An improved analytical approach for analyzing a circular opening excavated in a strain-softening rock mass

A broken zone usually exists in the deeply buried tunnels after excavation, and the rock mass in the broken zone is in the state of unloading failure and exhibiting a nonlinear dilatancy effect. In order to study the deformation of isotropic rock mass in an initial hydrostatic stress field, a method is proposed to calculate the radius of the broken zone of the surrounding rock in a circular tunnel. Based on the unloading experiment of rock samples, a layer-wise summation method is established to calculate the displacement of the circular tunnel after excavation. The results reflect the impact of the nonlinear dilatancy effect on the displacement of the tunnel wall along the radial direction. Moreover, the method does not include complex integral calculation. Comparing with the Kastner’s (Houska 1981 ) method and Y K Lee’s (Lee and Pietruszczak 2008 ) method. This article reveals that the residual strength parameters c r , φ r and dilation angle ψ , that are essential in Y K Lee’s method, are highly sensitive to displacement calculation, which makes the Y K Lee’s method difficult to apply. In contrast, the method proposed in this study provides accurate prediction and has access to obtain its parameters more easily, making it easy to popularize.