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| A MICROMECHANICAL MODEL FOR DAMAGE AND THERMAL CONDUCTIVITY OF BRITTLE ROCKS |
| CHEN Yifeng1,2,LI Dianqing1,2,RONG Guan1,2,JIANG Qinghui1,2,ZHOU Chuangbing1,2 |
(1. State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan,Hubei 430072,China;2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering,Ministry of Education,Wuhan University,
Wuhan,Hubei 430072,China) |
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Abstract An anisotropic damage model and an effective thermal conductivity model were presented based on homogenization techniques for low-porosity brittle rocks subjected to mechanical and thermal loadings. The thermal effect,the recovery of normal stiffness and the mobilized dilatancy behavior were incorporated in the damage model. The thermal conductivity model took into account the effects of damage-induced microstructure evolution,crack shape,porosity and saturation degree on the effective thermal conductivity of brittle rocks. The influences of crack shape and saturation degree on the effective thermal conductivity of low-porosity crystallized rocks were particularly discussed. The damage model was validated by the triaxial test data on an intact Äspö diorite;and the evolutions of porosity,crack density,crack shape,saturation degree and the effective thermal conductivity during the mechanical loading were demonstrated. The results may provide a helpful reference for better understanding the coupled thermo-mechanical behaviors of deep rocks.
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Received: 11 April 2011
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| [1] CHOW C L,WANG J. An anisotropic theory of elasticity for continuum damage mechanics[J]. International Journal of Fracture,1987,33(1):3–16.
[2] JU J W. On energy based coupled elastoplastic damage theories:constitutive modeling and computational aspects[J]. International Journal of Solids and Structures,1989,25(7):803–833.
[3] CHABOCHE J L. Damage induced anisotropy:on the difficulties associated with the active/passive unilateral condition[J]. International Journal of Damage Mechanics,1992,1(2):148–171.
[4] KRAJCINOVIC D. Damage mechanics[M]. Amsterdam:North-Holland,1996:221–414.
[5] HALM D,DRAGON A. A model of anisotropic damage by mesocrack growth:unilateral effect[J]. International Journal of Damage Mechanics,1996,5(4):384–402.
[6] SWOBODA G,YANG Q. An energy-based damage model of geomaterials II:deduction of damage evolution laws[J]. International Journal of Solids and Structures,1999,36(12):1 735–1 755.
[7] HASHIN Z. The differential scheme and its application to cracked materials[J]. Journal of the Mechanics and Physics of Solids,1988,36(6):719–734.
[8] NEMAT-NASSER S,HORI M. Micromechanics:overall properties of heterogeneous materials[M]. Amsterdam:North-Holland,1993:73–92.
[9] PENSEE V,KONDO D,DORMIEUX L. Micromechanical analysis of anisotropic damage in brittle materials[J]. Journal of Engineering Mechanics,ASCE,2002,128(8):889–897.
[10] ZHU Q Z,KONDO D,SHAO J F. Micromechanical analysis of coupling between anisotropic damage and friction in quasi brittle materials:Role of the homogenization scheme[J]. International Journal of Solids and Structures,2008,45(5):1 385–1 405.
[11] 朱其志,胡大伟,周 辉,等. 基于均匀化理论的岩石细观力学损伤模型及其应用研究[J]. 岩石力学与工程学报,2008,27(2):266–272.(ZHU Qizhi,HU Dawei,ZHOU Hui,et al. Research on homogenization-based mesomechanical damage model and its application[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(2):266–272.(in Chinese))
[12] ABOU-CHAKRA GUERY A,CORMERY F,SHAO J F,et al. A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial[J]. International Journal of Solids and Structures,2008,45(5):1 406–1 429.
[13] BARY B. Estimation of poromechanical and thermal conductivity properties of unsaturated isotropically microcracked cement pastes[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,doi:10.1002/nag.969.
[14] MORI T,TANAKA K. Averages stress in matrix and average elastic energy of materials with misfitting inclusions[J]. Acta Metall,1973,21(5):571–574.
[15] PONTE-CASTANEDA P,WILLIS J R. The effect of spatial distribution on the behavior of composite materials and cracked media[J]. Journal of the Mechanics and Physics of Solids,1995,43(12):1 919–1 951.
[16] ZHENG Q S,DU D X. An explicit and universally applicable estimate for the effective properties of multiphase composite which accounts for inclusion distribution[J]. Journal of the Mechanics and Physics of Solids,2001,49(11):2 765–2 788.
[17] ESHELBY J D. Elastic inclusions and inhomogeneities[C]// SNEDDON I N,HILL R ed. Progress in Solid Mechanics. Amsterdam:North-Holland,1961:87–140.
[18] ODA M,TAKEMURA T,AOKI T. Damage growth and permeability change in triaxial compression tests of Inada granite[J]. Mechanics of Materials,2002,34(6):313–331.
[19] SHAO J F,ZHOU H,CHAU K T. Coupling between anisotropic damage and permeability variation in brittle rocks[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2005,29(12):1 231–1 247.
[20] 胡大伟,朱其志,周 辉,等. 脆性岩石各向异性损伤和渗透性演化规律研究[J]. 岩石力学与工程学报,2008,27(9):1 822–1 827. (HU Dawei,ZHU Qizhi,ZHOU Hui,et al. Research on anisotropic damage and permeability evolutionary law for brittle rocks[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1 822–1 827. (in Chinese))
[21] ZIMMERMAN R W. Thermal conductivity of fluid-saturated rocks[J]. Journal of Petroleum Science and Engineering,1989,3(3):219–227.
[22] CLAUSER C,HUENGES E. Thermal conductivity of rocks and minerals[C]// AHRENS T J ed. Rock Physics and Phase Relations — a Handbook of Physical Constants. Washington:AGU Reference Shelf,1995:105–126.
[23] BERRYMAN J G. Generalization of Eshelby?s formula for a single ellipsoidal elastic inclusion to poroelasticity and thermoelasticity[J]. Physical Review Letters,1997,79(6):1 142–1 145.
[24] SEVOSTIANOV I. Thermal conductivity of a material containing cracks of arbitrary shape[J]. International Journal of Engineering Science,2006,44(8/9):513–528.
[25] GRUESCU C,GIRAUD A,HOMAND F,et al. Effective thermal conductivity of partially saturated porous rocks[J]. International Journal of Solids and Structures,2007,44(3/4):811–833.
[26] STAUB I,ANDERSSON J C,MAGNOR B. Äspö pillar stability experiment:geology and mechanical properties of the rock in TASQ[M]. [S.l.]:[s.n.],2004:39–54.
[27] STABLER J,BAKER G. Fractional step methods for thermo- mechanical damage analyses at transient elevated temperatures[J]. International Journal for Numerical Methods in Engineering,2000,48(5):761–785.
[28] BANDIS S C,LUMSDEN AC,BARTON N R. Fundamentals of rock joint deformation[J]. International Journal of Rock Mechanics and Mining Sciences,1983,20(6):249–268.
[29] 陈益峰,周创兵,盛永清. 应变敏感的裂隙及裂隙岩体水力传导特性研究[J]. 岩石力学与工程学报,2006,25(12):2 441–2 452. (CHEN Yifeng,ZHOU Chuangbing,SHENG Yongqing. Strain- dependent hydraulic conductivity for single rock fracture and fractured rock mass[J]. Chinese Journal of Rock Mechanics and Engineering,2006,25(12):2 441–2 452.(in Chinese))
[30] BAZANT ZP,OH B H. Efficient numerical integration on the surface of a sphere[J]. ZAMM,1986,66(1):37–49.
[31] CARSLAW H S,JAEGER J C. Conduction of heat in solids[M]. 2nd ed. New York:Oxford University Press,1959:230–254.
[32] CHEN Y F,ZHOU C B,JING L. Numerical modeling of coupled thermo-mechanical response of a rock pillar[J]. Journal of Rock Mechanics and Geotechnical Engineering,2010,2(3):262–273. |
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