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

Abstract

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.