A finite strain numerical procedure for a circular tunnel in strain-softening rock mass with large deformation

The reliable prediction of excavation responses for squeezing rock remains a challenging issue in rock engineering. This paper presents a numerical procedure for a strain-softening rock mass around highly deformed circular opening based on the finite strain theory, so the overall elasto-plastic analysis is a Lagrangian method which focuses on the motion of each material point and is well suited for the problems involving large deformation. The influence of axial in-situ stress is considered by introducing the initial axial stress into the elastic constitutive equations, and the axial plastic flow is realized by redefining the plastic internal variable and considering different stress distributions in the plastic zone. Thus, the numerical procedure enables prediction of the rock deformation and squeezing potential in a more rational and rigorous manner. The capability of the method for estimating the small strain and squeezing deformation is verified by being compared with the existing analytical results and the field measuring data. Negligence of the axial in-situ stress or the axial plastic flow underestimates the rock deformation, and the induced deviation essentially depends on the post-peak constitutive relation and the rock heterogeneity after rock yields. The higher level of the material homogeneity in the plastic zone, the lower effects of the axial in-situ stress on the rock responses. The stress distribution and strain-softening behavior of surrounding rock can be significantly affected by the axial in-situ stress and the critical plastic internal variable eta*. Tunnel instability is independent of large deformation for the high eta* but is closely associated with the squeezing problem when eta* is small. As eta* decreases, both of the plastic radius and wall convergence increase initially and remain constant afterwards. Lastly, the paper investigates the rock responses and ground-support interaction when the small strain theory is applied on the squeezing rock.