Stability of boreholes in a geologic medium including the effects of anisotropy

  • Dinesh Gupta
  • Musharraf Zaman


An analytical formulation is developed to investigate the stability of a deep, inclined borehole drilled in a geologic medium and subjected to an internal pressure and a non-hydrostatic stress field. The formulation consists of a three-dimensional (3-D) analysis of stresses around a borehole, combined with internal pressurization of the borehole to obtain an approximate solution of the overall stress distribution. The orientation of the borehole, the in-situ stresses and bedding plane can all be arbitrarily related to each other to represent the actual field situations. Both tensile failure and shear failure potentials of a borehole are investigated. The failure criteria applied assume that when the least principal stress exceeds the strength of the formation in tension, a tensile failure occurs. Shear failure is represented using the modified Drucker-Prager failure criterion for anisotropic materials. A parametric study is carried out to assess the effect of material anisotropy, bedding plane inclination and in-situ stress conditions on borehole stability. Results of the parametric study indicate that wellbore stability is significantly influenced by a high borehole inclination, high degree of material anisotropy, in-situ stress conditions and high formation bedding plane inclination.

The stability of a borehole in an elasto-plastic medium is also investigated. In order to evaluate the extent of the plastic zone around a borehole and the effect of anisotropy of the material on this plastic zone, a mathematical formulation is developed using theories of elasticity and plasticity. The borehole is assumed to be vertical, subjected to hydrostatic stresses, and drilled in a transversely isotropic geologic medium. A parametric study is carried out to investigate the effect of material anisotropy on the plastic behavior of the geologic medium. Results indicate that the stress distribution around a borehole, the extent of the plastic zone, and the failure pressure are influenced by the degree of material anisotropy and value of in-situ overburden stresses. It was observed that the borehole becomes less stable as the degree of anisotropy of the geologic medium increases.

Key words

stability of borehole tensile failure shear failure failure criteria stress distribution 

CLC number

TB122 TE21 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Dinesh Gupta
    • 1
  • Musharraf Zaman
    • 1
  1. 1.School of Civil Engineering and Environmental ScienceUniversity of OklahomaNormanU S A

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