A numerical algorithm for ground reaction curves of circular openings in strain-softening rock masses satisfying the generalized Hoek-Brown criterion

Based on the self-similarity method, a numerical algorithm for constructing ground reaction curves (GRC) of circular openings in elastic-strain softening rock mass that satisfies the generalized Hoek-Brown failure criterion is proposed. The algorithm is derived from the analysis of the axisymmetric plane strain model, where the far -field and excavation boundary are both axisymmetric stresses. Using the self-similar transformation, the plastic zone of the model was transformed into unit plane ring, which has unit radius at the boundary between the plastic zone and the elastic zone. The unit plane ring was dispersed into multiple concentric rings, for which the Runge-Kutta discrete equations of the stress and deformation were established based on corresponding self-similar governing equations. The equations were solved ring by ring in a successive manner, starting from the outer boundary to the excavation boundary. The comparison with the verified algorithm in literature shows that the results of the different algorithms are in good agreement and the relative errors of the plastic zone radius under various softening parameters are only 1.7%-2.0%. These results verified the correctness and reliability of the proposed new algorithm. Finally, the new algorithm is used to investigate the influence of the Hoek-Brown parameter a on GRC. A discussion of the potential capability of practical applications of this algorithm is also provided.