Polyaxial Failure Criteria in Borehole Breakout Stress Analysis

Abstract

ABSTRACT Analysis of borehole wall failures, breakouts, is the primary method of constraining the maximum horizontal stress in deep wells. To estimate stress using the breakout method, one needs to measure the breakout width from image or caliper logs, and use a failure theory to predict stress that led to the development of the measured breakout. Most commonly, Mohr-Coulomb failure criterion is used which disregards the influence of intermediate stress on strength. Different polyaxial criteria have been proposed to include this effect. Here, we first review selected polyaxial criteria: Drucker-Prager, Mogi and modified Wiebols-Cook, and we conclude that their application in breakout analysis is cumbersome and often unreliable. One reason for these problems is that the criteria are defined using octahedral stresses or invariants, while the breakout analysis is most easily done in the principal stress space. Therefore, the polyaxial criterion can be defined 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. INTRODUCTION Knowledge of in situ stress is essential for many geological engineering applications including: borehole stability, hydraulic stimulation, induced seismicity, and others (e.g. Zoback, 1992, 2007; Jaeger et al., 2007; Heidbach et al., 2018). Among the three principal stresses, the maximum horizontal stress (σH) is the most challenging to constrain (Zoback et al., 2003). The most commonly used method is based on analysis of borehole wall compressive failures, i.e. breakouts. Breakout analysis requires two components: i) the breakout geometry observed from image or caliper logs, and ii) a failure theory to predict stress that led to the development of a breakout with the measured geometry. Most commonly, the Mohr-Coulomb criterion is used in borehole wall strength analysis and its failure is predicted when the hoop stress reaches a critical value (Barton et al., 1988). However, such approach disregards the influence of the intermediate principal stress (σ2) on rock strength (understood as the maximum principal stress, σ1, at failure) which has been described in numerous experimental studies (e.g. Mogi, 1971; Michelis, 1985, 1987; Haimson and Chang, 2000; Chang and Haimson, 2000; Ingraham et al., 2013; Ma and Haimson, 2016; Lee and Haimson, 2011). Therefore, several polyaxial failure criteria which include the σ2 dependence of strength has been proposed and applied in borehole breakout analyses (Zhou, 1994; Ewy, 1999; Al-Ajmi and Zimmerman, 2005; Chang et al., 2010).