Development of new linear and nonlinear failure criteria of true triaxial stresses of rock by the critical analysis of various rocks test results

Author

Associate Professor, Dept. of Mining Engineering, Urmia University

Abstract

There are various failure criteria for true triaxial stresses, which have initially been developed for the fracture of solid material such as metals.  These criteria are applied for the stability analysis of wellbores and some storage caverns in rock media.  In this research, true triaxial failure criteria has been investigated comprehensively by a new method using 12 groups of true triaxial strength test results of rocks including granite, monzonite, amphibolite, andesite, dolomite, Limestone, trachyte, marble, sandstone and shale.  The Von Mises and Murrell criteria would not fit the test results due to their particular forms.  Neither, Drucker and Prager criterion would fit the test results because of non-correlation between its defined parameters and the mechanical properties such as internal friction angle (ϕ).  The relationship between octahedral shear stress (toct) and octahedral normal stress (σoct) having a constant exponent is shown to fit well the various groups of test results. The coefficient of this new criterion (B) that has been obtained by functional fitting is in good correlation with the parameters of ϕ, mi and σci. The power function relationship between toct and the mean of minimum and maximum principal stresses (σm,2) is found to be have a constant exponent also showing a good correlation with the various test results. The coefficient of this criterion (B') showed a good correlation with the parameters of ϕ, mi and σci., too. The linear relationship between toct and σoct of true triaxial strength test results was analyzed.  A linear failure criterion was obtained to fit the 12 groups of results, as acceptable correlations have been obtained between the constant and coefficient of this new criterion with the mechanical properties such as internal friction angle (ϕ) and cohesive strength (C).  Mogi-Coulomb linear criterion (relationship between toct and σm,2) also fitted the results and an acceptable correlation has been obtained between the defined constant and coefficient parameters of this criterion with the mechanical properties.  The linear failure criteria are preferred that is because of having the constant parameter which is a function of mechanical properties of internal friction angle (ϕ) and cohesive strength (C).

Keywords

References

[1]     Von‌Mises, R. (1913). “Mechanik der festen Krper in Plastisch deformablem Zustand [Mechanics of solid bodies undergoing plastic deformation]”. Goett. Nachr. Math. Phys. Kl., 582–92.
[2]     Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plastic analysis or limite design”. Quarterly of Applied Mathematics, 10: 157-165.
[3]     Murrell, S. A. F. (1962). “A criterion for brittle fracture of rocks and concrete under triaxial stress, and the effect of pore pressure on the criterion”. Fifth U.S. Symposium of Rock Mechanics, Minneapolis, Minnesota, 563 –577.
[4]     Mogi, K. (1971). “Fracture and Flow under High Triaxial Compression”. Journal of Geophysical Research,  76: 1255–1269.
[5]     Haimson, B. (2012). “A Failure criterion for rocks based on true triaxial testing”. Rock Mechanics and Rock Engineering, 45: 1007–1010.
[6]     Bradley, W. B. (1979). “Failure of inclined borehole”. Journal of Energy Resources Technology, 101: 232-239.
[7]     Aadnoy, B. S., and Chenevert, M. E. (1987). “Stability of highly inclined boreholes”. Journal of SPE Drilling Engineering, 2: 364-37.
[8]     McLean,  M. R., and Addis, M. A. (1990). “Wellbore Stability Analysis: A review of current methods of analysis and their field application IADC/SPE”. In proceeding of the IADC/SPE Drilling Conference, 27 February - 2 March, Houston, Texas, 261-274.
[9]     Rahimi, R. (2014). “The effect of using different rock failure criteria in wellbore Stability analysis”. MSc Thesis in Petroleum Engineering, Missouri University of Science and Technology.
[10] 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”. International Journal of Rock Mechanics and Mining Sciences, 39(6): 695-729.
[11] Al-Ajmi, A. M., and Zimmerman, R.W. (2005). “Relation between the Mogi and the Coulomb failure criteria”. International Journal of Rock Mechanics and Mining Sciences, 42: 431–439.
[12] فرهادی، محمد مهدی؛ 1391؛ "مدل سازی عددی پایداری چاه نفت بر اساس روش حفاری"، پایان نامه کارشناسی ارشد مکانیک سنگ، دانشکده مهندسی معدن، دانشگاه صنعتی سهند تبریز.
[13] Spetzler, H. A., Sobolev, G. A., Sondergeld, C. H., Salov, B. G., Getting, I. C., and Koltsov, A. (1981). “Surface deformation, crack formation, and acoustic velocity changes in pyrophyllite under polyaxial loading”. Journal of Geophysics Research, 86: 1070-1080.
[14] 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”. Rock at Great Depth, Ed. By Maury,V. and Fourmaintraux, D., Balkema, Rotterdam, 1: 19-26.
[15] Haimson, B. C., and Chang, C. (2002). “True triaxial strength of the KTB amphibolite under borehole wall conditions and its use to estimate the maximum horizontal in situ stress – art”. Journal of Geophysics Research-Solid Earth, 107(2257): 2257-2271.
[16] Haimson, B., and Rudnicki, J. W. (2010). “The effect of the intermediate principal stress on fault formation and fault angle in siltstone”. Journal of Structure Geology, 32(11): 1701- 1711.
[17] Al-Ajmi, A. M. (2006). “Wellbore stability analysis based on a new true-triaxial failure criterion”. TRITA-LWR PhD Thesis.
[18] Mogi, K. (2007). “Experimental Rock Mechanics”. University of Tokyo, Taylor and Francis Group, London, UK, 359 pages.
[19] Michelis, P. (1985).“Polyaxial yielding of granular rock”. Journal of Engineering Mechanics ASCE, 111(8): 1049-1066.
[20] Michelis, P. (1987). “True triaxial cyclic behavior of concrete and rock in compression”. International Journal of Plasticity, 3(3): 249-270.
[21] DataFit, (1992). “Data fitting by linear and multiple non-linear regression”. P.O.Box 1743, Macquarie Centre, N. S. W. 2113, Australia.
[22] Hoek E., Wood, D., and Shah, S. (1992). “A modified Heok-Brown failure criterion for jointed rock masses”. Eurock, London, 14-17 September, London, U.K., Thomas Telford, 209 – 214.
[23] Moomivand, H. (2011). “Development of a new method for estimating the indirect uniaxial compressive strength of rock using schmidt hammer”. Journal of BHM Berg- und Hüttenmännische Monatshefte (Journal of Mining, Metallurgical, Materials, Geotechnical and Plant Engineering), 156(4): 142 – 14.
Journal of Mineral Resources Engineering
Volume 2, Issue 1
June 2017
Pages 19-36

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  • Receive Date: 21 June 2017
  • Accept Date: 21 June 2017

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