Stability analysis of vertical boreholes using the Mogi-Coulomb failure criterion

A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, σ₁ and σ₃, and therefore assumes that the intermediate stress σ₂ has no influence on rock strength. As the Mohr-Coulomb criterion ignores the strengthening effect of the intermediate stress, it is expected to be too conservative in estimating the critical mud weight required to maintain wellbore stability. Recently, Al-Ajmi and Zimmerman [Relationship between the parameters of the Mogi and Coulomb failure criterion. Int J Rock Mech Min Sci 2005;42(3):431-39.] developed the Mogi-Coulomb failure criterion, and showed that it is reasonably accurate in modelling polyaxial failure data from a variety of rocks. We then develop a model for the stability of vertical boreholes, using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi-Coulomb criterion to predict failure. Our model leads to easily computed expressions for the critical mud weight required to maintain wellbore stability.