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 ABAQUS numerical simulation verify the reliability and applicability of the present closed-form solution. Extensive numerical results for the tangential and radial stress distributions are then provided to explore the influences of the friction angle and the plastic tangential modulus, for both strain hardening and softening cases. The important issue of critical mud density equivalent to wellbore radial controlled stresses that is required to maintain wellbore stability is also addressed.