Dimensionless Parameter Diagrams for the Active and Passive Stability of a Shallow 3D Tunnel Face

Abstract

The methods for calculating the elliptical cone’s geometric parameters of multiple elliptical cone sliders were improved by introducing expression of elliptical path in 3D space. This elliptical path is the intersecting line of a cone and inclined cutting plane. Based on upper-bound limit analysis method and an improved method, Sequential Quadratic Programming (SQP) method was employed to obtain optimal upper bound solutions of failure pressure. The effectiveness of this method was verified by a comparative analysis, and a detailed parametric study on the failure pressure and failure modes was presented. In this study, the stability and failure modes of tunnel face are significantly affected by internal friction angle φ and dimensionless parameter C/D for both active and passive failure; by contrast, dimensionless parameters γD/c and σs/c have small effects. It is also found that dimensionless parameters C/D and σs/c have no effect on the results if the failure region does not reach the ground surface.