Closed-Form Elastoplastic Solution for the Wellbore Problem in Strain Hardening/Softening Rock Formations

Abstract

This paper proposes an analytical approach predicting the development and progress of the plastic zone around a wellbore drilled in linear hardening or softening Drucker-Prager rocks in a theoretically consistent way. With some reasonable assumptions and simplifications on the definitions of stress invariants as well as the equivalent plastic strain, the wellbore boundary value problem is fully linearized, which leads to a simple ordinary differential equation with the radial displacement being the basic unknown. Explicit solutions for the stress and displacement fields due to wellbore drilling can thus be easily obtained. Comparisons between the analytical solution and the