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Tunneling in soft clay requires accurate estimation of the inner support pressure to prevent undesired ground settlement and maintain the overall soil stability. Previous researchers have shown that the stability factor approach, which is analogous to Terzaghi's bearing capacity factors [critical stability number (Nc), Ns, and Nγ)], is effective and efficient to determine the limit loads of many geotechnical stability problems. Therefore, this paper aims to study the stability factors of four various tunnel shapes in undrained clay: the two-dimensional (2D) tunnels of circular, square, and heading in plane strain, and the three-dimensional (3D) circular tunnel heading. Using the advanced finite-element limit analysis (FELA), rigorous upper-bound (UB) solutions of the undrained stability factors (Fc, Fs and Fγ) will be produced for various tunnel depth ratios (C/D). Numerical UB results are compared with lower bound (LB) solutions. Comprehensive design charts, tables, and equations will be presented for practitioners to estimate the critical tunnel support pressure at collapse. [ABSTRACT FROM AUTHOR]

This paper aims to study the three-dimensional (3D) tunnel heading pressure of twin circular tunnels in a drained cohesive–frictional soil using a stability factor approach and finite-element limit analysis (FELA). The primary concept adopted will be the use of a conventional equation that is similar to the traditional bearing capacity factors (e.g., Nc, Ns, and Nγ) in Terzaghi's bearing capacity equation. For various spacing ratios (S/D) between the tunnels, the stability of the tunnels is expressed in terms of nondimensional tunnel stability factors (e.g., Fc, Fs, and Fγ), which are functions of the depth ratio (C/D) and soil internal friction angle (ϕ). For conciseness, the results will be presented in charts and tables with the tunnel stability factors that used the rigorous FELA upper (UB) and lower bound (LB) solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the use of stability factors to estimate tunnel heading pressures. The primary method adopted is a conventional equation based on the soil property and stability factors, analogous to the bearing capacity factors (N c , N s and N γ) of strip footings. The finite element limit analysis (FELA) is employed to determine rigorous upper bound (UB) and lower bound (LB) solutions of stability factors (F c , F s and F γ), which are functions of the depth ratio (C/D) and soil internal friction angle (Ø). The obtained results are compared and validated by using the finite difference analysis as well as other available published results in the literature. A number of examples are illustrated on how to use the factors to estimate tunnel heading pressures. [ABSTRACT FROM AUTHOR]

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]