A graphical analysis-based elastoplastic solution for undrained wellbore drilling problem in Hoek-Brown rock formation

Document Type

Conference Proceeding

Publication Date

1-1-2023

Abstract

An analytical solution is developed for evaluating the stability of an impermeable wellbore in rock formation that obeys Hoek-Brown failure criterion in a hydrostatic stress field. The solution is derived in the framework of the graphical analysis method recently developed by Chen and Abousleiman (2022). The graphical analysis approach can effectively overcome two essential limitations that exist in the implementation of the Hoek-Brown model in the current literature, i.e., first, the mathematical difficulties involved in the treatment of corner singularity of the yield surface; and second, the intermediacy assumption for the axial stress with respect to other stresses. The graph-based solution procedure follows two steps: (1) to geometrically track the stress path trajectory laid out in the deviatoric stress plane; and (2) to formulate the constitutive equations and the radial equilibrium equation. It is found that the effective stress path corresponding to the borehole drilling process is composed of piecewise curved and straight lines in the deviatoric stress plane; it eventually terminates in the major sextant with the Lode angle θ ranging from π/2 to 2π/3 or, on the line of θ = π/2, depending on the mechanical properties of the rock. The analytical solution obtained is a rigorous and complete one for the borehole drilling problem.

Publication Source (Journal or Book title)

57th US Rock Mechanics/Geomechanics Symposium

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