Exact and approximate solutions for displacements around circular openings in elastic–brittle–plastic Hoek–Brown rock

Abstract

Abstract A simple exact solution is presented for the elastic–brittle–plastic plane strain analysis of displacements around circular openings in an isotropic Hoek–Brown rock subjected to a hydrostatic in situ stress. The integration involved in the solution is carried out by using a standard mathematical software. Results produced by using the present exact method are found to be identical to those obtained by using a recently published closed form but complicated solution based on a transformation technique. An extremely simple but approximate closed-form solution was earlier derived by making a simplifying assumption for the evaluation of the elastic part of the total strain in the plastic zone. Several example cases are analyzed to show that the simplifying assumption made in the derivation of the simple closed-form solution has an insignificant effect on the results for displacements for practical problems. The innovative approximation technique may be used to obtain simple solutions of a wide variety of complex plasticity problems in rock mechanics.