Mining of Mineral Deposits

ISSN 2415-3443 (Online)

ISSN 2415-3435 (Print)

Flag Counter

Simulation of sample testing under compression with the help of finite-element model of rocks being broken

A. Olovyannyy1, V. Chantsev2

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

2Peter the Great Saint-Petersburg Polytechnic University, Saint-Petersburg, Russian Federation


Min. miner. depos. 2018, 12(3):9-21


Full text (PDF)


      ABSTRACT

      Purpose of the paper is to develop mathematical model describing nature of argillous and salt samples under compression and to make available microdefects using finite-element method.

      Methods. To simulate behaviour of cylindrical rock samples under axial strain, finite-element model of rocks, being broken, is applied. In terms of the assumed model, components of medium with the disturbed continuity are calculated as those being continuous with anisotropic deformational and strength properties. Failure is considered as strength loss in terms of displacement and tensile on the anisotropy planes of the element. Within each point of the medium (if finite-element method is applied, then each element is meant) the limited number of planes of possible failure with 45° pitch is considered; they are used within each stage to evaluate potential failure resulting from displacement stresses or tensile ones. Coulomb-Mohr criteria as well as tensile strength are applied to determine potential failure on sites.

      Findings. It has been determined that mathematical modeling enables observing the process of disturbances within the sample. Stress-deformation diagrams, being a result of the modeling, demonstrate features of the sample beha-viour during different loading stages (i.e. nonlinear nature up to the peak load; decrease while breaking; residual strength; and hysteresis loops in terms of cyclic loading). It has been proved that if the model parameters are selected adequately, acceptable coincidence of both calculated and laboratory curves describing connections of axial strains and side strains with pressure on the samples of clay, sylvinite, and rock salt can be achieved.

      Originality. Finite-element has been developed. The model makes it possible to describe processes of strain and failure of rock samples in the context of laboratory tests; moreover, the model differs in the fact that it is added by the description of deformation processes taking place in microfissures and pores.

      Practical implications. Modeling with the use of finite-element method for rocks under breaking helps reach sufficient coincidence of the calculated diagrams of sample tests with graphs of stresses-deformations connection resul-ting from the laboratory studies. The obtained positive results confirm applicability of finite-element model of rock deformation and failure in terms of rock pressure problems.

      Keywords: rock, samples, deformation, failure, deformation of pores, mathematical modeling, finite-element method


      REFERENCES

Abdellah, W. (2007). Drilling parameters in relation to penetration rates, as a tool to predict the type of rock. PhD Thesis. Assiut, Egypt: University of Assiut.

Abouzeid, A.A., & Cooper, A.G. (2003). Experimental verification of drilling simulator. In 9th International Conference on Mining, Petroleum and Metallurgical Engineering. Ismailia, Egypt: Suez Canal University.

Chiarelli, A.S., Shao, J.F., & Hoteit, N. (2003). Modeling of elastoplastic damage behavior of a claystone. International Journal of Plasticity, 19(1), 23-45.
https://doi.org/10.1016/s0749-6419(01)00017-1

Cox, S.J.D., & Meredith, P.G. (1993). Microcrack formation and material softening in rock measured by monitoring acoustic emissions. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(1), 11-24.
https://doi.org/10.1016/0148-9062(93)90172-a

Fadeev, A.B. (1987). Metod konechnykh elementov v geome-khanike. Moskva: Nedra.

Fang, Z., & Harrison, J.P. (2002). Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks. International Journal of Rock Mechanics and Mining Sciences, 39(4), 443-457.
https://doi.org/10.1016/s1365-1609(02)00035-7

Fisenko, G.L. (1976). Predel’noe sostoyanie gornykh porod vokrug vyrabotok. Moskva: Nedra.

Hamdi, P., Stead, D., & Elmo, D. (2015). Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach. Journal of Rock Mechanics and Geotechnical Engineering, 7(6), 609-625.
https://doi.org/10.1016/j.jrmge.2015.07.005

Hoek, E., & Brown, E.T. (1980). Empirical strength criterion for rock masses. Journal of the Geotechnical Engineering Division, 106(15715), 1013-1035.

Hoxha, D., Giraud, A., Homand, F., & Auvray, C. (2007). Saturated and unsaturated behaviour modelling of Meuse-Haute/Marne argillite. International Journal of Plasticity, 23(5), 733-766.
https://doi.org/10.1016/j.ijplas.2006.05.002

Kartashov, Yu.M., Matveev, B.V., Mikheev, G.V., & Fadeev, A.B. (1979). Prochnost’ i deformiruemost’ gornykh porod. Moskva: Nedra.

Lee, Y.-K., & Pietruszczak, S. (2008). Application of critical plane approach to the prediction of strength anisotropy in transversely isotropic rock masses. International Journal of Rock Mechanics and Mining Sciences, 45(4), 513-523.
https://doi.org/10.1016/j.ijrmms.2007.07.017

Lisjak, A., Figi, D., & Grasselli, G. (2014). Fracture development around deep underground excavations: Insights from FDEM modelling. Journal of Rock Mechanics and Geotechnical Engineering, 6(6), 493-505.
https://doi.org/10.1016/j.jrmge.2014.09.003

Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A., & Sidorin, A. (1991). Quasi-static fault growth and shear fracture energy in granite. Nature, 350(6313), 39-42.
https://doi.org/10.1038/350039a0

Lydzba, D., Pietruszczak, S., & Shao, J.F. (2003). On anisotropy of stratified rocks: homogenization and fabric tensor approach. Computers and Geotechnics, 30(4), 289-302.
https://doi.org/10.1016/s0266-352x(03)00004-1

Ma, G.W., Wang, X.J., & Ren, F. (2011). Numerical simulation of compressive failure of heterogeneous rock-like materials using SPH method. International Journal of Rock Mecha-nics and Mining Sciences, 48(3), 353-363.
https://doi.org/10.1016/j.ijrmms.2011.02.001

Nova, R. (1980). The failure of transversely isotropic rocks in triaxial compression. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 17(6), 325-332.
https://doi.org/10.1016/0148-9062(80)90515-x

Nur, A., & Simmons, G. (1970). The origin of small cracks in igneous rocks. International Journal of Rock Mecha-nics and Mining Sciences & Geomechanics Abstracts, 7(3), 307-314.
https://doi.org/10.1016/0148-9062(70)90044-6

Olovyannyy, A.G. (2003). Nekotorye zadachi mekhaniki gornykh porod. Sankt-Petergurg: Stress.

Olovyannyy, A.G. (2012). Mekhanika gornykh porod. Mo-delirovanie razrusheniy. Sankt-Petergurg: Kosta.

Olovyannyy, A.G. (2016). Gravitatsionnye i tektonicheskie napryazheniya v massive gornykh porod. Gornyy Zhurnal, (4), 25-31.

Pan, X.D., & Hudson, J.A. (1989). Simplified three dimensional Hock-Braun yield criterion. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 26(2), 95-103.
https://doi.org/10.1016/0148-9062(89)90069-7

Pariseau, WG. (1968). Plasticity theory for anisotropic rocks and soils. Proceedings of the 10th Symposium on Rock Mechanics, 267-295.

Pells, P.J.N. (1993). Uniaxial strength testing. Rock Testing and Site Characterization, (3), 67-85.
https://doi.org/10.1016/B978-0-08-042066-0.50010-0

Petukhov, I.M., & Lin’kov, A.M. (1983). Mekhanika gornykh udarov i vybrosov. Moskva: Nedra.

Pietruszczak, S., & Mroz, Z. (2001). On failure criteria for anisotropic cohesive-frictional materials. International Journal for Numerical and Analytical Methods in Geomechanics, 25(5), 509-524.
https://doi.org/10.1002/nag.141

Shao, J.F., Jia, Y., Kondo, D., & Chiarelli, A.S. (2006). A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions. Mechanics of Materials, 38(3), 218-232.
https://doi.org/10.1016/j.mechmat.2005.07.002

Shen, W.Q., & Shao, J.F. (2017). Some micromechanical models of elastoplastic behaviors of porous geomaterials. Journal of Rock Mechanics and Geotechnical Engineering, 9(1), 1-17.
https://doi.org/10.1016/j.jrmge.2016.06.011

Stavrogin, A.N., & Tarasov, B.G. (1992). Eksperimental’naya fizika i mekhanika gornykh porod. Sankt-Petergurg: Nauka.

Tang, C., Liu, H., Lee, P.K., Tsui, Y., & Tham, L. (2000). Numerical studies of the influence of microstructure on rock failure in uniaxial compression – Part I: effect of heterogeneity. International Journal of Rock Mechanics and Mining Sciences, 37(4), 555-569.
https://doi.org/10.1016/s1365-1609(99)00121-5

Tang, C., Tham, L., Lee, P.K., Tsui, Y., & Liu, H. (2000). Numerical studies of the influence of microstructure on rock failure in uniaxial compression – Part II: constraint, slenderness and size effect. International Journal of Rock Mechanics and Mining Sciences, 37(4), 571-583.
https://doi.org/10.1016/s1365-1609(99)00122-7

Unteregger, D., Fuchs, B., & Hofstetter, G. (2015). A damage plasticity model for different types of intact rock. International Journal of Rock Mechanics and Mining Sciences, (80), 402-411.
https://doi.org/10.1016/j.ijrmms.2015.09.012

Walsh, J.B., & Brace, W.F. (1964). A fracture criterion for brittle anisotropic rock. Journal of Geophysical Research, 69(16), 3449-3456.
https://doi.org/10.1029/jz069i016p03449

Wawersik, W.R., & Fairhurst, C. (1970). A study of brittle rock fracture in laboratory compression experiments. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 7(5), 561-575.
https://doi.org/10.1016/0148-9062(70)90007-0

Wawersik, W.R., & Brace, W.F. (1971). Post-failure behavior of a granite and diabase. Rock Mechanics & Rock Engineering, 3(2), 61-85.
https://doi.org/10.1007/bf01239627

Лицензия Creative Commons