A Simple Solution and Dilatancy Characterization for a Circular Tunnel Excavated in the Nonlinear Strain-Softening and Nonlinear Dilatancy Rock Mass

Tunnel opening or excavation in the strain-softening rock masses primarily leads to initial stress release and rock deformation. The increasing plastic shear strain induces a nonlinear variation of dilatancy in rock masses. Therefore, tunnel stability is strongly dependent on the stress state and the strain-softening and dilatancy behaviors of rock masses. In view of this, this paper proposes an elastoplastic finite difference solution based on the triple-shear element (TS) unified strength criterion (USC) and the nonassociative flow law; thereafter, some typical examples are referred to verify its validity. This solution allows for the description of the intermediate principal stress effect, the nonlinear strain-softening and dilatancy behaviors of the rock mass. Parametric analysis finally determines the influence characteristics of the intermediate principal stress effect (b), the critical softening parameter (η∗), softening factor (δ), and support force (pi) on the dilation angle (ψ) of the rock mass in the plastic zone. The findings confirm that the intermediate principal stress mainly affects peak values of ψ, which increases as b grows. The rate of change of ψ mainly depends on η∗, which tends to be slower with increasing η∗. The variation pattern of ψ in the residual zone under different δ is generally consistent, while the variability of ψ in the softening zone is significant. For a given intermediate principal stress state and strain-softening behavior of the rock mass, the values and the developed form of ψ in the plastic zone is independent of pi.