Bifurcation analysis of deep boreholes: II. Scale effect

This paper is a continuation of a previous one on bifurcation of deep boreholes under uniform stress at infinity, 1 and it focuses on the effect of borehole radius on borehole stability. Rock is described by the equations of a deformation theory of plasticity for cohesive‐frictional, incompressible materials with Cosserat structure. The inhomogeneous bifurcation problem is formulated and the corresponding eigenvalue problem is solved numerically by the finite element method. It is demonstrated that the combined Cosserat and stress‐gradient effects lead to an increase of the bifurcation stress with decreasing borehole radius (scale effect).