用非连续变形分析方法模拟岩石裂纹扩展
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摘要
提出一种用非连续变形分析方法模拟岩石裂纹扩展的方法。将计算区域自动剖分成三角形块体单元,块体边界分为真实的节理边界和虚拟节理边界。裂纹扩展沿虚拟节理进行,按照界面破裂准则进行裂纹扩展分析。该方法可以模拟裂纹萌生、扩展、贯通和岩体破碎全过程,适用于完整岩石、断续岩体乃至完全不连续岩体等任意情形。由于该方法基于离散颗粒数值模型,其计算过程不会遇到数学上的困难。根据所提算法,编制VC++程序模块,并计算几个算例。模拟结果与已有的物理、数值试验结果吻合得较好,表明所提算法是有效的。
An approach for modeling rock crack propagation using discontinuous deformation analysis(DDA) method is presented.In the proposed approach,the triangular block system is automatically generated in the area of interest by adopting the advanced front method.During this process,numerous artificial joint interfaces,compared to real joint interfaces,come into being.These artificial joint interfaces provide the paths along where cracks generate and propagate.The strength of the artificial joint takes the same value as that of the intact rock;and the failure of the artificial joint is controlled by the maximum tensile-stress criterion and Mohr-Coulomb criterion.In this wayt,he proposed method can easily simulate the generation,propagation and coalescence of rock crack;the whole process of rock fragmentation is thereafter reproduced.Moreover,with the introduction of the artificial joint concept into the discontinuum-based modelt,he proposed approach can be used to simulate the cases of continuum,semicontiuum as well as discontinuum without any mathematic difficulty.Based on the proposed algorithm,the corresponding VC++ program module is developed.For verification,several numerical examples are computed to study the propagation and coalescence of the closed joints in rock mass under uniaxial compression.The simulated results are compared with the existing physical and numerical test ones.They show a favorable agreement,and the laws of the crack propagation are in accordance with the phenomena observed in the tests.These indicate that the proposed method for crack propagation analysis is correct and effective.
An approach for modeling rock crack propagation using discontinuous deformation analysis(DDA) method is presented.In the proposed approach,the triangular block system is automatically generated in the area of interest by adopting the advanced front method.During this process,numerous artificial joint interfaces,compared to real joint interfaces,come into being.These artificial joint interfaces provide the paths along where cracks generate and propagate.The strength of the artificial joint takes the same value as that of the intact rock;and the failure of the artificial joint is controlled by the maximum tensile-stress criterion and Mohr-Coulomb criterion.In this wayt,he proposed method can easily simulate the generation,propagation and coalescence of rock crack;the whole process of rock fragmentation is thereafter reproduced.Moreover,with the introduction of the artificial joint concept into the discontinuum-based modelt,he proposed approach can be used to simulate the cases of continuum,semicontiuum as well as discontinuum without any mathematic difficulty.Based on the proposed algorithm,the corresponding VC++ program module is developed.For verification,several numerical examples are computed to study the propagation and coalescence of the closed joints in rock mass under uniaxial compression.The simulated results are compared with the existing physical and numerical test ones.They show a favorable agreement,and the laws of the crack propagation are in accordance with the phenomena observed in the tests.These indicate that the proposed method for crack propagation analysis is correct and effective.
引文
[1]CHEN W Z,ZHU W S,SHAO J F.Damage coupled time-dependent model of a jointed rock mass and application to large underground cavern excavation[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(4):669–677.
[2]JIAO Y Y,ZHAO J,GE X R.New formulation and validation of the three-dimensional extension of a static relaxation method[J].Advances in Engineering Software,2004,35(6):317–323.
[3]JIAO Y Y,ZHAO J.On using DEM for simulating response of jointed rock to underground explosion[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(Supp.2):4 936–4 940.
[4]GOODMAN R E,TAYLOR R L,BREKKE T A.A model for the mechanics of jointed rock[J].Journal of Soil Mechanics and Foundation Division,ASCE,1968,94(3):637–659.
[5]KATONA M G.A simple contact-friction interface element with applications to buried culverts[J].International Journal for Numerical and Analytical Methods in Geomechanics,1983,7(3):371–384.
[6]王水林,冯夏庭,葛修润.高阶流形方法模拟裂纹扩展研究[J].岩土力学,2003,24(4):622–625.(WANG Shuilin,FENG Xiating,GE Xiurun.Study on crack propagation modeling by high order manifold method[J].Rock and Soil Mechanics,2003,24(4):622–625.(in Chinese))
[7]TANG C A.Numerical simulation of progressive rock failure and associated seismicity[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(2):249–261.
[8]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 Chun′an,ZHAO Wen.RFPA2D system for rock fracture process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507–508.(in Chinese))
[9]JING L,HUDSON J A.Numerical methods in rock mechanics[J].International Journal of Rock Mechanics and Mining Sciences,2002,39(4):409–427.
[10]CUNDALL P A.A computer model for simulating progressive large scale movements in blocky rock systems[C]//Proceedings of the International Symposium on Rock Fracture.Nancy,France:[s.n.],1971:1–8.
[11]SHI G H.Discontinuous deformation analysis:a new numerical model for the statics and dynamics of block system[Ph.D.Thesis][D].Berkeley:Department of Civil Engineering,University of California,1988.
[12]朱维申,李术才,陈卫忠.节理岩体破坏机制和锚固效应及工程应用[M].北京:科学出版社,2002.(ZHU Weishen,LI Shucai,CHEN Weizhong.The failure mechanism and anchorage effect of jointed rockmass and their application to engineering[M].Beijing:Science Press,2002.(in Chinese))
[13]LI Y P,CHEN L Z,WANG Y H.Experimental research on pre-cracked marble under compression[J].International Journal of Solids and Structures,2005,42(9/10):2 505–2 516.
[14]TANG C A,KOU S Q.Crack propagation and coalescence in brittle materials under compression[J].Engineering Fracture Mechanics,1998,61(3):311–324.
[15]DYSKIN A V,GERMANOVICH L N.A model of crack growth in microcracked rock[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1993,30(7):8l3–820.
[16]ASHBY M F,HALLAM S D.The failure of brittle solids containing small cracks under compressive stress states[J].Acta Metall.,1986,34(3):497–510.
[17]马瑾,马胜利,刘力强,等.断层几何结构与物理场的演化及失稳特征[J].地震学报,1996,l8(2):200–207.(MA Jin,MA Shengli,LIU Liqiang,et al.Geometrical structure,physical evolvement and failure characteristics of faults[J].Acta Seismologica Sinica,1996,l8(2):200–207.(in Chinese))
[18]WANG C Y,CHANG C T,SHENG J.Time intergration theories for the DDA method with finite element meshes[C]//Proc.of the 1st International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media.Berkeley,USA:TSI Press,1996:263–288.
[19]LIN C T,AMADEI B,JUNG J,et al.Extensions of discontinuous deformation analysis for jointed rock masses[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1996,33(7):671–694.
[20]黎勇,冯夏庭,栾茂田,等.非连续变形计算力学模型中的接触力元[J].东北大学学报(自然科学版),2002,23(11):1 112–1 115.(LI Yong,FENG Xiating,LUAN Maotiane,t al.Contact force element of discontinuous deformation computational mechanics model[J].Journal of Northeastern University(Natural Science),2002,23(11):1 112–1 115.(in Chinese))
[21]姜清辉.三维非连续变形分析方法的研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2000.(JIANG Qinghui.Research on three-dimensional discontinuous deformation analysis method[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2000.(in Chinese))
[22]邓建辉.节理岩体自适应有限元分析——方法与实现[博士学位论文][D].武汉:武汉水利电力大学,1994.(DENG Jianhui.Adaptive finite element analysis of jointed rock mass—method and implementation[Ph.D.Thesis][D].Wuhan:Wuhan University of Hydraulic and Electric Engineering,1994.(in Chinese))
[2]JIAO Y Y,ZHAO J,GE X R.New formulation and validation of the three-dimensional extension of a static relaxation method[J].Advances in Engineering Software,2004,35(6):317–323.
[3]JIAO Y Y,ZHAO J.On using DEM for simulating response of jointed rock to underground explosion[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(Supp.2):4 936–4 940.
[4]GOODMAN R E,TAYLOR R L,BREKKE T A.A model for the mechanics of jointed rock[J].Journal of Soil Mechanics and Foundation Division,ASCE,1968,94(3):637–659.
[5]KATONA M G.A simple contact-friction interface element with applications to buried culverts[J].International Journal for Numerical and Analytical Methods in Geomechanics,1983,7(3):371–384.
[6]王水林,冯夏庭,葛修润.高阶流形方法模拟裂纹扩展研究[J].岩土力学,2003,24(4):622–625.(WANG Shuilin,FENG Xiating,GE Xiurun.Study on crack propagation modeling by high order manifold method[J].Rock and Soil Mechanics,2003,24(4):622–625.(in Chinese))
[7]TANG C A.Numerical simulation of progressive rock failure and associated seismicity[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(2):249–261.
[8]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 Chun′an,ZHAO Wen.RFPA2D system for rock fracture process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507–508.(in Chinese))
[9]JING L,HUDSON J A.Numerical methods in rock mechanics[J].International Journal of Rock Mechanics and Mining Sciences,2002,39(4):409–427.
[10]CUNDALL P A.A computer model for simulating progressive large scale movements in blocky rock systems[C]//Proceedings of the International Symposium on Rock Fracture.Nancy,France:[s.n.],1971:1–8.
[11]SHI G H.Discontinuous deformation analysis:a new numerical model for the statics and dynamics of block system[Ph.D.Thesis][D].Berkeley:Department of Civil Engineering,University of California,1988.
[12]朱维申,李术才,陈卫忠.节理岩体破坏机制和锚固效应及工程应用[M].北京:科学出版社,2002.(ZHU Weishen,LI Shucai,CHEN Weizhong.The failure mechanism and anchorage effect of jointed rockmass and their application to engineering[M].Beijing:Science Press,2002.(in Chinese))
[13]LI Y P,CHEN L Z,WANG Y H.Experimental research on pre-cracked marble under compression[J].International Journal of Solids and Structures,2005,42(9/10):2 505–2 516.
[14]TANG C A,KOU S Q.Crack propagation and coalescence in brittle materials under compression[J].Engineering Fracture Mechanics,1998,61(3):311–324.
[15]DYSKIN A V,GERMANOVICH L N.A model of crack growth in microcracked rock[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1993,30(7):8l3–820.
[16]ASHBY M F,HALLAM S D.The failure of brittle solids containing small cracks under compressive stress states[J].Acta Metall.,1986,34(3):497–510.
[17]马瑾,马胜利,刘力强,等.断层几何结构与物理场的演化及失稳特征[J].地震学报,1996,l8(2):200–207.(MA Jin,MA Shengli,LIU Liqiang,et al.Geometrical structure,physical evolvement and failure characteristics of faults[J].Acta Seismologica Sinica,1996,l8(2):200–207.(in Chinese))
[18]WANG C Y,CHANG C T,SHENG J.Time intergration theories for the DDA method with finite element meshes[C]//Proc.of the 1st International Forum on Discontinuous Deformation Analysis(DDA)and Simulations of Discontinuous Media.Berkeley,USA:TSI Press,1996:263–288.
[19]LIN C T,AMADEI B,JUNG J,et al.Extensions of discontinuous deformation analysis for jointed rock masses[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1996,33(7):671–694.
[20]黎勇,冯夏庭,栾茂田,等.非连续变形计算力学模型中的接触力元[J].东北大学学报(自然科学版),2002,23(11):1 112–1 115.(LI Yong,FENG Xiating,LUAN Maotiane,t al.Contact force element of discontinuous deformation computational mechanics model[J].Journal of Northeastern University(Natural Science),2002,23(11):1 112–1 115.(in Chinese))
[21]姜清辉.三维非连续变形分析方法的研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2000.(JIANG Qinghui.Research on three-dimensional discontinuous deformation analysis method[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2000.(in Chinese))
[22]邓建辉.节理岩体自适应有限元分析——方法与实现[博士学位论文][D].武汉:武汉水利电力大学,1994.(DENG Jianhui.Adaptive finite element analysis of jointed rock mass—method and implementation[Ph.D.Thesis][D].Wuhan:Wuhan University of Hydraulic and Electric Engineering,1994.(in Chinese))
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