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 calculation of conformal mapping for irregular domains is a crucial step in deriving analytical and semi-analytical solutions for irregularly shaped tunnels in rock masses using complex theory. The optimization methods, iteration methods, and the extended Melentiev’s method have been developed and adopted to calculate the conformal mapping function in tunnel engineering. According to the strict definition and theorems of conformal mapping, it is proven that these three methods only map boundaries and do not guarantee the mapping’s conformal properties due to inherent limitations. Notably, there are other challenges in applying conformal mapping to tunnel engineering. To tackle these issues, a practical procedure is proposed for the conformal mapping of common tunnels in rock masses. The procedure is based on the extended SC transformation formulas and corresponding numerical methods. The discretization codes for polygonal, multi-arc, smooth curve, and mixed boundaries are programmed and embedded into the procedure, catering to both simply and multiply connected domains. Six cases of conformal mapping for typical tunnel cross sections, including rectangular tunnels, multi-arc tunnels, horseshoe-shaped tunnels, and symmetric and asymmetric multiple tunnels at depth, are performed and illustrated. Furthermore, this article also illustrates the use of the conformal mapping method for shallow tunnels, which aligns with the symmetry principle of conformal mapping. Finally, the discussion highlights the use of an explicit power function as an approximation method for symmetric tunnels, outlining its key points.

Fiberglass bolts are extensively used to control the extrusion of tunnel face and enhance tunnel stability. A novel computational approach based on the finite difference method is proposed to predict the extrusion of tunnel face reinforced with fiberglass bolts. Given the 3D stress state of the tunnel face, the spherical symmetric model is utilized. The strain-softening constitutive model effectively captures the characteristics of post-peak progressive failure in rock. To more realistically describe the interaction between the bolts and the rock mass, the model incorporates the relative shear deformation and the occurrence of interface debonding when the shear stress exceeds the ultimate shear strength. A robust iterative procedure is introduced to address the interaction. The effectiveness and high efficiency of the proposed method are validated through comparison with numerical simulations. Compared with previous studies, the proposed method emphasizes the importance of the rock softening characteristics and the debonding at the bolt-rock interface. Additionally, it employs a robust iterative computational procedure instead of predefined force patterns to obtain a more realistic representation of bolt stress conditions. The method has been applied to two real engineering projects, and the analysis results show satisfactory accuracy. Parameter analysis is conducted to evaluate the effects of the geological strength index, in situ stress, bolt density, and overlap length on the responses of the bolts and rock mass. The proposed approach provides an efficient and accurate predictive tool for the preliminary design of tunnels reinforced with fiberglass bolts.