基于裂纹扩展模型的脆性岩石破裂特征及力学性能研究
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摘要
为了探究初始微裂纹参数分布对岩石破裂特征及力学性能的影响,进一步系统地了解脆性岩石破裂演化过程,依据线弹性断裂力学理论,建立了非均质性二维细观弹性损伤模型,并运用FLAC~(2D)数值分析软件,数值模拟研究了单轴压缩条件下不同形态岩石试样的破裂过程。研究结果表明,当初始微裂纹长度和角度服从不同的随机分布时,岩石材料表现出不同的破裂特征,其中初始微裂纹长度和角度均服从正态分布时,岩石破裂区域较完整;初始微裂纹长度或角度服从均匀分布和指数分布时,岩石破裂区域较分散;初始微裂纹角度对于解释脆性岩石单轴抗压试验时岩石试样出现剪切破坏和劈裂破坏的原因具有一定的指导意义,且当初始微裂纹角度均值ɑ=45°时,模型具有最小的峰值强度和轴向最大应变。模型还模拟了脆性岩石单轴抗压试验、巴西劈裂试验和断裂韧度试验的演化过程,模拟结果与试验结果具有较高的一致性。
In order to study the influence of initial microcrack parameter distribution on fracture characteristics and mechanical properties of brittle rocks and further understand systematically the fracture evolution of brittle rocks,a two-dimensional mesoscopic elastic damage model of heterogeneity was established based on the theory of elastic fracture mechanics.The proposed model scheme was implemented through the two dimentional finite difference program FLAC~(2D). The zones in the model behave elastically before failure occurs,and lose tensile or shear load bearing capacity at corresponding mode of failure. Microcracks with different length and orientation distributions were defined in the zones of the model. The failure of the zone was controlled by the fracture propagation status of the microcrack inside.A failure criterion was adopted based on the stress intensity factor of the microcrack in each zone.The fracture process of rock specimens with different morphologies under distinct loading conditions was simulated using the proposed numerical model.The influence of the microcrack distributions on both the macroscopic fracture pattern and the mechanical response of the numerical model was analyzed.The results show that when the microcrack lengths and orientations are defined by different distributions,the different macroscopic fracture modes can be resulted. When the microcrack lengths and orientations are defined by normal distribution,failure band with clear shape can be formed. Failure zones are relatively dispersed if the microcrack lengths or orientations obey uniform or exponential distributions. For the reasons of shear failure and splitting failure of rock samples during the uniaxial compression test of brittle rock,the initial microcrack orientation was of guiding significance. When the mean initial microcrack orientation ɑ =45°,the minimum peak strength and axial maximum strain of model were obtained.The fracturing process of brittle rock uniaxial compression test,Brazilian splitting test and fracture toughness test were simulated.Good consistency was obtained with respect to both the mechanical response and fracture patterns. The model is valuable in rendering reliable results for rock mechanical tests which are difficult to realize in the laboratory. The inclusion of the influence of microcracks in simulating mechanical behavior of rock material also provide important insights into the failure process of rock under external load.
In order to study the influence of initial microcrack parameter distribution on fracture characteristics and mechanical properties of brittle rocks and further understand systematically the fracture evolution of brittle rocks,a two-dimensional mesoscopic elastic damage model of heterogeneity was established based on the theory of elastic fracture mechanics.The proposed model scheme was implemented through the two dimentional finite difference program FLAC~(2D). The zones in the model behave elastically before failure occurs,and lose tensile or shear load bearing capacity at corresponding mode of failure. Microcracks with different length and orientation distributions were defined in the zones of the model. The failure of the zone was controlled by the fracture propagation status of the microcrack inside.A failure criterion was adopted based on the stress intensity factor of the microcrack in each zone.The fracture process of rock specimens with different morphologies under distinct loading conditions was simulated using the proposed numerical model.The influence of the microcrack distributions on both the macroscopic fracture pattern and the mechanical response of the numerical model was analyzed.The results show that when the microcrack lengths and orientations are defined by different distributions,the different macroscopic fracture modes can be resulted. When the microcrack lengths and orientations are defined by normal distribution,failure band with clear shape can be formed. Failure zones are relatively dispersed if the microcrack lengths or orientations obey uniform or exponential distributions. For the reasons of shear failure and splitting failure of rock samples during the uniaxial compression test of brittle rock,the initial microcrack orientation was of guiding significance. When the mean initial microcrack orientation ɑ =45°,the minimum peak strength and axial maximum strain of model were obtained.The fracturing process of brittle rock uniaxial compression test,Brazilian splitting test and fracture toughness test were simulated.Good consistency was obtained with respect to both the mechanical response and fracture patterns. The model is valuable in rendering reliable results for rock mechanical tests which are difficult to realize in the laboratory. The inclusion of the influence of microcracks in simulating mechanical behavior of rock material also provide important insights into the failure process of rock under external load.
引文
[1]冯亚飞.单轴压缩下裂纹扩展相似模型试验研究[D].重庆:重庆大学,2012.Feng Yafei.Study on the Similar Model Test of Fissure Propagation under Uniaxial Compression[D].Chongqing:Chongqing University,2012.
[2]Atkinson B K.Fracture Mechanics of Rock[M].London:Academic Press INC,1987.
[3]Wong R H C,Chau K T,Tang C,et al.Analysis of crack coalescence in rock-like materials containing three flaws part I:Experimental approach[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(7):909-924.
[4]杨圣奇,吕朝辉,渠涛.含单个孔洞大理岩裂纹扩展细观试验和模拟[J].中国矿业大学学报,2009,38(6):774-781.Yang Shengqi,LüChaohui,Qu Tao.Investigations of crack expansion in marble having a single pre-existing hole:Experiment and simulations[J].Journal of China University of Mining&Technology,2009,38(6):774-781.
[5]王士民,刘丰军,叶飞,等.含预制裂纹脆性岩石破坏数值模拟研究[J].岩土力学,2006,27(增1):235-238.Wang Shimin,Liu Fengjun,Ye Fei,et al.The numerical simulation to model failure of brittle rock with prefab crack[J].Rock and Soil Mechanics,2006,27(Supp.1):235-238.
[6]王卫华,李坤,严哲,等.节理压缩闭合试验前后表面形态特征变化分析[J].黄金科学技术,2016,24(6):84-89.Wang Weihua,Li Kun,Yan Zhe,et al.Analysis on changes of surface morphological characteristics of joint under compression closed testing[J].Gold Science and Technology,2016,24(6):84-89.
[7]Tang CA,Lin P,Wong R H C,et al.Analysis of crack coalescence in rock-like materials containing three flawsPartⅡ:Numerical approach[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(7):925-939.
[8]黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4):468-471.Huang Mingli,Tang Chun’an,Zhu Wancheng.Numerical simulation on failure process of rock[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(4):468-471.
[9]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 Chun’an,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.
[10]李地元,李夕兵,李春林,等.单轴压缩下含预制孔洞板状花岗岩试样力学响应的试验和数值研究[J].岩石力学与工程学报,2011,30(6):1198-1206.Li Diyuan,Li Xibing,Li Chunlin,et al.Experimental and numerical studies of mechanical response of plate-shape granite samples containing prefabricated holes under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1198-1206.
[11]Konietzky H,Heftenberger A,Feige M.Life-time prediction for rocks under static compressive and tensile loads:Anew simulation approach[J].Acta Geotechnica,2009,4(1):73-78.
[12]Golshani A,Okui Y,Oda M,et al.A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite[J].Mechanicas of Materials,2006,38(4):287-303.
[13]Kranz R L.Microcracks in rocks:A review[J].Tectonophysics,1983,100(1):449-480.
[14]潘别桐,徐光黎.岩体节理几何特征的研究现状及趋向[J].工程勘察,1989(5):23-26.Pan Bietong,Xu Guangli.Research status and trend of rock joint geometry characteristics[J].Geotechnical Investigation and Surveying,1989(5):23-26.
[15]Lu Y L,Elsworth D,Wang L G.Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks[J].Computers&Geotechnics,2013,49(4):226-244.
[16]Li X,Konietzky H.Simulation of time-dependent crack growth in brittle rocks under constant loading conditions[J].Engineering Fracture Mechanics,2014,119(3):53-65.
[17]Li X,Konietzky H.Numericalsimulationschemesfortimedependent crack growth in hard brittle rock[J].Acta Geotechnica,2015,10(4):513-531.
[18]Itasca Consulting Group,Inc.FLAC:Fast Lagrangian Analysis of Continua-Theory and Background[M].Minnea-Polis:Itasca Consulting Group,2005.
[19]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,13(3):293-297.
[20]Zhu W C,Tang C A.Micromechanical model for simulating the fracture process of rock[J].Rock Mechanics and Rock Engineering,2004,37(1):25-56.
[21]Anderson T L.Fracture Mechanics-Fundamentals and Applications[M].Florida USA:CRC Press,1991.
[22]黄作宾.断裂力学基础[M].武汉:中国地质大学出版社,1991:121-128.Huang Zuobin.Fracture Mechanics Foundation[M].Wuhan:China University of Geosciences Press,1991:121-128.
[23]Li X,Konietzky H,Li X B.Numerical study on time depedent and time independent fracturing processes for brittle rocks[J].Engineering Fracture Mechanics,2016,163:89-107.
[24]Atkinson B K.Subcritical crack propagation in rocks:Theory,experimental results and applications[J].Journal of Structural Geology,1982,4(1):41-56.
[25]Dong S,Wang Y,Xia Y.Stress intensity factors for central cracked circular disk subjected to compression[J].Engineering Fracture Mechanics,2004,71(7):1135-1148.
[26]Liu H Y,Kou S Q,Lindqvist PA,et al.Numerical modelling of the heterogeneous rock fracture process using various test techniques[J].Rock Mechanics and Rock Engineering,2007,40(2):107-144.
[27]孙杨,罗黎明,邓红卫.金属矿山深部采场稳定性分析与结构参数优化[J].黄金科学技术,2017,25(1):99-105.Sun Yang,Luo Liming,Deng Hongwei.Stability analysis and parameter optimization of stope in deep metal mines[J].Gold Science and Technology,2017,25(1):99-105.
[28]李夕兵,姚金蕊,杜坤.高地应力硬岩矿山诱导致裂非爆连续开采初探——以开阳磷矿为例[J].岩石力学与工程学报,2013,32(6):1101-1111.Li Xibing,Yao Jinrui,Du Kun.Preliminary study for induced fracture and non-explosive continuous mining in high-geostress hard rock mine:A case study of Kaiyang phosphate mine[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1101-1111.
[2]Atkinson B K.Fracture Mechanics of Rock[M].London:Academic Press INC,1987.
[3]Wong R H C,Chau K T,Tang C,et al.Analysis of crack coalescence in rock-like materials containing three flaws part I:Experimental approach[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(7):909-924.
[4]杨圣奇,吕朝辉,渠涛.含单个孔洞大理岩裂纹扩展细观试验和模拟[J].中国矿业大学学报,2009,38(6):774-781.Yang Shengqi,LüChaohui,Qu Tao.Investigations of crack expansion in marble having a single pre-existing hole:Experiment and simulations[J].Journal of China University of Mining&Technology,2009,38(6):774-781.
[5]王士民,刘丰军,叶飞,等.含预制裂纹脆性岩石破坏数值模拟研究[J].岩土力学,2006,27(增1):235-238.Wang Shimin,Liu Fengjun,Ye Fei,et al.The numerical simulation to model failure of brittle rock with prefab crack[J].Rock and Soil Mechanics,2006,27(Supp.1):235-238.
[6]王卫华,李坤,严哲,等.节理压缩闭合试验前后表面形态特征变化分析[J].黄金科学技术,2016,24(6):84-89.Wang Weihua,Li Kun,Yan Zhe,et al.Analysis on changes of surface morphological characteristics of joint under compression closed testing[J].Gold Science and Technology,2016,24(6):84-89.
[7]Tang CA,Lin P,Wong R H C,et al.Analysis of crack coalescence in rock-like materials containing three flawsPartⅡ:Numerical approach[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(7):925-939.
[8]黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4):468-471.Huang Mingli,Tang Chun’an,Zhu Wancheng.Numerical simulation on failure process of rock[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(4):468-471.
[9]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 Chun’an,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.
[10]李地元,李夕兵,李春林,等.单轴压缩下含预制孔洞板状花岗岩试样力学响应的试验和数值研究[J].岩石力学与工程学报,2011,30(6):1198-1206.Li Diyuan,Li Xibing,Li Chunlin,et al.Experimental and numerical studies of mechanical response of plate-shape granite samples containing prefabricated holes under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1198-1206.
[11]Konietzky H,Heftenberger A,Feige M.Life-time prediction for rocks under static compressive and tensile loads:Anew simulation approach[J].Acta Geotechnica,2009,4(1):73-78.
[12]Golshani A,Okui Y,Oda M,et al.A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite[J].Mechanicas of Materials,2006,38(4):287-303.
[13]Kranz R L.Microcracks in rocks:A review[J].Tectonophysics,1983,100(1):449-480.
[14]潘别桐,徐光黎.岩体节理几何特征的研究现状及趋向[J].工程勘察,1989(5):23-26.Pan Bietong,Xu Guangli.Research status and trend of rock joint geometry characteristics[J].Geotechnical Investigation and Surveying,1989(5):23-26.
[15]Lu Y L,Elsworth D,Wang L G.Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks[J].Computers&Geotechnics,2013,49(4):226-244.
[16]Li X,Konietzky H.Simulation of time-dependent crack growth in brittle rocks under constant loading conditions[J].Engineering Fracture Mechanics,2014,119(3):53-65.
[17]Li X,Konietzky H.Numericalsimulationschemesfortimedependent crack growth in hard brittle rock[J].Acta Geotechnica,2015,10(4):513-531.
[18]Itasca Consulting Group,Inc.FLAC:Fast Lagrangian Analysis of Continua-Theory and Background[M].Minnea-Polis:Itasca Consulting Group,2005.
[19]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,13(3):293-297.
[20]Zhu W C,Tang C A.Micromechanical model for simulating the fracture process of rock[J].Rock Mechanics and Rock Engineering,2004,37(1):25-56.
[21]Anderson T L.Fracture Mechanics-Fundamentals and Applications[M].Florida USA:CRC Press,1991.
[22]黄作宾.断裂力学基础[M].武汉:中国地质大学出版社,1991:121-128.Huang Zuobin.Fracture Mechanics Foundation[M].Wuhan:China University of Geosciences Press,1991:121-128.
[23]Li X,Konietzky H,Li X B.Numerical study on time depedent and time independent fracturing processes for brittle rocks[J].Engineering Fracture Mechanics,2016,163:89-107.
[24]Atkinson B K.Subcritical crack propagation in rocks:Theory,experimental results and applications[J].Journal of Structural Geology,1982,4(1):41-56.
[25]Dong S,Wang Y,Xia Y.Stress intensity factors for central cracked circular disk subjected to compression[J].Engineering Fracture Mechanics,2004,71(7):1135-1148.
[26]Liu H Y,Kou S Q,Lindqvist PA,et al.Numerical modelling of the heterogeneous rock fracture process using various test techniques[J].Rock Mechanics and Rock Engineering,2007,40(2):107-144.
[27]孙杨,罗黎明,邓红卫.金属矿山深部采场稳定性分析与结构参数优化[J].黄金科学技术,2017,25(1):99-105.Sun Yang,Luo Liming,Deng Hongwei.Stability analysis and parameter optimization of stope in deep metal mines[J].Gold Science and Technology,2017,25(1):99-105.
[28]李夕兵,姚金蕊,杜坤.高地应力硬岩矿山诱导致裂非爆连续开采初探——以开阳磷矿为例[J].岩石力学与工程学报,2013,32(6):1101-1111.Li Xibing,Yao Jinrui,Du Kun.Preliminary study for induced fracture and non-explosive continuous mining in high-geostress hard rock mine:A case study of Kaiyang phosphate mine[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1101-1111.