Probabilistic Stability Assessment of Plane Strain Tunnel Headings in Spatially Random Clays

Estimating the face stability of tunnels is a major issue in tunnel design, especially for shallow shield tunnels. Many attempts have been made for the undrained stability of tunnels against face failure, but most available solutions were obtained from the deterministic analysis assuming homogeneous clay and a nonhomogeneous clay of depth-dependent strength. This paper describes the probabilistic stability analysis of plain strain tunnel headings in spatially varying clays with trends of undrained shear strength linearly increased with depth. Using the adaptive finite element limit analysis, the problem is solved based on the generation of nonstationary random fields with Monte Carlo simulations. The stability statistics and collapse mechanisms of pressurized headings under surcharge on the ground surface are presented, considering the effect of cover depth, unsupported length, and strength gradient. The worst-case correlation length where a mean heading stability reaches a minimum is examined. The safety factors are determined for headings at distinct target levels of failure probability. It is found that neglecting the clay randomness leads to the overprediction of heading stability, and it is more prominent for deeper headings. The results provide guidance for the practical estimation of tunnel headings in spatially varying undrained clay that can be encountered in tunneling.