A modified Hoek–Brown model considering softening effects and its applications

Abstract Considering that the traditional Hoek–Brown model only accounts for strain hardening effects in rock materials, while many rock materials exhibit strain softening effects under large deformation, a modified Hoek–Brown model has been developed to simultaneously describe both material hardening and softening characteristics. This enhancement builds upon the traditional Hoek–Brown model by introducing plastic internal variables that characterize material damage or degradation. To address numerical singularities and convergence difficulties encountered during the implementation of the modified Hoek–Brown model, a function smoothing method is employed. The physical significance of model parameters in the modified model is clarified through theoretical analysis and single-factor variable analysis methods. Finally, the modified Hoek–Brown model is applied to practical engineering calculations. The study results demonstrate that the modified Hoek–Brown model can effectively account for both strain hardening and strain softening effects in materials. The function smoothing method proves to be effective in mitigating numerical singularities and convergence issues encountered in the implementation of the modified Hoek–Brown model. For soft rock tunnels, when significant displacements occur in the surrounding rock, both displacements and stresses around the tunnel calculated using the modified Hoek–Brown model are more consistent with engineering reality than those obtained using the traditional Hoek–Brown model. It is recommended to consider applying the modified Hoek–Brown model in practical engineering calculations.