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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OFOEGBU G I, CURRAN J H. Deformability of intact rock [J]. Int J Rock Mech Min Sci Geomech Abstr, 1992, 29(1): 35–48.
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.
COSTIN L S. Damage mechanics in the post-failure regime [J]. Mech Mater, 1985, 4: 149–160.
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.
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.
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.
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.
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.
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.
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.
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.
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.
HOEK E, CARRANZA-TORRES C, CORKUM B. Hoek-Brown criterion-2002 edition [C]// Proc NARMS-TAC Conference. Toronto, 2002, 1: 267–273.
ANDREEV G E. Brittle failure of rock materials: Test results and constitutive models [M]. (1st ed) Rotterdam: Taylor & Francis, 1995.
HUDSON J A, HARRISON J P. Engineering rock mechanics—An introduction to the principles [M]. (4th ed) Amsterdam: Elsevier Ltd, 2005.
BRADY B H G, BROWN E T. Rock mechanics for underground mining [M]. (2nd ed) London: Chapman & Hall, 1992.
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.
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.
Itasca Consulting Group, Inc. FLAC3D fast lagrangian analysis of continua in 3 dimensions-theory and background [M]. Minneapolis: Itasca Consulting Group Inc, 2006.
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.
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.
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)
WEIBULL W A. Statistical distribution function of wide applicability [J]. Journal of Applied Mechanics, 1954, 18: 293–297.
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.
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)
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.
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.
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.
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.
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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