Stability analysis of tunnels and underground openings

Stability analysis of tunnels and underground openings

This thesis investigates both undrained and drained stability of three various configurations of underground openings related to tunnelling (i.e. tunnel heading, single circular tunnel and twin circular tunnels) in both two‐dimensional (2D) and three-dimensional (3D) spaces. Finite element limit analysis (FELA) is used to determine lower and upper bound stability limits for a range of various geometrical and material scenarios. The thesis is divided into two parts.

Part A focuses on the undrained stability analysis using Broms and Bennermarks’ original stability number (N). For the 2D undrained analysis, the factor of safety values was calculated using the shear strength reduction method (SSRM) in FELA, while for the 3D undrained analysis, the critical supporting pressure values were calculated using the load multiplier method (LMM) in FELA. The relationships between the factor of safety and the stability number (N), which includes design soil and geometry parameters, were investigated for active (collapse) and passive (blowout) failures. Several design charts, tables and equations were produced to better assist in understanding these relationships.

Part B focuses on drained analysis using tunnel stability factors (Fc, Fs and Fγ). This approach is convenient for stability analysis of underground openings with a wide range of angle of internal friction (ϕ = 0 - 40˚) and depth ratios (C/D = 1 - 10). The critical support pressure required to maintain stability can then be determined by substituting the corresponding factors in a conventional equation that is analogous to Terzaghi’s bearing capacity equation.

Although the FELA technique can define the actual failure load from below (lower bound solution) and from above (upper bound solution), the obtained results were compared with available solutions (theoretical, experimental and numerical) in the published literature. Also, the finite difference method (FDM), via the software FLAC 2D has been used over the same parametric range to validate the 2D (FELA) results for tunnel heading, single circular tunnel and twin circular tunnels under undrained condition.

This thesis contributes significantly to practising engineers as comprehensive design tables, figures and equations have been produced for the design of tunnel stability using the rigorous upper and lower bound solutions in both 2D and 3D spaces.