岩石损伤破坏过程中分形与逾渗演化特征
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摘要
通过细观非均匀单元破坏事件的累积来反映岩石宏观上的逐渐损伤,而通过分析破坏单元的三维空间位置来建立岩石破坏过程中的分形和逾渗模型,并采用RFPA3D软件来模拟不同随机分布的岩石在单轴加载条件下的破裂过程,研究岩石在逐渐损伤破裂过程中的微破裂的分形与逾渗演化特征。微破裂的分形和逾渗特征反映了岩石的非均匀程度,岩石损伤破裂分形维数随着均质度和单轴抗压强度的增加而变小。逾渗分析也表明,在非均匀程度较高的岩石中破坏单元分布更为弥散。当外加载荷逐渐增加时,破裂集团和分形维数都表现出逐渐增加的趋势,但外载达到临界值时,应力突然下降的同时伴随着破裂单元急剧增多、破裂集团合并减少以及微破裂、分形维数增加等突变行为。模拟结果表明,岩石破裂过程中的分形和逾渗变化的规律性并不是偶然的,不同层次(不同尺寸)的岩石材料其力学行为具有的自相似性才是问题的本质。
The formation process of the cracks in the rocks,including the initiation,propagation and coalescence of the micro-cracks,was of statistical fractal features.It was considered that the failure of the elements would cause acoustic emission and micro-cracks which led to gradual damage of the rocks.The fractal model and percolation model were established by statistically analyzing the spatial distribution of the failure elements and AE event locations.The evolution of fractal dimensions and percolation were obtained by simulating the failure process of the heterogeneous rock samples with a numerical code RFPA3D.The fractal and percolation features of the micro-fractures were obviously influenced by heterogeneities.During the complete loading process,the fractal dimension decreased with the increase of the heterogeneity and the uniaxial compressive strength of the rock samples.There was an increase tendency of the number of failure clusters and fractal dimensions at the first loading stage.When the peak value of the loading was reached,the fractal dimensions increased to a certain value and the number of the failure clusters abruptly decreased due to the combination of the small failure clusters into large clusters.It was shown that the fractal and percolation features were formed due to the self-familiarity of the rock materials at different scale levels.
The formation process of the cracks in the rocks,including the initiation,propagation and coalescence of the micro-cracks,was of statistical fractal features.It was considered that the failure of the elements would cause acoustic emission and micro-cracks which led to gradual damage of the rocks.The fractal model and percolation model were established by statistically analyzing the spatial distribution of the failure elements and AE event locations.The evolution of fractal dimensions and percolation were obtained by simulating the failure process of the heterogeneous rock samples with a numerical code RFPA3D.The fractal and percolation features of the micro-fractures were obviously influenced by heterogeneities.During the complete loading process,the fractal dimension decreased with the increase of the heterogeneity and the uniaxial compressive strength of the rock samples.There was an increase tendency of the number of failure clusters and fractal dimensions at the first loading stage.When the peak value of the loading was reached,the fractal dimensions increased to a certain value and the number of the failure clusters abruptly decreased due to the combination of the small failure clusters into large clusters.It was shown that the fractal and percolation features were formed due to the self-familiarity of the rock materials at different scale levels.
引文
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[14]梁正召.三维条件下岩石破裂过程分析及其数值试验方法研究[D].沈阳:东北大学,2005.(LIANG Zheng-zhao.Three-dimensional numerical modeling of rock failure process[D].Shenyang:Northeastern University,2005.(in Chinese))
[15]梁正召,唐春安,张永彬,张亚芳,马天辉.岩石三维破裂过程的数值模拟研究[J].岩石力学与工程学报,2006,25(5):931–936.(LIANG Zheng-zhao,TANG Chun-an,ZHANG Yong-bin,ZHANG Ya-fang,MA Tian-hui.3D numerical simulation of failure process of rock[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):931–936.(in Chinese))
[16]梁正召,杨天鸿,等.非均匀性岩石破坏过程的三维损伤软化模型与数值模拟[J].岩土工程学报,2005,27(12):1147–1152.(LIANG Zheng-zhao,YANG Tian-hong,et al.Three-dimensional damage soften model for failure process of heterogeneous rocks and associated numerical simulation[J].Chinese Journal of Geotechnical Engineering,2005,27(12):1147–1152.(in Chinese))
[2]高峰,谢和平,赵鹏.岩石块度的分形性质及细观结构特征[J].岩石力学与工程学报,1994,13(3):240–246.(GAO Feng,XIE He-ping,ZHAO Peng.Fractal properties of size-frequency distribution of rock fragments and the influence of meso-structure[J].Chinese Journal of Rock Mechanics and Engineering,1994,13(3):240–246.(in Chinese))
[3]张树光,张向东,易富.单轴压缩条件下冻土的动态损伤和分形演化规律[J].岩土力学,2004,24(S):185–187.(ZHANG Shu-guang,ZHANG Xiang-dong,YI Fu.A timely damage and fractal evolution rule of uniaxial compression for frozen soil[J].Rock and Soil Mechanics,2003,24(S):185–187.(in Chinese))
[4]易顺民,唐辉明.三轴压缩条件下三峡坝基岩石破裂的分形特征[J].岩土力学,1999,20(3):24–28.(YI Shun-min,TANG Hui-ming.The fractal characteristics of fracture of dam foundation rock under triaxial compression in the Three Gorges Project[J].Rock and Soil Mechanics,1999,20(3):24–28.(in Chinese))
[5]卫宏,张玉三,李太任,程东.岩石显微空隙粒度分布的分形特征与岩石强度的关系[J].岩石力学与工程学报,2000,19(3):318–320.(WEI Hong,ZHANG Yu-san,LI Tai-ren,CHEN Dong.Relationship between fractal features of micro void rains distribution and strength of rock[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(3):318–320.(in Chinese))
[6]张玉三,李太任,等.岩石结构分形维数与岩石压缩强度关系的探讨[J].煤田地质与勘探,1995,23(3):22–25.(ZHANG Yu-san,LI Tai-ren,et al.The relationship between fractal dimension of rock texture and compressive strength[J].Coalfield and Exploration,1995,23(3):22–25.(in Chinese))
[7]杨双锁,靳钟铭,王春夫.裂隙分布的分形特征与岩石强度的相关性研究[J].山西矿业学院学报,1996,14(2):119–124.(YANG Shuang-suo,JIN Zhong-ming,WANG Chun-fu.A study on the interrelationship between fractal feature of crack distribution and strength of rock[J].Shanxi Mining Institute Learned Journal,1996,14(2):119–124.(in Chinese))
[8]谢卫红,谢和平,赵鹏.光弹模拟岩石分形节理的抗剪强度[J].力学与实践,1996,18(5):39–43.(XIE Wei-hong,XIE He-ping,ZHAO Peng.Photoelastic simulation of shear strength of rock fractal joints[J].Mechanics and Practice,1996,18(5):39–43.(in Chinese))
[9]许强,黄润秋.岩石破裂过程的自组织临界特征初探[J].地质灾害与环境保护,1996,7(1):25–30.(XU Qiang,HUANG Run-qiu.Discussion on self-organized critical characters in the course of rock failure[J].Journal of Geological Hazards and Environment Preservation,1996,7(1):25–30.(in Chinese))
[10]彭自正,王殚业,许云廷,牛志仁.逾渗与岩石破裂的计算机模拟研究[J].西北地震学报,1996,18(1):22–28.(PENG Zi-zheng,WANG Dan-ye,XU Yun-ting,NIU Zhi-ren.A computer simulation study on percolation and rock fracture[J].Northwestern Seismological Journal,1996,18(1):22–28.(in Chinese))
[11]柯善明,顾浩鼎,翟文杰.地震活动的逾渗模型及临界状态的研究[J].地震学报,1999,21(4):379–386.(KE Shan-ming,GU Hao-ding,ZHAI Wen-jie.Study on percolation model and critical state in earthquake[J].Acta Seismological Sinica,1999,21(4):379–386.(in Chinese))
[12]吴忠良.逾渗模型的地震学含义[J].地球物理学进展.1992,7(4):38–45.(WU Zhong-liang.Implication of percolation model in seismology[J].Progress in Geophysics,1992,7(4):38–45.(in Chinese))
[13]LIANG Z Z,TANG C A,LI H X,ZHANG Y B.Numerical simulation of the 3D failure process in heterogeneous rocks[J].Int J Rock Mech Min Sci,41(3):419–419.
[14]梁正召.三维条件下岩石破裂过程分析及其数值试验方法研究[D].沈阳:东北大学,2005.(LIANG Zheng-zhao.Three-dimensional numerical modeling of rock failure process[D].Shenyang:Northeastern University,2005.(in Chinese))
[15]梁正召,唐春安,张永彬,张亚芳,马天辉.岩石三维破裂过程的数值模拟研究[J].岩石力学与工程学报,2006,25(5):931–936.(LIANG Zheng-zhao,TANG Chun-an,ZHANG Yong-bin,ZHANG Ya-fang,MA Tian-hui.3D numerical simulation of failure process of rock[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):931–936.(in Chinese))
[16]梁正召,杨天鸿,等.非均匀性岩石破坏过程的三维损伤软化模型与数值模拟[J].岩土工程学报,2005,27(12):1147–1152.(LIANG Zheng-zhao,YANG Tian-hong,et al.Three-dimensional damage soften model for failure process of heterogeneous rocks and associated numerical simulation[J].Chinese Journal of Geotechnical Engineering,2005,27(12):1147–1152.(in Chinese))
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