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Evaluation of the Depth and Width of Progressive Failure of Breakout Based on Different Failure Criteria, Using a Finite Element Numerical Model

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Abstract

Shear failure due to compressive stress around a borehole is called breakout. Breakout occurs along the minor principal stresses. Due to the change in the cross section of the borehole due to the collapse of the crushed layers of rock into the borehole, breakout is developed to achieve stability. Accurate estimation of breakout dimensions is important for two reasons; first, breakout in large volumes can cause borehole instability. Secondly, in recent years, efforts have been made to use breakout dimensions to estimate in situ stresses. Failure breakout area depends on the material properties, in situ stresses and the failure criterion. In this paper, using a simple numerical model based on the finite element method, a comprehensive analysis of the breakout phenomenon and its dimensions for 5 different failure criteria has been performed. The proposed numerical model examines breakout expansion step by step until stability is achieved. According to the obtained results, the failure criterion and intermediate principal stress are effective in the breakout dimensions, as the Drucker-Prager failure criterion suggests the smallest breakout failure area and the Mohr–Coulomb failure criterion provides the largest failure area due to not considering the intermediate principal stress, for this reason, Mohr–Coulomb criterion is not suitable for breakout analysis. Comparing the results of numerical analysis with the results of breakout experiments performed on Tablerock sandstone, it was observed that the breakout failure depth, for certain in situ stresses, could be close to the breakout failure depth obtained according to Drucker-Prager and modified Lade criteria.

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Appendix 1

Appendix 1

According to the analytical Kirsch’s relations, the stress around a borehole with radius shown in Fig. 1, is equal to [35]:

$$\sigma_{{{\text{rr}}}} = \frac{1}{2}\left( {\sigma_{{\text{H}}} + \sigma_{{\text{h}}} } \right).\left( {1 - \frac{{r_{o}^{2} }}{{r^{2} }}} \right) - \frac{1}{2}\left( {\sigma_{{\text{H}}} - \sigma_{{\text{h}}} } \right).\left( {1 - 4\frac{{r_{o}^{2} }}{{r^{2} }} + 3\frac{{r_{o}^{4} }}{{r^{4} }}} \right).{\text{cos}}2\;\theta + P_{{\text{b}}} \;\left( {\frac{{r_{o}^{2} }}{{r^{2} }}} \right)$$
(42)
$$\sigma_{\theta \theta } = \frac{1}{2}\left( {\sigma_{{\text{H}}} + \sigma_{{\text{h}}} } \right).\left( {1 + \frac{{r_{o}^{2} }}{{r^{2} }}} \right) + \frac{1}{2}\left( {\sigma_{{\text{H}}} - \sigma_{{\text{h}}} } \right).\left( {1 + 3\frac{{r_{o}^{4} }}{{r^{4} }}} \right).{\text{cos}}2\theta - P_{{\text{b}}} \;\left( {\frac{{r_{o}^{2} }}{{r^{2} }}} \right)$$
(43)
$$\sigma_{{{\text{zz}}}} = \sigma_{{\text{v}}} + 2\;\nu \,\left( {\sigma_{{\text{H}}} - \sigma_{{\text{h}}} } \right).\left( {\frac{{r_{o}^{2} }}{{r^{2} }}} \right).{\text{cos}}2\theta$$
(44)
$$\tau_{r\theta } = \frac{1}{2}\left( {\sigma_{{\text{H}}} - \sigma_{{\text{h}}} } \right).\left( {1 + 2\frac{{r_{o}^{2} }}{{r^{2} }} - 3\frac{{r_{o}^{4} }}{{r^{4} }}} \right).{\text{sin}}2\theta$$
(45)

In these relations \(\sigma_{{\text{H}}}\) and \(\sigma_{{\text{h}}}\) are major and minor horizontal in situ stresses, respectively, and \(P_{{\text{b}}}\) is internal borehole pressure and \(\nu\) is the Poisson’s ratio.

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Bahrehdar, M., Lakirouhani, A. Evaluation of the Depth and Width of Progressive Failure of Breakout Based on Different Failure Criteria, Using a Finite Element Numerical Model. Arab J Sci Eng 47, 11825–11839 (2022). https://doi.org/10.1007/s13369-022-06640-9

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