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.

中文翻译：

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使用钻孔破裂进行原位应力分析的多轴失效准则：回顾现有方法并开发经验替代方法


井眼压缩破坏或破裂分析是限制深井最大水平应力的主要方法之一。为了通过观察破裂来估计应力，需要从图像记录中测量破裂宽度，并使用失效理论来预测导致所测量的破裂发展的应力。最常见的是，使用莫尔-库仑失效准则，该准则忽略了中间应力对强度的影响。因此，已经提出了各种多轴标准来包括这种效应。在这里，我们首先回顾一些选定的多轴标准：Drucker-Prager、Mogi、Modified Wiebols-Cook 和 Modified Lade，我们得出的结论是，它们在突破分析中的应用可能很麻烦而且通常不可靠。这些问题的原因之一是标准是使用应力不变量定义的，而应力估计最容易在主应力空间中执行和分析。因此，另一种方法是将多轴准则定义为最大应力和中间应力之间的简单关系。我们建议将这样的经验标准定义为二阶多项式，它符合多轴实验室强度数据中观察到的趋势。这种方法可以限制通常与先前多轴标准的使用相关的强度高估，并且可以轻松地将强度估计中的不确定性与最大水平应力预测中的不确定性联系起来。