Elastoplastic analysis of tunnels in Hoek–Brown rock masses exhibiting strain softening

This paper proposes an adaptive ring-by-ring semi-analytical framework for elastoplastic analysis of circular tunnels in strain-softening Hoek–Brown rock under hydrostatic in-situ stress. The excavation unloading process is discretized via equal radial stress increments, with the number of concentric calculation rings dynamically growing synchronously with plastic zone expansion from 1 to a preset maximum value n . The solution is implemented outward-inward to track the full evolution of surrounding rock stress and displacement. Three key improvements are made over existing fixed-ring algorithms: (1) an adaptive ring strategy balancing computational efficiency and precision; (2) elimination of extra geometric interpolation assumptions between adjacent ring radii; (3) a normalized radius transformation technique to avoid numerical termination. Convergence analysis shows that negligible calculation error is achieved when n = 1000, and the linear degradation relation of Hoek–Brown strength parameters with plastic shear strain is adopted, whose applicability range for fractured rock masses is clarified. Three groups of comparative cases (existing analytical solutions and FLAC3D numerical results) verify the accuracy and reliability of the proposed method, with relative errors below 3.4%. The proposed approach provides an efficient, stable tool for ground response curve calculation and stability evaluation of fractured tunnel rock masses.