Numerical solution of loose earth pressure in tunnels considering elliptical slip surface and soil arching effect

The loose earth pressure in tunnels is closely related to the soil arching effect and the development of the loosening zone. Current methods overlook changes in the shape and position of the slip surface at different stages of the loosening zone, neglecting the relationship between these changes and principal stress rotation. An elliptical slip surface model has been developed to accurately capture variations in the shape and position of the slip surface as the loosening zone evolves. A lateral earth pressure coefficient for various inclinations of the slip surface was established to illustrate the relationship between the geometry of the slip surface and the rotation of principal stresses. Factors such as ground loss, soil arching effect, and elliptical slip surfaces, were integrated into the Terzaghi model, deriving and validating a numerical method for tunnel loose earth pressure. Parametric analysis targeting the volume loss ratio (VL) and cover-to-diameter ratio (C/D) revealed that linear, parabolic, and other slip surface forms presented are approximations of the elliptical slip surface at various stages. Loose earth pressure increases rapidly with C/D and then grows slowly but steadily. It decreases quickly with an increasing VL, then increases gradually and stabilizes.