A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium

A theoretically consistent closed-form solution for a spherical cavity in a brittle-plastic infinite medium subject to a hydrostatic stress field was derived. Both linear Mohr-Coulomb (M-C) and nonlinear Hoek-Brown (H-B) yield criteria are considered, and a non-associated flow rule is employed in the solution. Plastic radius, stresses and displacements are explicitly expressed as the functions of radial coordinates, internal pressure and strength parameters. In elastic-perfectly plastic analysis, results for displacements and stresses are in good agreement with those published. Comparison of brittle-plastic solutions with the elasto-plastic ones indicates that brittle-plastic behavior of rock mass increase the extent of plastic zone and the displacements around the cavity significantly. Ground response curves (GRC) are constructed for both M-C and H-B criteria and the potential applications are discussed.