Theoretical Solutions for Tunnels Excavated in Strain-Softening Rock Masses Considering Support

The collaborative load-bearing behavior between the rock mass and support is critical for tunnel support design. This study proposes a strain-softening analysis method for circular tunnels during construction and presents an efficient solution strategy, termed the “Support Load Approximation Strategy” (SLAS), to solve the collaborative load-bearing problem. The rock mass is assumed to be isotropic, following the Mohr–Coulomb criterion, under hydrostatic stress conditions. During the stepwise calculation, a new ring is automatically added at each step, and the positions of all previous rings are updated, with elastic or plastic formulations automatically selected based on the state of each ring. The GRC and plastic radii (Rp and Rs) curves obtained by the proposed method show excellent agreement with existing benchmark results, with relative errors of 3.73% for the GRC, 1.47% for Rs, and 3.40% for Rp, confirming the correctness and accuracy of the proposed algorithm. Furthermore, when compared to the Incremental Support Load Method (ISLM) and the binary search method, SLAS improves computational efficiency by 14.2 times and 67%, and accuracy by 70% and 53%, respectively. When higher precision is required, SLAS maintains an efficiency gain of 82.8 times over ISLM with comparable accuracy. Compared to traditional elastic-plastic analysis methods, the proposed approach simplifies the computational process, reduces complexity, offers both high accuracy and fast computation speed, and serves as a practical tool for tunnel engineering support design.