Numerical modelling of shield tunnel face failure through a critical state sand plasticity model with nonlocal regularization

During shield tunneling in sand strata, variations in the state of sand can lead to localized instability and strength loss, which brings about numerical difficulties. This paper numerically investigates how nucleation and propagation of plastic deformation zones, including those leading to localized banding, possibly promote failure of shield tunnel faces excavated in sand. To this end, a material state-dependent model is used to capture the mechanical responses of sand. Nonlocal enhancement is introduced, through the volumetric strain increment that drives the change of void ratio and related material hardening/softening behavior, to regularize ill-posed boundary value problems caused by the activation of strain localization. Simulations of tunnel face failure indicate that lower initial void ratios result in more concentrated plastic deformation in the vicinity region near the face and a strain-softening trend in global deformation responses. Conversely, initial looser states drive the deformation zone to propagate spatially to the ground surface, and the resultant global deformation responses exhibit strain-hardening. The second-order work is used to explain the link between material instability around the tunnel faces and initial density. It was found that material instability usually occupies a fraction of plastic deformation regions, and shrinks as sand initial density increases.