formula can be used for the calculation of the loosening earth pressure around tunnels and pipelines in sandy strata.