脆性各向异性岩石破坏过程数值模拟
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摘要
在改进刚体弹簧方法的基础上,采用Hoek-Brown准则判断界面破坏,提出各向异性Voronoi网格的生成方法,并引入界面细观参数各向异性的赋值函数,最终建立了脆性各向异性岩石损伤破坏过程的数值模拟方法。利用该方法对文献中的试验结果进行了模拟。计算表明,该方法不仅能成功模拟岩石抗压强度随软弱面倾角变化的"U"形规律,定量上与试验结果吻合良好,而且能同时定量模拟岩石变形特性即弹性模量和泊松比的各向异性特征。
Based on an improved rigid block spring method, using Hoek-Brown criterion as a failure criterion, a numerical model for the simulation of failure process of brittle anisotropic rock is established. In this model, a method for generating anisotropic Voronoi mesh and a function for anisotropic micro parameters assignment are introduced. Then the model is used for the simulation of experiments in published literatures. It indicates that: this method cannot only capture the ‘U' type curve of compressive strength with regards to the bedding plane orientation and matches well with experiment results in a quantitative manner, but also has the ability to simulate the anisotropic characteristics of deformation qualitatively and quantitatively at the same time.
Based on an improved rigid block spring method, using Hoek-Brown criterion as a failure criterion, a numerical model for the simulation of failure process of brittle anisotropic rock is established. In this model, a method for generating anisotropic Voronoi mesh and a function for anisotropic micro parameters assignment are introduced. Then the model is used for the simulation of experiments in published literatures. It indicates that: this method cannot only capture the ‘U' type curve of compressive strength with regards to the bedding plane orientation and matches well with experiment results in a quantitative manner, but also has the ability to simulate the anisotropic characteristics of deformation qualitatively and quantitatively at the same time.
引文
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[5]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.
[6]Chow C L,Wang J.An anisotropic theory of elasticity for continuum damage mechanics[J].International Journal of Fracture,1987,33(1):3―16.
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[18]Potyondy D O,Cundall P A.A bonded-particle model for rock[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1329―1364.
[19]Munjiza A,Owen D R J,Bicanic N.A combined finite-discrete element method in transient dynamics of fracturing solids[J].Engineering Computations,1995,12(2):145―174.
[20]唐春安,赵文.岩石破裂全过程分析软件系统RFPA2D[J].岩石力学与工程学报,1997,16(5):507―508.Tang Chunan,Zhao Wen.RFPA2D system for rock failure process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507―508.(in Chinese)
[21]Zhang Z N.Discretized virtual internal bond model for nonlinear elasticity[J].International Journal of Solids and Structures,2013,50(22-23):3618―3625.
[22]Zhang Z N,Yao Y,Mao X.Modeling wave propagation induced fracture in rock with correlated lattice bond cell[J].International Journal of Rock Mechanics and Mining Sciences,2015,78:262―270.
[23]潘鹏志,丁梧秀,冯夏庭,等.预制裂纹几何与材料属性对岩石裂纹扩展的影响研究[J].岩石力学与工程学报,2008,27(9):1882―1889.Pan Pengzhi,Ding Wuxiu,Feng Xiating,et al.Research on influence of pre-existing crack geometrical and material properties on crack propagation in rocks[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1882―1889.(in Chinese)
[24]姚池,姜清辉,邵建富,等.一种模拟岩石破裂的细观数值计算模型[J].岩石力学与工程学报,2013,32(增刊2):3146―3153.Yao Chi,Jiang Qinghui,Shao Jianfu,et al.A mesoscopic numerical model for simulation of rock fracturing[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(Suppl 2):3146―3153.(in Chinese)
[25]Yao C,Jiang Q H,Shao J F.Numerical simulation of damage and failure in brittle rocks using a modified rigid block spring method[J].Computers and Geotechnics,2015,64:48―60.
[26]梁正召,唐春安,李厚祥,等.单轴压缩下横观各向同性岩石破裂过程的数值模拟[J].岩土力学,2005,26(1):57―62.Liang Zhengzhao,Tang Chunan,Li Houxiang,et al.Anumerical study on failure process of transversely isotropic rock subjected to uniaxial compression[J].Rock and Soil Mechanics,2005,26(1):57―62.(in Chinese)
[27]Lisjak A,Tatone B S A,Grasselli G,et al.Numerical modelling of the anisotropic mechanical behaviour of opalinus clay at the laboratory-scale using fem/dem[J].Rock Mechanics and Rock Engineering,2014,47(1):187―206.
[28]姚池,李瑶,姜清辉,等.应力作用下软硬互层岩石破裂过程的细观模拟[J].岩石力学与工程学报,2015,34(8):1542―1551.Yao Chi,Li Yao,Jiang Qinghui,et al.Mesoscopic model of failure process of interlayered rock under compression[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1542―1551.(in Chinese)
[29]Zhang Z N,Chen Y.Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(6):1010―1022.
[30]张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法[J].岩土工程学报,2009,31(12):1858―1865.Zhang Zhennan,Chen Yongquan.Novel numerical approach to jointed rock mass simulation:Element partition method[J].Chinese Journal of Rock Mechanics and Engineering,2009,31(12):1858―1865.(in Chinese)
[31]姚池,李瑶,姜清辉,等.基于改进刚体弹簧方法的开挖损伤演化分析[J].岩石力学与工程学报,2015,34(10):1959―1966.Yao Chi,Li Yao,Jiang Qinghui,et al.Numerical simulation of excavation damaged zone using the modified rigid body spring method[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(10):1959―1966.(in Chinese)
[32]Fortune S.A sweepline algorithm for Voronoi diagrams[J].Algorithmica,1987,2(1/2/3/4):153―174.
[33]Niandou H,Shao J F,Henry J P,et al.Laboratory investigation of the mechanical behaviour of tournemire shale[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(1):3―16.
[2]Kranz R L.Microcracks in rocks:a review[J].Tectonophysics,1983,100(1):449―480.
[3]杨雪强,李子生,燕全会,等.横观各向同性岩石类材料的破坏准则[J].工程力学,2012,29(12):328―333.Yang Xueqiang,Li Zisheng,Yan Quanhui,et al.Failure criterion for transversely isotropic rock materials[J].Engineering Mechanics,2012,29(12):328―333.(in Chinese)
[4]赵颖.各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型[J].工程力学,2012,29(2):222―229.Zhao Ying.Fully coupled dual-porosity model for oil-water two-phase flow in anisotropic formations[J].Engineering Mechanics,2012,29(2):222―229.(in Chinese)
[5]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.
[6]Chow C L,Wang J.An anisotropic theory of elasticity for continuum damage mechanics[J].International Journal of Fracture,1987,33(1):3―16.
[7]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):1735―1755.
[8]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):1822―1827.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):1822―1827.(in Chinese)
[9]周建军,周辉,邵建富.脆性岩石各向异性损伤和渗流耦合细观模型[J].岩石力学与工程学报,2007,26(2):368―373.Zhou Jianjun,Zhou Hui,Shao Jianfu.Coupled micromechanical model for anisotropic damage and permeability variation in brittle rocks[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(2):368―373.(in Chinese)
[10]朱合华,黄伯麒,张琦,等.基于广义Hoek-Brown准则的弹塑性本构模型及其数值实现[J].工程力学,2016,33(2):41―49.Zhu Hehua,Huang Boqi,Zhang Qi,et al.Elastoplastic rock constitutive model based on generalized Hoek-Brown strength criterion and its numerical implementation[J].Engineering Mechanics,2016,33(2):41―49.(in Chinese)
[11]Andrieux S,Bamberger Y,Marigo J J.Un modèle de matériau microfissurépour les roches et les bétons[J].Journal de Mécanique Théorique et Appliquée,1986,5(3):471―513.
[12]Gambarotta L,Lagomarsino S.A microcrack damage model for brittle materials[J].International Journal of Solids and Structures,1993,30(2):177―198.
[13]Pensee V,Kondo D,Dormieux L.Micromechanical analysis of anisotropic damage in brittle materials[J].Journal of Engineering Mechanics,2002,128(8):889―897.
[14]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].2008,27(2):266―272.(in Chinese)
[15]陈进,陈祥福.岩石工程渐进破坏分析的边界元法[J].工程力学,1991,8(4):128―137.Chen Jin,Chen Xiangfu.Boundary element method for non-linear analysis the progressive failure of rock engineering[J].Engineering Mechanics,1991,8(4):128―137.(in Chinese)
[16]Moulinec H,Suquet P.A fast numerical method for computing the linear and nonlinear mechanical properties of composites[J].Comptes Rendus de l'Académie des Sciences.Série II,Mécanique,Physique,Chimie,Astronomie,1994,318(11):1417―1423.
[17]Moulinec H,Suquet P.A numerical method for computing the overall response of nonlinear composites with complex microstructure[J].Computer Methods in Applied Mechanics and Engineering,1998,157(1):69―94.
[18]Potyondy D O,Cundall P A.A bonded-particle model for rock[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1329―1364.
[19]Munjiza A,Owen D R J,Bicanic N.A combined finite-discrete element method in transient dynamics of fracturing solids[J].Engineering Computations,1995,12(2):145―174.
[20]唐春安,赵文.岩石破裂全过程分析软件系统RFPA2D[J].岩石力学与工程学报,1997,16(5):507―508.Tang Chunan,Zhao Wen.RFPA2D system for rock failure process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507―508.(in Chinese)
[21]Zhang Z N.Discretized virtual internal bond model for nonlinear elasticity[J].International Journal of Solids and Structures,2013,50(22-23):3618―3625.
[22]Zhang Z N,Yao Y,Mao X.Modeling wave propagation induced fracture in rock with correlated lattice bond cell[J].International Journal of Rock Mechanics and Mining Sciences,2015,78:262―270.
[23]潘鹏志,丁梧秀,冯夏庭,等.预制裂纹几何与材料属性对岩石裂纹扩展的影响研究[J].岩石力学与工程学报,2008,27(9):1882―1889.Pan Pengzhi,Ding Wuxiu,Feng Xiating,et al.Research on influence of pre-existing crack geometrical and material properties on crack propagation in rocks[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1882―1889.(in Chinese)
[24]姚池,姜清辉,邵建富,等.一种模拟岩石破裂的细观数值计算模型[J].岩石力学与工程学报,2013,32(增刊2):3146―3153.Yao Chi,Jiang Qinghui,Shao Jianfu,et al.A mesoscopic numerical model for simulation of rock fracturing[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(Suppl 2):3146―3153.(in Chinese)
[25]Yao C,Jiang Q H,Shao J F.Numerical simulation of damage and failure in brittle rocks using a modified rigid block spring method[J].Computers and Geotechnics,2015,64:48―60.
[26]梁正召,唐春安,李厚祥,等.单轴压缩下横观各向同性岩石破裂过程的数值模拟[J].岩土力学,2005,26(1):57―62.Liang Zhengzhao,Tang Chunan,Li Houxiang,et al.Anumerical study on failure process of transversely isotropic rock subjected to uniaxial compression[J].Rock and Soil Mechanics,2005,26(1):57―62.(in Chinese)
[27]Lisjak A,Tatone B S A,Grasselli G,et al.Numerical modelling of the anisotropic mechanical behaviour of opalinus clay at the laboratory-scale using fem/dem[J].Rock Mechanics and Rock Engineering,2014,47(1):187―206.
[28]姚池,李瑶,姜清辉,等.应力作用下软硬互层岩石破裂过程的细观模拟[J].岩石力学与工程学报,2015,34(8):1542―1551.Yao Chi,Li Yao,Jiang Qinghui,et al.Mesoscopic model of failure process of interlayered rock under compression[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1542―1551.(in Chinese)
[29]Zhang Z N,Chen Y.Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(6):1010―1022.
[30]张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法[J].岩土工程学报,2009,31(12):1858―1865.Zhang Zhennan,Chen Yongquan.Novel numerical approach to jointed rock mass simulation:Element partition method[J].Chinese Journal of Rock Mechanics and Engineering,2009,31(12):1858―1865.(in Chinese)
[31]姚池,李瑶,姜清辉,等.基于改进刚体弹簧方法的开挖损伤演化分析[J].岩石力学与工程学报,2015,34(10):1959―1966.Yao Chi,Li Yao,Jiang Qinghui,et al.Numerical simulation of excavation damaged zone using the modified rigid body spring method[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(10):1959―1966.(in Chinese)
[32]Fortune S.A sweepline algorithm for Voronoi diagrams[J].Algorithmica,1987,2(1/2/3/4):153―174.
[33]Niandou H,Shao J F,Henry J P,et al.Laboratory investigation of the mechanical behaviour of tournemire shale[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(1):3―16.