Polyaxial failure criteria for in situ stress analysis using borehole breakouts: Review of existing methods and development of an empirical alternative

Analysis of compressive wellbore failure, or breakouts, is one of the primary methods of constraining the maximum horizontal stress in deep boreholes. To estimate stress using the observation of breakouts, one needs to measure the breakout width from image logs and use a failure theory to predict the stress that led to the development of the measured breakout. Most commonly, Mohr–Coulomb failure criterion has been used which disregards the influence of intermediate stress on strength. Hence, various polyaxial criteria have been proposed to include this effect. Here, we first review some selected polyaxial criteria: Drucker–Prager, Mogi, Modified Wiebols–Cook, and Modified Lade, and we conclude that their application in breakout analysis may be cumbersome and often unreliable. One reason for these problems is that the criteria are defined using stress invariants, while the stress estimation is most easily performed and analyzed in the principal stress space. Therefore, an alternative is to define the polyaxial criterion as a simple relation between maximum and intermediate stresses. We propose to define such an empirical criterion as a second order polynomial which fits trends observed in polyaxial laboratory strength data. Such approach allows to limit strength overestimation, often associated with the use of previous polyaxial criteria, and to easily relate uncertainties in strength estimation to uncertainty in maximum horizontal stress prediction.