Probabilistic analysis of tunnel face stability in spatially variable soil

the limit analysis incorporated with the random field theorem is an effective approach for the probabilistic analysis of tunnel face stability. However, the existing incorporation procedure is not sufficiently efficient and accurate. A modified random field model, which is directly superimposed onto the rotational failure mechanism, is proposed to address this issue. In comparison with previous methods, the proposed approach avoids the generation of redundant random field elements and evades the inaccurate matching procedure of the elements, thereby enabling efficient and accurate estimation of the failure probability of a tunnel face. Moreover, cross-correlated random fields with the rotated anisotropy are readily generated with the proposed approach. Parametric sensitivity analysis is performed with Monte Carlo simulations to investigate the effects of the coefficient of variation, the scale of fluctuation, cross-correlation coefficient, and rotated anisotropy on the failure probability of a tunnel face. It is found that: (1) the failure probability is more sensitive to the scale of fluctuation in the vertical direction than that in the horizontal direction; (2) neglecting the cross-correlation of soil shear strength parameters leads to a slightly conservative design for tunnel face stability; (3) the influence of rotated anisotropy on the failure probability of a tunnel face is limited unless the soil exhibits high levels of uncertainty in its friction angle. Application of the proposed approach to multi-layered soil demonstrates its superiority in the probabilistic analysis of tunnel face stability in spatially variable soil.