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This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial stresses. By simplifying the strain-softening process of the post-failure region as a Multi-step Brittle-Plastic model (MBPM), analytical solutions of the spherical cavity are derived with the consideration of the deterioration of elastic parameters. Meanwhile, critical deterioration conditions of elastic parameters are established theoretically. Both Mohr-Coulomb (M-C) and Hoek-Brown (H-B) criteria are included in the analysis. The results are compared with those obtained by former numerical methods, and the solutions are validated. Moreover, the presented results show that deteriorated elastic parameters for post-failure rock mass only has a little influence on stresses, softening radius and residual radius, but influences the deformation significantly.

Analytical Strain-softening Solutions of a spherical cavity