Cylindrical cavity expansion from a finite radius

Solutions of cavity expansion have many practical applications in geotechnical engineering. In the large body of literature on the cavity expansion models for cohesive frictional materials, the solutions have mostly been derived by adopting a finite logarithmic strain definition in the plastic zone. A more rigorous alternative approach using the rate formulation for cylindrical cavity expansion from a finite radius is presented in this paper. The material is assumed to behave as elasto-perfectly plastic, obeying a Mohr-Coulomb yield criterion and the associated or nonassociated flow rule. The "time" (or evolution) variable is chosen to be the current cavity radius. The solution for the onset of plasticity serve as both the continuity condition for the elastoplastic interface and the initial condition for cavity expansion. The pressure-expansion relationship obtained is a first order ordinary differential equation and converges to a self-similar solution for expansion at a large radius.