循环载荷作用下岩石单轴压缩破坏过程的平面弹塑性细胞自动机模型
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摘要
采用平面弹塑性细胞自动机模型在细观尺度上模拟应变软化岩石类材料的单轴压缩破坏过程。在平面弹性力学细胞自动机的基础上,推导分析平面弹塑性问题的细胞自动机更新规则,开发二维岩石弹塑性细胞自动机数值模拟软件;模拟不同均质度岩石的单轴压缩破坏过程,并在应力峰值后区考虑反复加卸载过程。模拟得到的岩石单轴压缩条件下的全程应力-应变曲线与典型的加卸载应力-应变试验曲线吻合较好,模拟得到的声发射曲线很好地反映出岩石声发射的Kaiser效应。
The elastoplastic cellular automata model for plane problem is set up to model failure process of rocks under uniaxial compression in meso-scope.The cellular automaton is an efficient method to model the process of self-organization of complex system by constructing some local simple rules.It has advantages of localization,parallelization etc..Also,it can consider the heterogeneity of materials.Based on elastic cellular automata,the elastoplastic updating rule is proposed and the numerical program of two-dimensional elastoplastic cellular automata for rocks is developed.The basic thought to model failure process of rocks is to(1) discretize the rock sample into the system which is composed of cell elements;(2) introduce the heterogeneity of rock by generating mechanical parameters such as strength,elastic modulus etc.for each cell elements randomly;(3) update the states of all the cells according to the elastoplastic updating rule;(4) judge whether the cell elements fail or not according to certain failure criterion;and(5) perform the failure analysis to the failed cell elements with elastoplastic theory.The model is used to simulate the failure process of inhomogeneous rocks,and the unloading-loading process in the post peak region is considered.The complete stress-strain curve perfectly agrees with the experimental one.Meanwhile,the strain-acoustic emission(AE) curve obviously indicates the Kaiser effect.
The elastoplastic cellular automata model for plane problem is set up to model failure process of rocks under uniaxial compression in meso-scope.The cellular automaton is an efficient method to model the process of self-organization of complex system by constructing some local simple rules.It has advantages of localization,parallelization etc..Also,it can consider the heterogeneity of materials.Based on elastic cellular automata,the elastoplastic updating rule is proposed and the numerical program of two-dimensional elastoplastic cellular automata for rocks is developed.The basic thought to model failure process of rocks is to(1) discretize the rock sample into the system which is composed of cell elements;(2) introduce the heterogeneity of rock by generating mechanical parameters such as strength,elastic modulus etc.for each cell elements randomly;(3) update the states of all the cells according to the elastoplastic updating rule;(4) judge whether the cell elements fail or not according to certain failure criterion;and(5) perform the failure analysis to the failed cell elements with elastoplastic theory.The model is used to simulate the failure process of inhomogeneous rocks,and the unloading-loading process in the post peak region is considered.The complete stress-strain curve perfectly agrees with the experimental one.Meanwhile,the strain-acoustic emission(AE) curve obviously indicates the Kaiser effect.
引文
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[12]Blair S C,Cook N G W.Analysis of compressive fracture in rock using statistical techniques—part II.Effect of microscale heterogeneity on macroscopic deformation[J].International Journal of Rock Mechanics and Mining Sciences,1998,35(7):849-862.
[13]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 failure process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507-508.(in Chinese))
[14]冯夏庭,周辉,李明田.岩石破坏过程的细胞自动机方法[A].见:全球华人中青年学者岩土力学与工程学术论坛[C].武汉:[s.n.],2003.75-89.(Feng Xiating,Zhou Hui,Li Mingtian.Cellular automata method for rock failure process analysis[A].In:Soil Mechanics and Engineering Forum for Global Chinese Youth[C].Wuhan:[s.n.],2003.75-89.(in Chinese))
[15]Li M T,Feng X T,Zhou H.Cellular automata simulation of the interaction mechanism of two cracks in rock under uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(3):452.
[16]沈成武,戴诗亮,杨吉新,等.平面弹性力学中的细胞自动机方法[J].清华大学学报(自然科学版),2001,41(11):35-38.(Shen Chengwu,Dai Shiliang,Yang Jixin,et al.Cellular automata for analysis of plane problem in theory of elasticity[J].Journal of Tsinghua University(Science and Technology),2001,41(11):35-38.(in Chinese))
[17]沈成武,唐小兵,杨吉新.平面桁架力学分析的细胞自动机方法初探[J].武汉交通科技大学学报,2000,24(2):105-108.(Shen Chengwu,Tang Xiaobing,Yang Jixin.An approach to mechanical analysis of plane truss using cellular automata[J].Journal of Wuhan Transportation University,2000,24(2):105-108.(in Chinese))
[18]Gurdal Z,Tatting B.Cellular automata for design of truss structures with linear and nonlinear response[A].In:Proceedings of the 41st AIAA/ASME/ASCE/AHS Structure,Structural Mechanics and Materials Conference[C].Atlanta,USA:[s.n.],2000.1 580-1 591.
[19]Tatting B,Gurdal Z.Cellular automata for design of two-dimensional continuum structure[A].In:Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization[C].[s.l.]:[s.n.],2000.4 832-4 841.
[20]Owen D R J,Hinton E.Finite Element in Plasticity—Theory and Practice[M].Swansea:Pinerige Press Limited,1980.
[21]唐春安,徐小荷.缺陷的演化繁衍与Kaiser效应函数[J].地震研究,1990,13(2):90-100.(Tang Chan′an,Xu Xiaohe.Evolution and propagation of material defects and Kaiser effect function[J].Journal of Seismological Research,1990,13(2):90-100.(in Chinese))
[22]张承娟,盛祝平.利用岩石记忆特性量测钻孔地应力[J].水力发电学报,1990,29(2):72-81.(Zhang Chengjuan,Sheng Zhuping.Measurement of bored geo-stress with the memory property of rock[J].Journal of Hydroelectric Engineering,1990,29(2):72-81.(in Chinese)).
[23]张晖辉,颜玉定,余怀忠,等.循环载荷下大试件岩石破坏声发射试验——岩石破坏前兆的研究[J].岩石力学与工程学报,2004,23(21):3 621-3 628.(Zhang Huihui,Yan Yuding,Yu Huaizhong,et al.Acoustic emission experimental research on large-scaled rock failure under cycling load—fracture precursor of rock[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3 621-3 628.(in Chinese))
[24]Hudson J A,Harrison J P.Engineering Rock Mechanics:Illustrative Worked Examples[M].New York:Pergamon Press,2000.
[2]凌建明.节理岩体损伤力学及时效损伤特性的研究[博士学位论文][D].上海:同济大学,1992.55-59.(Ling Jianming.Study on damage mechanics and damaged characteristic for jointed rock mass[Ph.D.Thesis][D].Shanghai:Tongji University,1992.55-59.(in Chinese)).
[3]吴紫汪,马巍,蒲毅彬,等.冻土蠕变变形特征的细观分析[J].岩土工程学报,1997,19(3):1-6.(Wu Ziwang,Ma Wei,Pu Yibin,et al.Meso analysis of deformation characteristics in creep process of frozen soil[J].Chinese Journal of Geotechnical Engineering,1997,19(3):1-6.(in Chinese)).
[4]杨更社,谢定义,张长庆,等.岩石损伤特性的CT识别[J].岩石力学与工程学报,1996,15(1):48-54.(Yang Gengshe,Xie Dingyi,Zhang Changqing,et al.CT identification of rock damage properties[J].Chinese Journal of Rock Mechanics and Engineering,1996,15(1):48-54.(in Chinese))
[5]杨更社,谢定义,张长庆.岩石损伤CT数分布规律的定量分析[J].岩石力学与工程学报,1998,17(3):279-285.(Yang Gengshe,Xie Dingyi,Zhang Changqing.The quantitative analysis of distribution regulation of the CT values of rock damage[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(3):279-285.(in Chinese)).
[6]Kawakata H,Cho A,Kiyama T,et al.Three-dimensional observations of faulting process in Westerly granite under uniaxial and triaxial conditions by X-ray CT scan[J].Tectonophysics,1999,313(3):293-305.
[7]葛修润,任建喜,蒲毅彬,等.煤岩三轴细观损伤演化规律的CT动态试验[J].岩石力学与工程学报,1999,18(5):497-502.(Ge Xiurun,Ren Jianxi,Pu Yibin,et al.A real-in-time CT triaxial testing study of meso-damage evolution law of coal[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(5):497-502.(in Chinese)).
[8]Sarkar P.A brief history of cellular automats[J].ACM Computing Surveys,2000,32(1):80-107.
[9]Hillerborg A,Modeer M,Petersson P E.Analysis of crack formation and crack growth in concrete by means of fracture,mechanics and finite element[J].Cement and Concrete Research,1976,6(6):773-782.
[10]Bazant Z P,Tabbara M R,Kazemi M T,et al.Random particle model for fracture of aggregate or fiber composites[J].Journal of Engineering Mechanics,1990,116(8):1 686-1 705.
[11]Blair S C,Cook N G W.Analysis of compressive fracture in rock using statistical techniques—part I.A nonlinear rule-based model[J].International Journal of Rock Mechanics and Mining Sciences,1998,35(7):837-848.
[12]Blair S C,Cook N G W.Analysis of compressive fracture in rock using statistical techniques—part II.Effect of microscale heterogeneity on macroscopic deformation[J].International Journal of Rock Mechanics and Mining Sciences,1998,35(7):849-862.
[13]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 failure process analysis[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):507-508.(in Chinese))
[14]冯夏庭,周辉,李明田.岩石破坏过程的细胞自动机方法[A].见:全球华人中青年学者岩土力学与工程学术论坛[C].武汉:[s.n.],2003.75-89.(Feng Xiating,Zhou Hui,Li Mingtian.Cellular automata method for rock failure process analysis[A].In:Soil Mechanics and Engineering Forum for Global Chinese Youth[C].Wuhan:[s.n.],2003.75-89.(in Chinese))
[15]Li M T,Feng X T,Zhou H.Cellular automata simulation of the interaction mechanism of two cracks in rock under uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(3):452.
[16]沈成武,戴诗亮,杨吉新,等.平面弹性力学中的细胞自动机方法[J].清华大学学报(自然科学版),2001,41(11):35-38.(Shen Chengwu,Dai Shiliang,Yang Jixin,et al.Cellular automata for analysis of plane problem in theory of elasticity[J].Journal of Tsinghua University(Science and Technology),2001,41(11):35-38.(in Chinese))
[17]沈成武,唐小兵,杨吉新.平面桁架力学分析的细胞自动机方法初探[J].武汉交通科技大学学报,2000,24(2):105-108.(Shen Chengwu,Tang Xiaobing,Yang Jixin.An approach to mechanical analysis of plane truss using cellular automata[J].Journal of Wuhan Transportation University,2000,24(2):105-108.(in Chinese))
[18]Gurdal Z,Tatting B.Cellular automata for design of truss structures with linear and nonlinear response[A].In:Proceedings of the 41st AIAA/ASME/ASCE/AHS Structure,Structural Mechanics and Materials Conference[C].Atlanta,USA:[s.n.],2000.1 580-1 591.
[19]Tatting B,Gurdal Z.Cellular automata for design of two-dimensional continuum structure[A].In:Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization[C].[s.l.]:[s.n.],2000.4 832-4 841.
[20]Owen D R J,Hinton E.Finite Element in Plasticity—Theory and Practice[M].Swansea:Pinerige Press Limited,1980.
[21]唐春安,徐小荷.缺陷的演化繁衍与Kaiser效应函数[J].地震研究,1990,13(2):90-100.(Tang Chan′an,Xu Xiaohe.Evolution and propagation of material defects and Kaiser effect function[J].Journal of Seismological Research,1990,13(2):90-100.(in Chinese))
[22]张承娟,盛祝平.利用岩石记忆特性量测钻孔地应力[J].水力发电学报,1990,29(2):72-81.(Zhang Chengjuan,Sheng Zhuping.Measurement of bored geo-stress with the memory property of rock[J].Journal of Hydroelectric Engineering,1990,29(2):72-81.(in Chinese)).
[23]张晖辉,颜玉定,余怀忠,等.循环载荷下大试件岩石破坏声发射试验——岩石破坏前兆的研究[J].岩石力学与工程学报,2004,23(21):3 621-3 628.(Zhang Huihui,Yan Yuding,Yu Huaizhong,et al.Acoustic emission experimental research on large-scaled rock failure under cycling load—fracture precursor of rock[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3 621-3 628.(in Chinese))
[24]Hudson J A,Harrison J P.Engineering Rock Mechanics:Illustrative Worked Examples[M].New York:Pergamon Press,2000.
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