Bifurcation analysis of deep boreholes: I. Surface instabilities

In this paper a bifurcation analysis of boreholes in deep rock formations under uniform stress at infinity is presented. Rock is described by the constitutive equations of a deformation theory of plasticity for rigidplastic, incompressible and cohesive‐frictional material. The corresponding bifurcation problem is solved numerically by the finite element method. The evidence gained from the numerical solution is utilized to establish a simplified borehole stability analysis that combines Biot's hodograph method with a surface instability analysis.