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Numerical simulation of triaxial compression test for brittle rock sample using a modified constitutive law considering degradation and dilation behavior

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Abstract

The understanding of the rock deformation and failure process and the development of appropriate constitutive models are the basis for solving problems in rock engineering. In order to investigate progressive failure behavior in brittle rocks, a modified constitutive model was developed which follows the principles of the continuum damage mechanics method. It incorporates non-linear Hoek-Brown failure criterion, confining pressure-dependent strength degradation and volume dilation laws, and is able to represent the nonlinear degradation and dilation behaviors of brittle rocks in the post-failure region. A series of triaxial compression tests were carried out on Eibenstock (Germany) granite samples. Based on a lab data fitting procedure, a consistent parameter set for the modified constitutive model was deduced and implemented into the numerical code FLAC3D. The good agreement between numerical and laboratory results indicates that the modified constitutive law is well suited to represent the nonlinear mechanical behavior of brittle rock especially in the post-failure region.

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References

  1. OFOEGBU G I, CURRAN J H. Deformability of intact rock [J]. Int J Rock Mech Min Sci Geomech Abstr, 1992, 29(1): 35–48.

    Article  Google Scholar 

  2. KRAJCINOVIC D, FONSEKA G U. The continuous damage theory of brittle materials—Part 1: general theory [J]. J Appl Mech Trans ASME, 1981, 48: 809–815.

    Article  MATH  Google Scholar 

  3. COSTIN L S. Damage mechanics in the post-failure regime [J]. Mech Mater, 1985, 4: 149–160.

    Article  Google Scholar 

  4. BASISTA M, GROSS D. The sliding crack model of brittle deformation: An internal variable approach [J]. Int J Solids Struct, 1998, 35(5/6): 487–509.

    Article  MATH  Google Scholar 

  5. YUAN S C, HARRISON J P. A review of the state of the art in modelling progressive mechanical breakdown and associated fluid flow in intact heterogeneous rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(7): 1001–1022.

    Article  Google Scholar 

  6. MARTIN C D, CHANDLER N A. The progressive fracture of Lac du Bonnet granite [J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1994, 31(6): 643–659.

    Article  Google Scholar 

  7. HAJIABDOLMAJID V, KAISERAR P K, MARTIN C D. Modelling brittle failure of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(6): 731–741.

    Article  Google Scholar 

  8. FANG Z, HARRISON J P. A mechanical degradation index for rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(8): 1193–1199.

    Article  Google Scholar 

  9. FANG Z, HARRISON J P. Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(4): 443–457.

    Article  Google Scholar 

  10. FANG Z, HARRISON J P. Application of a local degradation model to the analysis of brittle fracture of laboratory scale rock specimens under triaxial conditions [J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(4): 459–476.

    Article  Google Scholar 

  11. YUAN S C, HARRISON J P. An empirical dilatancy index for the dilatant deformation of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(4): 679–686.

    Article  Google Scholar 

  12. ZHAO X G, CAI M. A mobilized dilation angle model for rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2010, 47(3): 368–384.

    Article  MathSciNet  Google Scholar 

  13. HOEK E, CARRANZA-TORRES C, CORKUM B. Hoek-Brown criterion-2002 edition [C]// Proc NARMS-TAC Conference. Toronto, 2002, 1: 267–273.

    Google Scholar 

  14. ANDREEV G E. Brittle failure of rock materials: Test results and constitutive models [M]. (1st ed) Rotterdam: Taylor & Francis, 1995.

    Google Scholar 

  15. HUDSON J A, HARRISON J P. Engineering rock mechanics—An introduction to the principles [M]. (4th ed) Amsterdam: Elsevier Ltd, 2005.

    Google Scholar 

  16. BRADY B H G, BROWN E T. Rock mechanics for underground mining [M]. (2nd ed) London: Chapman & Hall, 1992.

    Google Scholar 

  17. KARSTUNEN M, PANDE G N, DESRUES J. Strain localisation and rotation of principal stress axis in biaxial test [C]// Proc 9th Conference of Computer Methods and Advances in Geomechanics. Wuhan, 1997.

    Google Scholar 

  18. ALONSO E, ALEJANO L R, VARAS F, FDEZ-MANIN G, CARRANZA-TORRES C. Ground response curves for rock masses exhibiting strain-softening behavior [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(13): 1153–1185.

    Article  MATH  Google Scholar 

  19. Itasca Consulting Group, Inc. FLAC3D fast lagrangian analysis of continua in 3 dimensions-theory and background [M]. Minneapolis: Itasca Consulting Group Inc, 2006.

  20. LADANYI B, ARCHAMBAULT G. Simulation of shear behaviour of a jointed rock mass [C]// The 11 th U.S. Symposium on Rock Mechanics. Berkeley: American Rock Mechanics Association, 1969.

    Google Scholar 

  21. CHEN S, YUE Z Q, THAM L G. Digital image-based numerical modeling method for prediction of inhomogeneous rock failure [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 41(6): 939–957.

    Article  Google Scholar 

  22. CHEN Sha, YUE Zhong-qi, THAM L G. Actual mesostructure based three-dimensinal numerical modeling, method for heterogeneous geomaterials [J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(10): 1951–1959. (in Chinese)

    Google Scholar 

  23. WEIBULL W A. Statistical distribution function of wide applicability [J]. Journal of Applied Mechanics, 1954, 18: 293–297.

    Google Scholar 

  24. BLAIR S C, COOK N G W. Analysis of compressive fracture in rock using statistical techniques: Part I. A non-linear rule—based model [J]. Int J Rock Mech Min Sci, 1998, 35: 837–848.

    Article  Google Scholar 

  25. CAO Wen-gui, ZHAO Ming-hua, LIU Cheng-xue. Study on the model and its modifying method for rock softening and damage based on Weibull random distribution [J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(19): 3226–3231. (in Chinese)

    Google Scholar 

  26. LIU H, ROQUETE M, KOU S Q, LINDQVIST P A. Characterization of rock heterogeneity and numerical verification [J]. Engineering Geology, 2004, 72(1/2): 89–119.

    Article  Google Scholar 

  27. FENG X T, PAN P Z, ZHOU H. Simulation of the rock micro-fracturing process under uniaxial compression using an elasto-plastic cellular automaton [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(7): 1091–1108.

    Article  Google Scholar 

  28. HUET C. An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behavior of microcracked heterogeneous materials with delayed response [J]. Engineering Fracture Mechanics, 1997, 58(5/6): 459–556.

    Article  Google Scholar 

  29. TAN X, KONIETZKY H. Laboratory observation and numerical simulation of permeability evolution during progressive failure of brittle rocks [J]. International Journal of Rock Mechanics & Mining Sciences, 2014, 68: 167–176.

    Article  Google Scholar 

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Correspondence to Xin Tan  (谭鑫).

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Foundation item: Project(2015M570678)supported by China Postdoctoral Science Foundation funded project

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Tan, X., Konietzky, H. & Frühwirt, T. Numerical simulation of triaxial compression test for brittle rock sample using a modified constitutive law considering degradation and dilation behavior. J. Cent. South Univ. 22, 3097–3107 (2015). https://doi.org/10.1007/s11771-015-2846-6

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  • DOI: https://doi.org/10.1007/s11771-015-2846-6

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