Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation-based approach

The contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post-failure softening response of geomaterials, are observed in the form of spiral-shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral-shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr-Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic-like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases.