Large strain similarity solution for a spherical or circular opening excavated in elastic-perfectly plastic media

This paper deals with the unloading problem of a spherical or circular opening excavated in elastic-perfectly plastic media with a nonassociated Mohr-Coulomb yield criterion. A large strain similarity solution, using incremental velocity approach, is presented by replacing partial differential equations from stress equilibrium, constitutive law, consistency condition, and displacement equation with first-order ordinary differential equations. The classical Runge-Kutta method is used to solve the first-order ordinary differential equations. Comparisons among small and large strain solutions are made using some data sets of soil and rock. The results show that the displacements by large strain similarity solution are smaller than those by exact small strain solution and somewhat larger than those by large strain solution using total strain approach. Copyright (c) 2014 John Wiley & Sons, Ltd.