Nonlinear criteria and the influence of the average principal stress on rocks destruction
A. Olovyannyy1
1Saint-Petersburg Branch of the Federal State Budgetary Institution of Science of the Institute of Geoecology named after E.M. Sergeev of the Russian Academy of Sciences, Saint-Petersburg, Russian Federation
Min. miner. depos. 2018, 12(4):37-45
https://doi.org/10.15407/mining12.04.037
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ABSTRACT
Purpose. Consider possible series methods of Mohr-Coulomb nonlinear criterion that takes into account stresses in the plane of fracture. Investigate the influence of the average principal stress on rocks destruction when cylinder modeling under axial and side load conditions. Determine the weakening effect on the internal friction angle in the rocks under study using the examples of sample testing simulation.
Methods. To study the processes in rock samples, we used a finite-element method DESTROCK-FE for modeling the deformation of rocks decomposes. The parameters of the deformation and fracture model are determined by comparing the deformation curves obtained by the modeling and experimental approaches.
Findings. Modeling of rocks deformation under various loading conditions with a nonlinear criterion of fracture variants, in which destructive stresses can grow limited or unlimited or even decrease with increasing pressure, is performed. The design charts of axial and side deformations of the samples with a good approximation coincide with the experimental ones. The model parameters, including those for triaxial load conditions, are determined with a mathematic method using simulation laboratory tests under axial compression. Modeling with an upgrade fracture criterion showed that the load-bearing strength of salt rock samples under side load is greater than with axial pressure. Internal friction angle reduction with loss of strength reaches 15%.
Originality. The Mohr-Coulomb series criterion is proposed, which makes it possible to set the nonlinearity in accordance with experimental data. Mechanical model parameters of rocks can be determined according to the results of single sample testing using the finite-element method DESTROCK-FE of decomposed rocks. The simulation was performed taking into account microdeformation, the influence of which is described by equations for a nonlinear-elastic condition.
Practical implications. Cylinder modeling showed that the load-bearing strength of samples under side load is 10% for sylvinite and 20% more for rock salt than at axial loading. The obtained results indicate the ability of the finite-element method DESTROCK-FE of rocks destruction modeling while geomechanics survey conducting. Using this method, based on single sample simulation results, tested at simple compression, the parameters of elasticity, plasticity, viscosity, crisping can be obtained, suitable for deformation and fracture processes studies under various loading conditions.
Keywords: rock, mathematic simulation of rock deformation and fracture, microdeformation, finite-element method, fracture criteria, internal friction angle
REFERENCES
Barton, N. (1976). The shear strength of rock and rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 13(9), 255-279.
https://doi.org/10.1016/0148-9062(76)90003-6
Barton, N. (2013). Shear strength criteria for rock, rock joints, rockfill and rock masses: Problems and some solutions. Journal of Rock Mechanics and Geotechnical Engineering, 5(4), 249-261.
https://doi.org/10.1016/j.jrmge.2013.05.008
Benz, T., Schwab, R., Kauther, R.A., & Vermeer, P.A. (2008). A Hoek-Brown criterion with intrinsic material strength factorization. International Journal of Rock Mechanics and Mining Sciences, 45(2), 210-222.
https://doi.org/10.1016/j.ijrmms.2007.05.003
Bieniawski, Z.T. (1974). Estimating the strength of rock materials. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 11(8), A160.
https://doi.org/10.1016/0148-9062(74)91782-3
Drucker, D.C., & Prager, W. (1952). Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics, 10(2), 157-165.
https://doi.org/10.1090/qam/48291
Hoek, E., & Brown, E. (1980). Empirical strength criterion for rock masses. Journal of the Geotechnical Engineering Division, 106(9), 1013-1035.
Hoek, E. (1994). Strength of rock and rock masses. ISRM News, 2(2), 4-16.
Lade, P.V. (1977). Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. International Journal of Solids and Structures, 13(11), 1019-1035.
https://doi.org/10.1016/0020-7683(77)90073-7
Litvinskiy, G.G. (2008). Analiticheskaya teoriya prochnosti gornykh porod i massivov. Donetsk: Nord-Press.
Maïolino, S. (2005). Proposition of a general yield function in geomechanics. Comptes Rendus Mécanique, 333(3), 279-284.
https://doi.org/10.1016/j.crme.2004.11.008
Matsuoka, H., & Nakai, T. (1982). A new failure criterion for soils in three dimensional stresses. In IUTAM Conference on Deformation and Failure of Granular Materials (pp. 253-263). Rotterdam, The Netherlands: A.A. Balkema.
Matsuoka, H., & Nakai, T. (1985). Relationship among Tresca, Mises, Mohr-Coulomb and Matsuoka-Nakai failure criteria. Soils and Foundations, 25(4), 123-128.
https://doi.org/10.3208/sandf1972.25.4_123
Mogi, K. (1967). Effect of the intermediate principal stress on rock failure. Journal of Geophysical Research, 72(20), 5117-5131.
https://doi.org/10.1029/jz072i020p05117
Mogi, K. (2007). Experimental rock mechanics. London, Uni-ted Kingdom: CRC Press, Taylor & Francis Group.
https://doi.org/10.1201/9780203964446
Olovyannyy, A.G. (2003). Nekotorye zadachi mekhaniki gornykh porod. Sankt-Petergurg: Stress.
Olovyannyy, A.G. (2012). Mekhanika gornykh porod. Modeli-rovanie razrusheniy. Sankt-Petergurg: Kosta.
Protod’yakonov, M.M. (1962). Obobshchennoe uravnenie ogibayushchikh k predel’nym krugam napryazhenii Mora. Issledovanie Fiziko-Mekhanicheskikh Svoistv Gornykh Porod Primenitel’no k Zadacham Upravleniya Gornym Davleniem, 82-89.
Ramamurthy, T., Rao, G.V., & Rao, K.S. (1985). A strength criterion for rocks. Indian Geotechnical Conference, 1(1), 59-64.
Roscoe, K.H., & Burland, J.B. (1968). On the generalized stress-strain behavior of “wet” clay. Cambridge, United Kingdom: Cambridge University Press.
Ruppeneit, K.V., & Liberman, Yu.M. (1960). Vvedenie v mekhaniku gornykh porod. Moskva: Gosgortekhizdat.
Shashenko, A.N., & Pustovoitenko, V.P. (2001). Raschet nesu-shchikh elementov podzemnykh sooruzheniy. Kyiv: Naukova dumka.
Sheorey, P.R. (1997). Empirical rock failure criteria. Rotterdam, The Netherlands: A.A. Balkema.
Singh, M., Raj, A., & Singh, B. (2011). Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. International Journal of Rock Mechanics and Mining Sciences, 48(4), 546-555.
https://doi.org/10.1016/j.ijrmms.2011.02.004
Singh, M., & Singh, B. (2012). Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks. International Journal of Rock Mechanics and Mining Sciences, 51(1), 43-52.
https://doi.org/10.1016/j.ijrmms.2011.12.007
Ulitskiy, V.M., Shashkin, A.H., & Shashkin, K.H. (2010). Geo-tekhnicheskoe soprovozhdenie razvitiya gorodov. Sankt-Peterburg: Stroyizdat Severo-Zapad.
Wiebols, G.A., & Cook, N.G.W. (1968). An energy criterion for the strength of rock in polyaxial compression. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 5(6), 529-549.
https://doi.org/10.1016/0148-9062(68)90040-5
You, M. (2009). True-triaxial strength criteria for rock. International Journal of Rock Mechanics and Mining Sciences, 46(1), 115-127.
https://doi.org/10.1016/j.ijrmms.2008.05.008
You, M. (2013). Discussion on “A generalized three-dimensional failure criterion for rock masses.” Journal of Rock Mecha-nics and Geotechnical Engineering, 5(5), 412-416.
https://doi.org/10.1016/j.jrmge.2013.07.006
Yu, M., Xia, G., & Kolupaev, V.A. (2009). Basic characteristics and development of yield criteria for geomaterials. Journal of Rock Mechanics and Geotechnical Engineering, 1(1), 71-88.
https://doi.org/10.3724/sp.j.1235.2009.00071
