Geomechanics and Engineering

  • 제32권1호
  • /
  • Pages.49-68
  • /
  • 2023
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new extended Mohr-Coulomb criterion in the space of three-dimensional stresses on the in-situ rock

  • Mohatsim, Mahetaji (Department of Petroleum Engineering, School of Energy Technology, Pandit Deendayal Energy University- PDEU) ;
  • Jwngsar, Brahma (School of Technology, Pandit Deendayal Energy University- PDEU) ;
  • Rakesh Kumar, Vij (Department of Petroleum Engineering, School of Energy Technology, Pandit Deendayal Energy University- PDEU)
  • 투고 : 2022.06.11
  • 심사 : 2022.12.23
  • 발행 : 2023.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

The three-dimensional failure criterion is essential for maintaining wellbore stability and sand production problem. The convenient factor for a stable wellbore is mud weight and borehole orientation, i.e., mud window design and selection of borehole trajectory. This study proposes a new three-dimensional failure criterion with linear relation of three in-situ principal stresses. The number of failure criteria executed to understand the phenomenon of rock failure under in-situ stresses is the Mohr-Coulomb criterion, Hoek-Brown criterion, Mogi-Coulomb criterion, and many more. A new failure criterion is the extended Mohr-Coulomb failure criterion with the influence of intermediate principal stress (σ2). The influence of intermediate principal stress is considered as a weighting of (σ2) on the mean effective stress. The triaxial compression test data for eleven rock types are taken from the literature for calibration of material constant and validation of failure prediction. The predictions on rock samples using new criteria are the best fit with the triaxial compression test data points. Here, Drucker-Prager and the Mogi-Coulomb criterion are also implemented to predict the failure for eleven different rock types. It has been observed that the Drucker-Prager criterion gave over prediction of rock failure. On the contrary, the Mogi-Coulomb criterion gave an equally good prediction of rock failure as our proposed new 3D failure criterion. Based on the yield surface of a new 3D linear criterion it gave the safest prediction for the failure of the rock. A new linear failure criterion is recommended for the unique solution as a linear relation of the principal stresses rather than the dual solution by the Mogi-Coulomb criterion.

키워드

참고문헌

  1. Al-Ajmi, A.M. and Zimmerman, R.W. (2005), "Relation between the Mogi and the Coulomb failure criteria", Int. J. Rock Mech. Min. Sci., 42(3), 431-439. https://doi.org/10.1016/j.ijrmms.2004.11.004. 
  2. Al-Ajmi, A.M. and Zimmerman, R.W. (2006), Stability analysis of vertical boreholes using the Mogi-Coulomb failure criterion". Int. J. Rock Mech. Min. Sci., 43(8), 1200-1211. https://doi.org/10.1016/j.ijrmms.2006.04.001. 
  3. Aslannezhad, M., Keshavarz, A. and Kalantariasl, A. (2020), "Evaluation of mechanical, chemical, and thermal effects on wellbore stability using different rock failure criteria", J. Nat. Gas Sci. Eng., 78, 103276. https://doi.org/10.1016/j.jngse.2020.103276 . 
  4. Barsanescu, P., Sandovici, A. and Serban, A. (2018), "Mohr-Coulomb criterion with circular failure envelope, extended to materials with strength-differential effect", Mater. Design, 148, 49-70. https://doi.org/10.1016/j.matdes.2018.03.043. 
  5. Brannon, Rebecca Moss, Fossum, Arlo Frederick, and Strack, Otto Eric. KAYENTA : theory and user's guide.. United States: N. p., 2009. Web. doi:10.2172/984159. KAYENTA : theory and user's guide. (Technical Report) | OSTI.GOV 
  6. Chai, Z., Bai, J. and Sun, Y. (2019), "Change of pore structure and Uniaxial compressive strength of sandstone under electrochemical coupling", Geomech. Eng., 17(2), 157-164. https://doi.org/10.12989/gae.2019.17.2.157. 
  7. Chinaei, F., Ahangari, K. and Shirinabadi, R. (2021), "Hoek-Brown failure criterion for damage analysis of tunnels subjected to blast load", Geomech. Eng., 26(1), 41-47. https://doi.org/10.12989/gae.2021.26.1.041 
  8. Colmenares, L.B. and Zoback, M.D. (2002), "A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks", Int. J. Rock Mech. Min. Sci., 39(6), 695-729. https://doi.org/10.1016/S1365-1609(02)00048-5. 
  9. Comanici, A.M. and Barsanescu, P.D. (2018), "Modification of Mohr's criterion in order to consider the effect of the intermediate principal stress", Int. J. Plasticity, 108, 40-54. https://doi.org/10.1016/j.ijplas.2018.04.010 
  10. Das, B. and Chatterjee, R. (2017), "Wellbore stability analysis and prediction of minimum mud weight for few wells in Krishna-Godavari Basin, India", Int. J. Rock Mech. Min. Sci., 93, 30-37. https://doi.org/10.1016/j.ijrmms.2016.12.018. 
  11. Drucker, D.C. and Prager, W. (1952), "Soil mechanics and plastic analysis or limit design", Quarterly Appl. Math., 10(2), 157-165.  https://doi.org/10.1090/qam/48291
  12. Haimson, B. and Chang, C. (2000), "A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite", Int. J. Rock Mech. Min. Sci., 37(1-2), 285-296. https://doi.org/10.1016/S1365-1609(99)00106-9. 
  13. He, P.F., Ma, X.D., He, M.C., Tao, Z.G. and Liu, D.Q. (2022), "Comparative study of nine intact rock failure criteria via analytical geometry", Rock Mech. Rock Eng., 1-24. https://doi.org/10.1007/s00603-022-02816-9. 
  14. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", Int. J. Rock Mech. Min. Sci., 34(8), 1165-1186. https://doi.org/10.1016/S1365-1609(97)80069-X. 
  15. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), "Hoek-Brown failure criterion-2002 edition", Proceedings of NARMSTac, 1(1), 267-273. 
  16. Jiang, H. (2015), "Failure criteria for cohesive-frictional materials based on Mohr-Coulomb failure function", Int. J. Numer. Anal. Method. Geomech., 39(13), 1471-1482. https://doi.org/10.1002/nag.2366. 
  17. Jiang, H. (2018), "Simple three-dimensional Mohr-Coulomb criteria for intact rocks", Int. J. Rock Mech. Min. Sci., 105, 145-159. https://doi.org/10.1016/j.ijrmms.2018.01.036. 
  18. Kim, M.K. and Lade, P.V. (1984), "February. modelling rock strength in three dimensions", Int. J. Rock Mech. Min. Sci. Geomech. Abstracts, 21(1), 21-33. https://doi.org/10.1016/0148-9062(84)90006-8. 
  19. Krabbenhoft, K., Lyamin, A.V. and Sloan, S.W. (2008), "Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming", Commun. Numer. Method. Eng., 24(11), 1107-1119. https://doi.org/10.1002/cnm.1018. 
  20. Labuz, J.F. and Zang, A. (2012), "Mohr-Coulomb failure criterion", Rock Mech. Rock Eng., 45(6), 975-979. https://doi.org/10.1007/s00603-012-0281-7. 
  21. Lee, C., Nam, H., Lee, W., Choo, H. and Ku, T. (2019), "Estimating UCS of cement-grouted sand using characteristics of sand and UCS of pure grout", Geomech. Eng., 19(4), 343-352. https://doi.org/10.12989/gae.2019.19.4.343. 
  22. Lee, Y.K., Pietruszczak, S. and Choi, B.H. (2012), "Failure criteria for rocks based on smooth approximations to Mohr-Coulomb and Hoek-Brown failure functions", Int. J. Rock Mech. Min. Sci., 56, 146-160. https://doi.org/10.1016/j.ijrmms.2012.07.032. 
  23. Lian, J., Sharaf, M., Archie, F. and Muenstermann, S. (2013), "A hybrid approach for modelling of plasticity and failure behaviour of advanced high-strength steel sheets", Int. J. Damage Mech., 22, 188-218. https://doi.org/10.1177/1056789512439319. 
  24. Ma, X. and Haimson, B.C. (2016), "Failure characteristics of two porous sandstones subjected to true triaxial stresses", J. Geophys. Res.: Solid Earth, 121(9), 6477-6498. https://doi.org/10.1002/2016JB012979. 
  25. Meyer, J.P. and Labuz, J.F. (2013), "Linear failure criteria with three principal stresses", Int. J. Rock Mech. Min. Sci., 60, 180-187. https://doi.org/10.1016/j.ijrmms.2012.12.040. 
  26. Mogi, K. (1971), "Fracture and flow of rocks under high triaxial compression", J. Geophys. Res., 76(5), 1255-1269. https://doi.org/10.1029/JB076i005p01255. 
  27. Mogi, K. (2006.), Experimental rock mechanics, 3, CRC Press. 
  28. Noohnejad, A., Ahangari, K. and Goshtasbi, K. (2021), "Quantitative risk assessment for wellbore stability analysis using different failure criteria", Geomech. Eng., 24(3), 281-293. https://doi.org/10.12989/gae.2021.24.3.281. 
  29. Ottosen, N.S. (1977), "A failure criterion for concrete", J. Eng. Mech. Div., 103(4), 527-535. https://doi.org/10.1061/JMCEA3.0002248. 
  30. Qi, W., Shuo, X., Ke, G.H., Peng, Z., Bei, J. and Hong, L.B. (2020), "Energy analysis-based core drilling method for the prediction of rock uniaxial compressive strength", Geomech. Eng., 23(1), 61-69. https://doi.org/10.12989/gae.2020.23.1.061. 
  31. Rahimi, R. and Nygaard, R. (2018), "Effect of rock strength variation on the estimated borehole breakout using shear failure criteria", Geomech. Geophys. Geo-energ. Geo-resour., 4(4), 369-382. https://doi.org/10.1007/s40948-018-0093-7. 
  32. Si, X., Gong, F., Li, X., Wang, S. and Luo, S. (2019), "Dynamic Mohr-Coulomb and Hoek-Brown strength criteria of sandstone at high strain rates", Int. J. Rock Mech. Min. Sci., 115, 48-59. https://doi.org/10.1016/j.ijrmms.2018.12.013. 
  33. Singh, A., Rao, K.S. and Ayothiraman, R. (2019), "An analytical solution to wellbore stability using Mogi-Coulomb failure criterion", J. Rock Mech. Geotech. Eng., 11(6), 1211-1230. https://doi.org/10.1016/j.jrmge.2019.03.004. 
  34. Staat, M. (2021), "An extension strain type Mohr-Coulomb criterion", Rock Mech. Rock Eng., 54(12), 6207-6233. https://doi.org/10.1007/s00603-021-02608-7. 
  35. Takahashi, M. and Koide, H. (1989), "Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m", Proceedings of the ISRM international symposium. International Society for Rock Mechanics and Rock Engineering. 
  36. Ulusay, R. (Ed.) (2014), The ISRM suggested methods for rock characterization, testing and monitoring: 2007-2014. 
  37. Yan, C., Ren, X., Cheng, Y., Zhao, K., Deng, F., Liang, Q., Zhang, J., Li, Y. and Li, Q. (2019), "An experimental study on the hydraulic fracturing of radial horizontal wells", Geomech. Eng., 17(6), 535-541. https://doi.org/10.12989/gae.2019.17.6.535. 
  38. Yi, X., Valko, P.P. and Russell, J.E. (2005), "Effect of rock strength criterion on the predicted onset of sand production", Int. J. Geomech., 5(1), 66-73. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:1(66). 
  39. Yu, L. and Wang, T.C. (2019), "Generalized Mohr-Coulomb strain criterion for bulk metallic glasses under complex compressive loading", Sci Rep 9, 12554. https://doi.org/10.1038/s41598-019-49085-1 
  40. Zhang, J.J. (2019), Applied petroleum geomechanics, Gulf Professional Publishing. 
  41. Zhang, L., Cao, P. and Radha, K.C. (2010), "Evaluation of rock strength criteria for wellbore stability analysis", Int. J. Rock Mech. Min. Sci., 47(8), 1304-1316. https://doi.org/10.1016/j.ijrmms.2010.09.001.