The small strain theory underestimates the self-bearing capacity of rock masses, especially for a soft rock tunnel under high geostress. To perform an efficient and accurate calculation and provide a reference for the stiffness design of a tunnel, the finite strain solution for a circular tunnel in Mohr–Coulomb strain-softening rock masses with a non-associated flow rule was derived as three sets of differential equations under the Lagrangian coordinate, which are in the residue region, the softening region, and the elastic region, respectively. Based on the bisection method, an iteration procedure for solving the finite strain solution was proposed to approximate the boundary condition at infinity, the values of two adjacent boundaries, and the initial values on the excavation boundary. This numerical procedure was verified by comparing with self-similar solutions, recursive solutions, and FLAC simulation results. In the calculation example, the relative error on boundaries can be decreased to less than 10⁻⁸ after only 10 times iteration and the time for each calculation is less than 15 s. Applying this procedure on the sensibility analysis and stiffness reliability design for the Zhongyi tunnel, a support stiffness of 4.3 MPa/m is recommended to guarantee a tunnel displacement lower than 0.5 m.

The evaluation of the roof collapse in tunnels or cavities remains one of the most complex issues in geotechnical engineering. Taking the detaching surface of the tunnel roof collapse as an orthotropic weak interlayer, an analytical approach for determining the limit collapse range considering the arch effect of the tunnel is presented in this paper by the variation calculus. A discontinuity criterion moving from the anisotropic criterion proposed by the present authors is applied to the orthotropic interlayer. The phenomenon of sharp points in collapse blocks is further analyzed. Based on the proposed approach, illustrated examples are analyzed to investigate the effect of the strength parameters and the consideration of the collapse cusp, which show different influence laws on the range of collapse blocks. Those interesting conclusions can provide guidance for the prediction of the collapse mechanism of the tunnel.