Underground circular openings in elastoplastic rocks: Strain gradient and size effects

Abstract

A special form of gradient elasticity and a deformation version of gradient plasticity are employed to derive analytical solutions for the problem of an unsupported underground circular opening in an elastoplastic rock subjected to an isotropic far-field compressive stress. In the gradient elasticity model, the classical Hooke’s law is extended to include the Laplacian of the hydrostatic part of the strain tensor, while the gradient plasticity model is based on the modification of the flow stress (an effective stress measure) to include the Laplacian of a corresponding effective strain. The boundary value problem is solved analytically and exact expressions for the displacement, strain and stress distributions are obtained. The presence of size effects which contribute to the circular opening stability is illustrated and discussed. This includes size-dependent yield stresses and plastic region diameters, while a maximum strain failure criterion is adopted to discuss size effects on the macroscopic fracture of the rock medium. © International Society for Rock Mechanics and Rock Engineering Norwegian Group for Rock Mechanics.