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This paper investigates the three-dimensional (3D) stability of a circular tunnel in drained cohesive-frictional soil. Numerical simulations are performed to study the face stability of a circular tunnel for various soil properties and tunnel diameter-to-depth ratios. The finite element limit analysis (FELA) is employed to determine rigorous upper and lower bounds solutions of tunnel stability factors (F c , F s and F γ), which are functions of the depth ratio and soil internal friction angle. These stability factors are used to estimate the critical heading pressures at collapse. The obtained results are compared with existing published solutions in the literature. The study aims to improve the available solutions by using the latest 3D finite element limit analysis technique. A number of examples are provided, which demonstrate the practical use of the three stability factors in estimating tunnel heading pressures. [ABSTRACT FROM AUTHOR]

The use of finite elements and limit analysis in the stability analysis of geo-structures is not uncommon nowadays, with the assumption of associated flow rule and rigid perfectly plastic constitutive soil model. Nevertheless, the simplified assumption may lead to misevaluation of the objective function for the nonlinear optimisation solution, thus giving rise to uncertainty in the design of geo-structures. In this study, the influence of non-associated flow rule on the stability evaluations for obliquely- and eccentrically-loaded shallow foundations, as well as for retaining structures with cohesionless granular backfill, is examined using lower bound finite elements and second-order cone programming (SOCP). A wide range of dilation angles (ψ) is considered for the study (e.g., from zero to a maximum of soil internal friction angle φ), and it is generally observed that failing to consider the non-associated flow rule in the soil constitutive model would yield non-conservative designs of geo-structures. These inaccurate predictions and subsequent unreliable stability analysis are more pronounced in cases of large soil internal friction angles. The findings in this study would be of great importance for practical design applications. [ABSTRACT FROM AUTHOR]