基于微缺陷成核序列的岩石微裂纹生长和损伤演化模型
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摘要
岩石在承载之初,由于微缺陷无序成核和有限生长,在材料内部形成大量分布性微裂纹。在该文中,这种演化机制被归结为:微缺陷随机、孤立成核生成最小微裂纹和微缺陷无重叠聚集成核、排列生长形成大尺度微裂纹,裂纹尺度生长是微缺陷成核数的函数。利用微裂纹尺度-频数分布分形以及微裂纹粗糙表面分形,建立基于微缺陷累计成核数序列的裂纹尺度生长模型和损伤演化模型。通过对二维岩石试件破坏过程的微裂纹尺度统计和损伤测试表明,模型的预测结果与观测值符合较好。由于微缺陷成核与声发射源机制具有相似性以及微缺陷成核数序列与声发射数序列具有相似性,所以该模型可用于通过声发射参数序列跟踪微裂纹生长和损伤演化。裂纹尺度生长对于完整认识材料宏观力学性质演化和预测材料灾变具有重要意义。
At the initial stage of rock bearing load,a great amount of microcracks appeared in the material due to microdefects random nucleation and limited growth.In the paper,the mechanism of microcracks evolution at the initial stage rock damage was generalized that the isolated nucleation of microdefects formed the initial microcracks of the smallest size,and the clustering nucleation of microdefects close next to the initial microcracks formed the large-scale microcracks,in which the microcracks size growth was the function of the number of microdefects nucleation.By using the microcracks size and frequency distribution fractal and the microcrack rough surface fractal,two models were established.One was a relationship formula between accumulated number of microdefects nucleation and microcracks size,which was called the Crack Growth Model(CGM).The other was an isotropic damage model based on microdefects nucleation number series,which was called the Damage Evolution Model(DEM).The statistics analysis on the microcracks evolution in a gradually fractured rock plate shows that the predictive cracks growth and microcracks damage evolution are in good agreement with the measured values.Since a microdefect nucleation being accompanied by a acoustic emission(AE) and the number series of microdefectsnucleations was similar to the AE series,the two models could be used to predict microcrack growth and microdamage evolution by the use of AE series.It is important to study microcracksgrowth and damage to the macro mechanical properties for the understanding of the whole course of evolution and prediction of catastrophe.
At the initial stage of rock bearing load,a great amount of microcracks appeared in the material due to microdefects random nucleation and limited growth.In the paper,the mechanism of microcracks evolution at the initial stage rock damage was generalized that the isolated nucleation of microdefects formed the initial microcracks of the smallest size,and the clustering nucleation of microdefects close next to the initial microcracks formed the large-scale microcracks,in which the microcracks size growth was the function of the number of microdefects nucleation.By using the microcracks size and frequency distribution fractal and the microcrack rough surface fractal,two models were established.One was a relationship formula between accumulated number of microdefects nucleation and microcracks size,which was called the Crack Growth Model(CGM).The other was an isotropic damage model based on microdefects nucleation number series,which was called the Damage Evolution Model(DEM).The statistics analysis on the microcracks evolution in a gradually fractured rock plate shows that the predictive cracks growth and microcracks damage evolution are in good agreement with the measured values.Since a microdefect nucleation being accompanied by a acoustic emission(AE) and the number series of microdefectsnucleations was similar to the AE series,the two models could be used to predict microcrack growth and microdamage evolution by the use of AE series.It is important to study microcracksgrowth and damage to the macro mechanical properties for the understanding of the whole course of evolution and prediction of catastrophe.
引文
[1]夏蒙棼,韩闻生,柯孚久,等.统计细观损伤力学和损伤演化诱致突变[J].力学进展,1995,25(1):1―40.Xia Mengfen,Han Wensheng,KeFujiu,et al.Statisticalmeso-scopic damage mechanics and damage evolutioninduced catastrophe[J].Advances in Mechanics,1995,25(1):1―40.(in Chinese)
[2]王利,李示波.准脆性材料损伤斑图生长的数值模拟[J].工程力学,2011,28(4):238―244,256.Wang Li,Li Shibo.Numerical simulation of damagepattern growth in quasi-brittle materials[J].EngineeringMechanics,2011,28(4):238―244,256.(in Chinese)
[3]Dragon A,Mroz Z.A continuum model for plastic brittlebehavior of rock and concrete[J].Int.J.Eng.Sci.,1979,17(1):121―137.
[4]Krajcinovic D.Continuum damage mechanics[J].Appl.Mech.Rev.,1984,37(1):33―36.
[5]谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990:10―30.XieHeping.Rock and concrete damage mechanics[M].Xuzhou:China Mineral University Press,1990:10―30.(in Chinese)
[6]王利,高谦.基于强度理论的岩石损伤弹塑性模型.北京科技大学学报,2008,30(5):461―467.Wang Li,GaoQian.The elasto-plastic damage model ofrock based on strength theory[J].Journal of University ofScience and Technology Beijing,2008,30(5):461―467.(in Chinese)
[7]Hashin Z.Mesco damage mechanics of brittle material[J].J.Mech.Phys.Solids,1988,36:719.
[8]冯西桥.脆性材料的细观损伤理论和损伤机构的安定性分析[D].北京:清华大学,1995.FengXiqiao.The meso damage theory of brittle materialsand stability analysis on damage structure[D].Beijing:Tingshua University,1995.(in Chinese)
[9]白以龙,汪海英,夏蒙棼,等.固体的统计细观力学―连接多个耦合的时空尺度[J].力学进展,2006,36(2):286―305.BaiYilong,Wang Haiying,Xia Mengfen,et al.Statisticalmesomechanics of solid,linking coupled multiple spaceand time scales[J].Applied MechanicsReviews,2006,36(2):286―305.(in Chinese)
[10]夏蒙棼,韩闻生,柯浮久,等.统计细观损伤力学和损伤演化诱致突变(I)[J].力学进展,1995,25(1):1―24.Xia Mengfen,Han Wensheng,KeFujiu,et al.Statisticalmeso-scopic damage mechanics and damage evolutioninduced catastrophe[J].Advances in Mechanics,1995,25(1):1―24.(in Chinese)
[11]Bazant Z.结构破坏的尺度律[J].力学进展,1999,29(3):383―433.Bazant Z.Scale law of structure fracture[J].Advances inMechanics,1999,29(3):383―433.(in Chinese)
[12]Tang Chunan,XuXiaohe.Evolution and propagation ofmaterial defects and kaiser effect function[J].Journal ofSeismological Research,1989,13(2):203―213.
[13]张明,李仲奎,杨强,等.准脆性材料声发射的损伤模型及统计分析[J].岩石力学与工程学报,2006,25(12):2493―2501.Zhang Ming,Li Zhongkui,Yang Qiang,et al.A damagemodel and statistical analysis of acoustic emission forquasi-brittle materials[J].Chinese Journal of RockMechanics and Engineering,2006,25(12):2493―2501.(in Chinese)
[14]纪洪广,贾立宏,李造鼎.混凝土损伤的声发射模式研究[J].声学学报,1996,21(Suppl):601―608.JiHongguang,JiaLihong,LiZaoding.Study on theAE-model of concrete damage[J].ActaAcustica,1996,21(Suppl):601―608.(in Chinese)
[15]薛云亮,李庶林,林峰,等.类岩石材料声发射参数与应力和应变耦合本构关系[J].北京科技大学学报,2011,33(6):664―670.XueYunliang,Li Shulin,Lin Feng,et al.Couplingconstitutive relations of AE parameter versus stress andstrain for rock-like materials[J].Journal of University ofScience and Technology Beijing,2011,33(6):664―670.(in Chinese)
[16]王金安,谢和平,田晓燕,等.一种新的断裂表面分形测量方法[J].北京科技大学学报,1999,21(3):6―9.Wang Jinan,XieHeping,TianXiaoyan,et al.Directfractal measurement of fracture surfaces[J].Journal ofUniversity of Science and TechnologyBeijing,1999,21(3):6―9.(in Chinese)
[17]谢和平,陈至达.分形(fractal)几何与岩石断裂[J].力学学报,1988,20(3):264―271.XieHeping,Chen Zhida.Fractal geometry and fracture ofrock[J].ActaMechanicaSinica,1988,20(3):264―271.(inChinese)
[18]谢和平,冯志刚,陈至达.星积分形曲面及其维数[J].应用数学和力学,1999,20(11):1101―1106.XieHeping,FengZhigang,Chen Zhida.On star productfractal surfaces and their dimensions[J].AppliedMathematics and Mechanics,1999,20(11):1101―1106.(in Chinese)
[19]周宏伟,谢和平,Kwasn.粗糙表面分维计算的立方体覆盖法[J].摩擦学报,2000,20(6):455―459.Zhou Hongwei,XieHeping,Kwasn.Fractal dimension ofrough surface estimated by the cubic covering method[J].Tribology,2000,20(6):455―459.(in Chinese)
[20]彭成斌,陈颙.地震中的分形结构[J].中国地震,1989,5(2):19―26.PengChengbin,Chen Yong.On the fractal structure ofearthquakes[J].Earthquake Research in China,1989,5(2):19―26.(in Chinese)
[21]谢和平,高峰.岩石类材料损伤演化的分形特征[J].岩石力学与工程学报,1991,10(1):74―82.XieHeping,GaoFeng.The fractal features of the damageevolution of rock materials[J].Chinese Journal of RockMechanics and Engineering,1991,10(1):74―82.(inChinese)
[22]白以龙,柯孚久,夏蒙棼.固体中微裂纹系统统计演化的基本描述[J].力学学报,1991,23(3):290―298.BaiYilong,KeFujiu,Xia Mengfen.Formulation ofstatistical evolution of microcracks insolids[J].ActaMechanicaSinica,1991,23(3):290―298.(inChinese)
[23]吕培苓,吴开统,焦远碧,等.岩石蠕变过程中声发射活动的实验研究[J].地震学报,1991,13(1):104―112.Lu Peiling,Wu Kaitong,Jiao Yuanbi,et al.Theexperimental study of acoustic emission during creep ofrocks[J].Acta,SeismologicaSinica,1991,13(1):104―112.(in Chinese)
[24]陈颙.地震预报中的几个科学问题的讨论[J].中国地震,1988,4(2):1―8.Chen Yong.Discussion on some scientific issues inearthquake prediction[J].Earthquake Research inChina,1988,4(2):1―8.(in Chinese)
[25]牛志仁,施行觉.岩石分形断裂的统计理论[J].地球物理学报,1992,35(5):595―603.NiuZhiren,ShiXingjue.Statistical theory of rock fractalfracture[J].ActaFeophysicaSinica,1992,35(5):595―603.(in Chinese)
[26]耿乃光.b值模拟实验的进展和我国b值模拟实验的开端[J].地震学报,1986,8(3):330―333.GengNaiguang.The development of b-value simulatedexperiments and the beging of b-value simulatedexperiments in China[J].Acta Seismological Sinica,1986,8(3):330―333.(in Chinese)
[27]Landis Eric N.Micro-macro fracture relationships andacoustic emissions in concrete[J].Construction andBuilding Materials,1999,13:65―72.
[28]Chang S-H,Lee C-I.Estimation of cracking and damagemechanisms in rock under triaxial compression bymoment tensor analysis of acoustic emission[J].International Journal of Rock Mechanics&MiningSciences,2004,41:1069―1086.
[29]Kao C-S,Carvalho FCS,Labuz JF.Micromechanisms offracture from acoustic emission[J].International Journalof Rock Mechanics&Mining Sciences,2011,48:686―673.
[2]王利,李示波.准脆性材料损伤斑图生长的数值模拟[J].工程力学,2011,28(4):238―244,256.Wang Li,Li Shibo.Numerical simulation of damagepattern growth in quasi-brittle materials[J].EngineeringMechanics,2011,28(4):238―244,256.(in Chinese)
[3]Dragon A,Mroz Z.A continuum model for plastic brittlebehavior of rock and concrete[J].Int.J.Eng.Sci.,1979,17(1):121―137.
[4]Krajcinovic D.Continuum damage mechanics[J].Appl.Mech.Rev.,1984,37(1):33―36.
[5]谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990:10―30.XieHeping.Rock and concrete damage mechanics[M].Xuzhou:China Mineral University Press,1990:10―30.(in Chinese)
[6]王利,高谦.基于强度理论的岩石损伤弹塑性模型.北京科技大学学报,2008,30(5):461―467.Wang Li,GaoQian.The elasto-plastic damage model ofrock based on strength theory[J].Journal of University ofScience and Technology Beijing,2008,30(5):461―467.(in Chinese)
[7]Hashin Z.Mesco damage mechanics of brittle material[J].J.Mech.Phys.Solids,1988,36:719.
[8]冯西桥.脆性材料的细观损伤理论和损伤机构的安定性分析[D].北京:清华大学,1995.FengXiqiao.The meso damage theory of brittle materialsand stability analysis on damage structure[D].Beijing:Tingshua University,1995.(in Chinese)
[9]白以龙,汪海英,夏蒙棼,等.固体的统计细观力学―连接多个耦合的时空尺度[J].力学进展,2006,36(2):286―305.BaiYilong,Wang Haiying,Xia Mengfen,et al.Statisticalmesomechanics of solid,linking coupled multiple spaceand time scales[J].Applied MechanicsReviews,2006,36(2):286―305.(in Chinese)
[10]夏蒙棼,韩闻生,柯浮久,等.统计细观损伤力学和损伤演化诱致突变(I)[J].力学进展,1995,25(1):1―24.Xia Mengfen,Han Wensheng,KeFujiu,et al.Statisticalmeso-scopic damage mechanics and damage evolutioninduced catastrophe[J].Advances in Mechanics,1995,25(1):1―24.(in Chinese)
[11]Bazant Z.结构破坏的尺度律[J].力学进展,1999,29(3):383―433.Bazant Z.Scale law of structure fracture[J].Advances inMechanics,1999,29(3):383―433.(in Chinese)
[12]Tang Chunan,XuXiaohe.Evolution and propagation ofmaterial defects and kaiser effect function[J].Journal ofSeismological Research,1989,13(2):203―213.
[13]张明,李仲奎,杨强,等.准脆性材料声发射的损伤模型及统计分析[J].岩石力学与工程学报,2006,25(12):2493―2501.Zhang Ming,Li Zhongkui,Yang Qiang,et al.A damagemodel and statistical analysis of acoustic emission forquasi-brittle materials[J].Chinese Journal of RockMechanics and Engineering,2006,25(12):2493―2501.(in Chinese)
[14]纪洪广,贾立宏,李造鼎.混凝土损伤的声发射模式研究[J].声学学报,1996,21(Suppl):601―608.JiHongguang,JiaLihong,LiZaoding.Study on theAE-model of concrete damage[J].ActaAcustica,1996,21(Suppl):601―608.(in Chinese)
[15]薛云亮,李庶林,林峰,等.类岩石材料声发射参数与应力和应变耦合本构关系[J].北京科技大学学报,2011,33(6):664―670.XueYunliang,Li Shulin,Lin Feng,et al.Couplingconstitutive relations of AE parameter versus stress andstrain for rock-like materials[J].Journal of University ofScience and Technology Beijing,2011,33(6):664―670.(in Chinese)
[16]王金安,谢和平,田晓燕,等.一种新的断裂表面分形测量方法[J].北京科技大学学报,1999,21(3):6―9.Wang Jinan,XieHeping,TianXiaoyan,et al.Directfractal measurement of fracture surfaces[J].Journal ofUniversity of Science and TechnologyBeijing,1999,21(3):6―9.(in Chinese)
[17]谢和平,陈至达.分形(fractal)几何与岩石断裂[J].力学学报,1988,20(3):264―271.XieHeping,Chen Zhida.Fractal geometry and fracture ofrock[J].ActaMechanicaSinica,1988,20(3):264―271.(inChinese)
[18]谢和平,冯志刚,陈至达.星积分形曲面及其维数[J].应用数学和力学,1999,20(11):1101―1106.XieHeping,FengZhigang,Chen Zhida.On star productfractal surfaces and their dimensions[J].AppliedMathematics and Mechanics,1999,20(11):1101―1106.(in Chinese)
[19]周宏伟,谢和平,Kwasn.粗糙表面分维计算的立方体覆盖法[J].摩擦学报,2000,20(6):455―459.Zhou Hongwei,XieHeping,Kwasn.Fractal dimension ofrough surface estimated by the cubic covering method[J].Tribology,2000,20(6):455―459.(in Chinese)
[20]彭成斌,陈颙.地震中的分形结构[J].中国地震,1989,5(2):19―26.PengChengbin,Chen Yong.On the fractal structure ofearthquakes[J].Earthquake Research in China,1989,5(2):19―26.(in Chinese)
[21]谢和平,高峰.岩石类材料损伤演化的分形特征[J].岩石力学与工程学报,1991,10(1):74―82.XieHeping,GaoFeng.The fractal features of the damageevolution of rock materials[J].Chinese Journal of RockMechanics and Engineering,1991,10(1):74―82.(inChinese)
[22]白以龙,柯孚久,夏蒙棼.固体中微裂纹系统统计演化的基本描述[J].力学学报,1991,23(3):290―298.BaiYilong,KeFujiu,Xia Mengfen.Formulation ofstatistical evolution of microcracks insolids[J].ActaMechanicaSinica,1991,23(3):290―298.(inChinese)
[23]吕培苓,吴开统,焦远碧,等.岩石蠕变过程中声发射活动的实验研究[J].地震学报,1991,13(1):104―112.Lu Peiling,Wu Kaitong,Jiao Yuanbi,et al.Theexperimental study of acoustic emission during creep ofrocks[J].Acta,SeismologicaSinica,1991,13(1):104―112.(in Chinese)
[24]陈颙.地震预报中的几个科学问题的讨论[J].中国地震,1988,4(2):1―8.Chen Yong.Discussion on some scientific issues inearthquake prediction[J].Earthquake Research inChina,1988,4(2):1―8.(in Chinese)
[25]牛志仁,施行觉.岩石分形断裂的统计理论[J].地球物理学报,1992,35(5):595―603.NiuZhiren,ShiXingjue.Statistical theory of rock fractalfracture[J].ActaFeophysicaSinica,1992,35(5):595―603.(in Chinese)
[26]耿乃光.b值模拟实验的进展和我国b值模拟实验的开端[J].地震学报,1986,8(3):330―333.GengNaiguang.The development of b-value simulatedexperiments and the beging of b-value simulatedexperiments in China[J].Acta Seismological Sinica,1986,8(3):330―333.(in Chinese)
[27]Landis Eric N.Micro-macro fracture relationships andacoustic emissions in concrete[J].Construction andBuilding Materials,1999,13:65―72.
[28]Chang S-H,Lee C-I.Estimation of cracking and damagemechanisms in rock under triaxial compression bymoment tensor analysis of acoustic emission[J].International Journal of Rock Mechanics&MiningSciences,2004,41:1069―1086.
[29]Kao C-S,Carvalho FCS,Labuz JF.Micromechanisms offracture from acoustic emission[J].International Journalof Rock Mechanics&Mining Sciences,2011,48:686―673.
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