Comparison of predicted failure area around the boreholes in the strike-slip faulting stress regime with Hoek-Brown and Fairhurst generalized criteria
Abstract
Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics are effective in developing the breakout failure area, As the ratio of in-situ stresses increases, the breakout area becomes deeper and wider. Because in the shear zone, the failure envelope of the Fairhurst criterion is lower than the Hoek-Brown failure criterion, the Fairhurst criterion provides more depth for breakout than the Hoek-Brown criterion. However, due to the same compressive strength of the rock in these two criteria, the same failure width for breakout is obtained from these two criteria. Also, the results obtained for the depth of failure from the theoretical model based on the Fairhurst criterion are in good agreement with the laboratory results on Westerly granite.
Keyword : borehole breakout, damage zone, Hoek-Brown failure criterion, Fairhurst generalized fracture criterion, in situ stress, Westerly granite
How to Cite
Lakirouhani, A., Bahrehdar, M., Medzvieckas, J., & Kliukas, R. (2021). Comparison of predicted failure area around the boreholes in the strike-slip faulting stress regime with Hoek-Brown and Fairhurst generalized criteria. Journal of Civil Engineering and Management, 27(5), 346-354. https://doi.org/10.3846/jcem.2021.15020
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Cai, M. (2010). Practical estimates of tensile strength and Hoek– Brown strength parameter mi of brittle rocks. Rock Mechanics and Rock Engineering, 43(2), 167–184. https://doi.org/10.1007/s00603-009-0053-1
Carr, W. J. (1974). Summary of tectonic and structural evidence for stress orientation at the Nevada Test Site (74-176). http://pubs.er.usgs.gov/publication/ofr74176
Cheng, W., Jiang, G., Zhou, Z., Wei, Z., & Li, X. (2019). Numerical simulation for the dynamic breakout of a borehole using boundary element method. Geotechnical and Geological Engineering, 37(4), 2873–2881. https://doi.org/10.1007/s10706-019-00802-7
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Delonca, A., & Vallejos, J. A. (2020). Incorporating scale effect into a failure criterion for predicting stress-induced overbreak around excavations. International Journal of Rock Mechanics and Mining Sciences, 127, 104213. https://doi.org/10.1016/j.ijrmms.2020.104213
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Gough, D. I., & Bell, J. S. (1982). Stress orientations from borehole wall fractures with examples from Colorado, east Texas, and northern Canada. Canadian Journal of Earth Sciences, 19(7), 1358–1370. https://doi.org/10.1139/e82-118
Haimson, B. (2007). Micromechanisms of borehole instability leading to breakouts in rocks. International Journal of Rock Mechanics and Mining Sciences, 44(2), 157–173. https://doi.org/10.1016/j.ijrmms.2006.06.002
Haimson, B. C., & Herrick, C. G. (1985). In-situ stress evaluation from borehole breakouts: experimental studies. In Proceedings of 26th US Symposium on Rock Mechanics (pp. 1207–1218). Rapid City, Balkema, Rotterdam.
Haimson, B. C., & Herrick, C. G. (1986). Borehole breakouts — a new tool for estimating in situ stress?. In Proceedings of International Symposium on Rock Stress and Rock Stress Measurements (pp. 271–280). Stockholm, Centek Publ., Luleå.
Haimson, B., & Lee, H. (2004). Borehole breakouts and compaction bands in two high-porosity sandstones. International Journal of Rock Mechanics and Mining Sciences, 41(2), 287–301. https://doi.org/10.1016/j.ijrmms.2003.09.001
Haimson, B. C., & Song, I. (1993). Laboratory study of borehole breakouts in Cordova Cream: a case of shear failure mechanism. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1047–1056. https://doi.org/10.1016/0148-9062(93)90070-T
Herrick, C. G., & Haimson, B. C. (1994, June). Modeling of episodic failure leading to borehole breakouts in Alabama limestone. In 1st North American Rock Mechanics Symposium (Paper Number: ARMA-1994-0217). Austin, Texas.
Hickman, S., & Zoback, M. (2004). Stress orientations and magnitudes in the SAFOD pilot hole. Geophysical Research Letters, 31(15). https://doi.org/10.1029/2004GL020043
Hoek, E. (1983). Strength of jointed rock masses. Géotechnique, 33(3), 187–223. https://doi.org/10.1680/geot.1983.33.3.187
Hoek, E., & Brown, E. (1980). Empirical strength criterion for rock masses. Journal of Geotechnical and Geoenvironmental Engineering, 106, 1013–1035. https://doi.org/10.1061/AJGEB6.0001029
Hoek, E., & Martin, C. D. (2014). Fracture initiation and propagation in intact rock – A review. Journal of Rock Mechanics and Geotechnical Engineering, 6(4), 287–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Huber, K., Fuchs, K., Palmer, J., Roth, F., Khakhaev, B. N., VanKin, L. E., Pevzner, L. A., Hickman, S., Moos, D., Zoback, M. D. & Schmitt, D. (1997). Analysis of borehole televiewer measurements in the Vorotilov drillhole, Russia – first results. Tectonophysics, 275(1–3), 261–272. https://doi.org/10.1016/S0040-1951(97)00031-0
Jaeger, J. C., Cook, N. G., & Zimmerman, R. (2009). Fundamentals of rock mechanics. John Wiley & Sons.
Lakirouhani, A., Asemi, F., Zohdi, A., Medzvieckas, J., & Kliukas, R. (2020). Physical parameters, tensile and compressive strength of dolomite rock samples: influence of grain size. Journal of Civil Engineering and Management, 26(8), 789–799. https://doi.org/10.3846/jcem.2020.13810
Lakirouhani, A., Detournay, E., & Bunger, A. P. (2016). A reassessment of in situ stress determination by hydraulic fracturing. Geophysical Journal International, 205(3), 1859–1873. https://doi.org/10.1093/gji/ggw132
Lee, M., & Haimson, B. (1993). Laboratory study of borehole breakouts in Lac du Bonnet granite: a case of extensile failure mechanism. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1039–1045. https://doi.org/10.1016/0148-9062(93)90069-P
Leeman, E. R. (1964a). The measurement of stress in rock: Part I: The principles of rock stress measurements. Journal of the Southern African Institute of Mining and Metallurgy, 65(2), 45–81.
Leeman, E. R. (1964b). The measurement of stress in rock: Part II: Borehole rock stress measuring instruments. Journal of the Southern African Institute of Mining and Metallurgy, 65(2), 82–114.
Leeman, E. R. (1964c, October). Absolute rock stress measurements using a borehole trepanning stress-relieving technique. In The 6th U.S Symposium on Rock Mechanics (USRMS) (Paper Number: ARMA-64-407). Rolla, Missouri, USA.
Lin, H., Kang, W. H., Oh, J., & Canbulat, I. (2020). Estimation of in-situ maximum horizontal principal stress magnitudes from borehole breakout data using machine learning. International Journal of Rock Mechanics and Mining Sciences, 126, 104199. https://doi.org/10.1016/j.ijrmms.2019.104199
Mastin, L. G. (1984). Development of borehole breakouts in sandstone [MSc thesis]. Stanford University, Palo Alto.
Martin, C. D., Martino, J. B., & Dzik, E. J. (1994, August). Comparison of borehole breakouts from laboratory and field tests. In Rock Mechanics in Petroleum Engineering (Paper Number: SPE-28050-MS). Delft, Netherlands. https://doi.org/10.2118/28050-MS
Okland, D., & Cook, J. M. (1998, July). Bedding-related borehole instability in high-angle wells. In SPE/ISRM Rock Mechanics in Petroleum Engineering (Paper Number: SPE-47285-MS). Trondheim, Norway. https://doi.org/10.2118/47285-MS
Ramsey, J. M., & Chester, F. M. (2004). Hybrid fracture and the transition from extension fracture to shear fracture. Nature, 428, 63–66. https://doi.org/10.1038/nature02333
Reinecker, J., Heidbach, O., Tingay, M., Sperner, B., & Müller, B. (2005). The release 2005 of the World Stress Map. http://www.world-stress-map.org/
Setiawan, N. B., & Zimmerman, R. W. (2018). Wellbore breakout prediction in transversely isotropic rocks using true-triaxial failure criteria. International Journal of Rock Mechanics and Mining Sciences, 112, 313–322. https://doi.org/10.1016/j.ijrmms.2018.10.033
Shalev, E., Bauer, S. J., Homel, M. A., Antoun, T. H., Herbold, E. B., Vorobiev, O. Y., Levin, H., Oren, V., & Lyakhovsky, V. (2021). Borehole breakout modeling in arkose and granite rocks. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 7(1), 15. https://doi.org/10.1007/s40948-021-00215-y
Shamir, G., & Zoback, M. D. (1992). Stress orientation profile to 3.5 km depth near the San Andreas Fault at Cajon Pass, California. Journal of Geophysical Research: Solid Earth, 97(B4), 5059–5080. https://doi.org/10.1029/91JB02959
Song, I. (1998). Borehole breakouts and core disking in Westerly granite: Mechanisms of formation and relationship to in situ stress (Publication No. AAI9825734) [Doctoral dissertation, Wilmington University]. ProQuest Dissertations & Theses Global.
Song, I., & Haimson, B. C. (1997). Polyaxial strength criteria and their use in estimating in situ stress magnitudes from borehole breakout dimensions. International Journal of Rock Mechanics and Mining Sciences, 34(3–4), 116.e1–116.e16. https://doi.org/10.1016/S1365-1609(97)00240-2
Syarifuddin, N., & Busono, I. (1999). Regional stress alignments in the Kutai Basin, East Kalimantan, Indonesia: a contribution from a borehole breakout study. Journal of Asian Earth Sciences, 17(1), 123–135. https://doi.org/10.1016/S0743-9547(98)00049-X
van den Hoek, P. J. (2001, July). Prediction of different types of cavity failure using bifurcation theory. In The 38th U.S. Symposium on Rock Mechanics (USRMS) (Paper Number: ARMA01-0045). DC Rocks 2001, Washington, D.C.
Wu, H., Guo, N., & Zhao, J. (2017). Borehole instabilities in granular rocks revisited: A multiscale perspective. In E. Papamichos, P. Papanastasiou, E. Pasternak, & A. Dyskin A. (Eds.), Bifurcation and degradation of geomaterials with engineering applications (IWBDG 2017). Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-319-56397-8_54
Yousefian, H., Fatehi Marji, M., Soltanian, H., Abdollahipour, A., & Pourmazaheri, Y. (2020). Wellbore trajectory optimization of an Iranian oilfield based on mud pressure and failure zone. Journal of Mining and Environment, 11(1), 193–220. https://doi.org/10.22044/jme.2020.8779.1768
Zoback, M. D., Moos, D., Mastin, L., & Anderson, R. N. (1985). Well bore breakouts and in situ stress. Journal of Geophysical Research, 90(B7), 5523–5530. https://doi.org/10.1029/JB090iB07p05523
Zoback, M. D., Barton, C. A., Brudy, M., Castillo, D. A., Finkbeiner, T., Grollimund, B. R., Moos, D. B., Peska, P., Ward, C. D., & Wiprut, D. J. (2003). Determination of stress orientation and magnitude in deep wells. International Journal of Rock Mechanics and Mining Sciences, 40(7), 1049–1076. https://doi.org/10.1016/j.ijrmms.2003.07.001
Abdelghany, W. K., Radwan, A. E., Elkhawaga, M. A., Wood, D. A., Sen, S., & Kassem, A. A. (2021). Geomechanical modeling using the depth-of-damage approach to achieve successful underbalanced drilling in the Gulf of Suez rift basin. Journal of Petroleum Science and Engineering, 202, 108311. https://doi.org/10.1016/j.petrol.2020.108311
Bell, J. S., & Gough, D. I. (1979). Northeast-southwest compressive stress in Alberta evidence from oil wells. Earth and Planetary Science Letters, 45(2), 475–482. https://doi.org/10.1016/0012-821X(79)90146-8
Brudy, M., Zoback, M. D., Fuchs, K., Rummel, F., & Baumgärtner, J. (1997). Estimation of the complete stress tensor to 8 km depth in the KTB scientific drill holes: Implications for crustal strength. Journal of Geophysical Research: Solid Earth, 102(B8), 18453–18475. https://doi.org/10.1029/96JB02942
Cai, M. (2010). Practical estimates of tensile strength and Hoek– Brown strength parameter mi of brittle rocks. Rock Mechanics and Rock Engineering, 43(2), 167–184. https://doi.org/10.1007/s00603-009-0053-1
Carr, W. J. (1974). Summary of tectonic and structural evidence for stress orientation at the Nevada Test Site (74-176). http://pubs.er.usgs.gov/publication/ofr74176
Cheng, W., Jiang, G., Zhou, Z., Wei, Z., & Li, X. (2019). Numerical simulation for the dynamic breakout of a borehole using boundary element method. Geotechnical and Geological Engineering, 37(4), 2873–2881. https://doi.org/10.1007/s10706-019-00802-7
Cox, J. W. (1972). The high-resolution dipmeter reveals diprelated borehole and formation characteristics. Journal of Canadian Petroleum Technology, 11(1), PETSOC-72-01-02. https://doi.org/10.2118/72-01-02
Delonca, A., & Vallejos, J. A. (2020). Incorporating scale effect into a failure criterion for predicting stress-induced overbreak around excavations. International Journal of Rock Mechanics and Mining Sciences, 127, 104213. https://doi.org/10.1016/j.ijrmms.2020.104213
Fairhurst, C. (1964). On the validity of the ‘Brazilian’ test for brittle materials. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1(4), 535–546. https://doi.org/10.1016/0148-9062(64)90060-9
Feininger, T. (1968). The updip termination of a large dike of Westerly Granite and the regional distribution of the Westerly and Narragansett Pier Granites in Rhode Island and Connecticut. In Geological survey research (pp. D181–D185). United States Government Printing Office.
Gough, D. I., & Bell, J. S. (1982). Stress orientations from borehole wall fractures with examples from Colorado, east Texas, and northern Canada. Canadian Journal of Earth Sciences, 19(7), 1358–1370. https://doi.org/10.1139/e82-118
Haimson, B. (2007). Micromechanisms of borehole instability leading to breakouts in rocks. International Journal of Rock Mechanics and Mining Sciences, 44(2), 157–173. https://doi.org/10.1016/j.ijrmms.2006.06.002
Haimson, B. C., & Herrick, C. G. (1985). In-situ stress evaluation from borehole breakouts: experimental studies. In Proceedings of 26th US Symposium on Rock Mechanics (pp. 1207–1218). Rapid City, Balkema, Rotterdam.
Haimson, B. C., & Herrick, C. G. (1986). Borehole breakouts — a new tool for estimating in situ stress?. In Proceedings of International Symposium on Rock Stress and Rock Stress Measurements (pp. 271–280). Stockholm, Centek Publ., Luleå.
Haimson, B., & Lee, H. (2004). Borehole breakouts and compaction bands in two high-porosity sandstones. International Journal of Rock Mechanics and Mining Sciences, 41(2), 287–301. https://doi.org/10.1016/j.ijrmms.2003.09.001
Haimson, B. C., & Song, I. (1993). Laboratory study of borehole breakouts in Cordova Cream: a case of shear failure mechanism. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1047–1056. https://doi.org/10.1016/0148-9062(93)90070-T
Herrick, C. G., & Haimson, B. C. (1994, June). Modeling of episodic failure leading to borehole breakouts in Alabama limestone. In 1st North American Rock Mechanics Symposium (Paper Number: ARMA-1994-0217). Austin, Texas.
Hickman, S., & Zoback, M. (2004). Stress orientations and magnitudes in the SAFOD pilot hole. Geophysical Research Letters, 31(15). https://doi.org/10.1029/2004GL020043
Hoek, E. (1983). Strength of jointed rock masses. Géotechnique, 33(3), 187–223. https://doi.org/10.1680/geot.1983.33.3.187
Hoek, E., & Brown, E. (1980). Empirical strength criterion for rock masses. Journal of Geotechnical and Geoenvironmental Engineering, 106, 1013–1035. https://doi.org/10.1061/AJGEB6.0001029
Hoek, E., & Martin, C. D. (2014). Fracture initiation and propagation in intact rock – A review. Journal of Rock Mechanics and Geotechnical Engineering, 6(4), 287–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Huber, K., Fuchs, K., Palmer, J., Roth, F., Khakhaev, B. N., VanKin, L. E., Pevzner, L. A., Hickman, S., Moos, D., Zoback, M. D. & Schmitt, D. (1997). Analysis of borehole televiewer measurements in the Vorotilov drillhole, Russia – first results. Tectonophysics, 275(1–3), 261–272. https://doi.org/10.1016/S0040-1951(97)00031-0
Jaeger, J. C., Cook, N. G., & Zimmerman, R. (2009). Fundamentals of rock mechanics. John Wiley & Sons.
Lakirouhani, A., Asemi, F., Zohdi, A., Medzvieckas, J., & Kliukas, R. (2020). Physical parameters, tensile and compressive strength of dolomite rock samples: influence of grain size. Journal of Civil Engineering and Management, 26(8), 789–799. https://doi.org/10.3846/jcem.2020.13810
Lakirouhani, A., Detournay, E., & Bunger, A. P. (2016). A reassessment of in situ stress determination by hydraulic fracturing. Geophysical Journal International, 205(3), 1859–1873. https://doi.org/10.1093/gji/ggw132
Lee, M., & Haimson, B. (1993). Laboratory study of borehole breakouts in Lac du Bonnet granite: a case of extensile failure mechanism. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1039–1045. https://doi.org/10.1016/0148-9062(93)90069-P
Leeman, E. R. (1964a). The measurement of stress in rock: Part I: The principles of rock stress measurements. Journal of the Southern African Institute of Mining and Metallurgy, 65(2), 45–81.
Leeman, E. R. (1964b). The measurement of stress in rock: Part II: Borehole rock stress measuring instruments. Journal of the Southern African Institute of Mining and Metallurgy, 65(2), 82–114.
Leeman, E. R. (1964c, October). Absolute rock stress measurements using a borehole trepanning stress-relieving technique. In The 6th U.S Symposium on Rock Mechanics (USRMS) (Paper Number: ARMA-64-407). Rolla, Missouri, USA.
Lin, H., Kang, W. H., Oh, J., & Canbulat, I. (2020). Estimation of in-situ maximum horizontal principal stress magnitudes from borehole breakout data using machine learning. International Journal of Rock Mechanics and Mining Sciences, 126, 104199. https://doi.org/10.1016/j.ijrmms.2019.104199
Mastin, L. G. (1984). Development of borehole breakouts in sandstone [MSc thesis]. Stanford University, Palo Alto.
Martin, C. D., Martino, J. B., & Dzik, E. J. (1994, August). Comparison of borehole breakouts from laboratory and field tests. In Rock Mechanics in Petroleum Engineering (Paper Number: SPE-28050-MS). Delft, Netherlands. https://doi.org/10.2118/28050-MS
Okland, D., & Cook, J. M. (1998, July). Bedding-related borehole instability in high-angle wells. In SPE/ISRM Rock Mechanics in Petroleum Engineering (Paper Number: SPE-47285-MS). Trondheim, Norway. https://doi.org/10.2118/47285-MS
Ramsey, J. M., & Chester, F. M. (2004). Hybrid fracture and the transition from extension fracture to shear fracture. Nature, 428, 63–66. https://doi.org/10.1038/nature02333
Reinecker, J., Heidbach, O., Tingay, M., Sperner, B., & Müller, B. (2005). The release 2005 of the World Stress Map. http://www.world-stress-map.org/
Setiawan, N. B., & Zimmerman, R. W. (2018). Wellbore breakout prediction in transversely isotropic rocks using true-triaxial failure criteria. International Journal of Rock Mechanics and Mining Sciences, 112, 313–322. https://doi.org/10.1016/j.ijrmms.2018.10.033
Shalev, E., Bauer, S. J., Homel, M. A., Antoun, T. H., Herbold, E. B., Vorobiev, O. Y., Levin, H., Oren, V., & Lyakhovsky, V. (2021). Borehole breakout modeling in arkose and granite rocks. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 7(1), 15. https://doi.org/10.1007/s40948-021-00215-y
Shamir, G., & Zoback, M. D. (1992). Stress orientation profile to 3.5 km depth near the San Andreas Fault at Cajon Pass, California. Journal of Geophysical Research: Solid Earth, 97(B4), 5059–5080. https://doi.org/10.1029/91JB02959
Song, I. (1998). Borehole breakouts and core disking in Westerly granite: Mechanisms of formation and relationship to in situ stress (Publication No. AAI9825734) [Doctoral dissertation, Wilmington University]. ProQuest Dissertations & Theses Global.
Song, I., & Haimson, B. C. (1997). Polyaxial strength criteria and their use in estimating in situ stress magnitudes from borehole breakout dimensions. International Journal of Rock Mechanics and Mining Sciences, 34(3–4), 116.e1–116.e16. https://doi.org/10.1016/S1365-1609(97)00240-2
Syarifuddin, N., & Busono, I. (1999). Regional stress alignments in the Kutai Basin, East Kalimantan, Indonesia: a contribution from a borehole breakout study. Journal of Asian Earth Sciences, 17(1), 123–135. https://doi.org/10.1016/S0743-9547(98)00049-X
van den Hoek, P. J. (2001, July). Prediction of different types of cavity failure using bifurcation theory. In The 38th U.S. Symposium on Rock Mechanics (USRMS) (Paper Number: ARMA01-0045). DC Rocks 2001, Washington, D.C.
Wu, H., Guo, N., & Zhao, J. (2017). Borehole instabilities in granular rocks revisited: A multiscale perspective. In E. Papamichos, P. Papanastasiou, E. Pasternak, & A. Dyskin A. (Eds.), Bifurcation and degradation of geomaterials with engineering applications (IWBDG 2017). Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-319-56397-8_54
Yousefian, H., Fatehi Marji, M., Soltanian, H., Abdollahipour, A., & Pourmazaheri, Y. (2020). Wellbore trajectory optimization of an Iranian oilfield based on mud pressure and failure zone. Journal of Mining and Environment, 11(1), 193–220. https://doi.org/10.22044/jme.2020.8779.1768
Zoback, M. D., Moos, D., Mastin, L., & Anderson, R. N. (1985). Well bore breakouts and in situ stress. Journal of Geophysical Research, 90(B7), 5523–5530. https://doi.org/10.1029/JB090iB07p05523
Zoback, M. D., Barton, C. A., Brudy, M., Castillo, D. A., Finkbeiner, T., Grollimund, B. R., Moos, D. B., Peska, P., Ward, C. D., & Wiprut, D. J. (2003). Determination of stress orientation and magnitude in deep wells. International Journal of Rock Mechanics and Mining Sciences, 40(7), 1049–1076. https://doi.org/10.1016/j.ijrmms.2003.07.001