基于CT三维重构的深部煤体损伤演化规律
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摘要
为研究不同应力条件下深部煤体损伤演化规律及破坏机理,以平煤十二矿己15-17220工作面的深部煤体为研究对象,进行了单轴压缩的实时CT扫描实验,结合细观统计损伤力学,提出了一种基于CT图像灰度值定义损伤变量的方法,定量分析了煤样单轴压缩过程中损伤演化规律。通过CT扫描实验、压汞实验和室内基本力学实验,建立了能够反映固体基质分布的深部非均质煤样的三维数值几何模型,进行了合理的网格划分,确定了不同材料组分的本构模型及其物理力学参数,在位移控制加载条件下开展了煤样单轴压缩的数值模拟,定性研究了煤样单轴压缩过程中的损伤演化规律及破坏机理。进一步,在单轴压缩数值模拟基础上,通过对煤样施加不同的环向应力,进行了5种不同围压条件下煤样三轴压缩的数值模拟,从应力-应变曲线形态、煤样破裂形态及破裂角大小等方面定性分析了三轴压缩条件下深部煤体损伤演化规律。结果表明:单轴压缩数值模拟的应力-应变曲线及损伤演化特征与CT实时扫描实验得到的结果具有较好的一致性。随着轴向应力的逐渐增加,煤样损伤依次经历了零损伤阶段、局部损伤产生阶段、损伤线性和非线性稳定增长阶段和损伤加速增长致使完全破坏阶段。试件最终破坏时其最大剪切应变率区域及塑性区都近似平行或垂直于煤基质和煤杂质的交界面,且损伤发生的两个主破坏面相互垂直。单轴压缩的整个过程煤样主要发生拉伸破坏,屈服应力后由于煤样的不均匀变形才发生剪切破坏。基于CT重构的煤样三轴压缩的数值模拟得到的损伤演化特征和经典的岩石损伤演化的6个阶段能够很好的吻合,煤样主要发生剪切破坏;随着围压的增大,峰值强度、扩容点应力和残余强度均逐渐增大,破裂角逐渐减小,破裂角与围压之间近似呈负线性相关。在数值模拟的网格划分、几何模型建立、材料参数和本构模型的选取以及应力应变的计算方法等方面做出了优化,取得了较好的数值模拟效果,能够消除实验样品差异性带来的影响,且能够直观准确地定性描述单轴和三轴压缩过程中的损伤演化规律。
In order to study the damage evolution characteristics and failure mechanism of deep coal under different stress conditions,the coal at the No.17220 working face of the Ji-15 coal seam in No.12 Pingdingshan Coal Mine was sampled for this study. The CT real-time testing of uniaxial compression was carried out. Combining with the meso-statistical damage mechanics,a method of defining the damage variable based on the gray value of CT images was proposed to quantitatively analyze the damage evolution characteristics during the uniaxial compression of coal samples.Based on CT scanning experiment,mercury intrusion experiment and indoor basic mechanics experiment,a three-dimensional numerical geometric model of deep heterogeneous coal sample was established to reflect the distribution of solid matrix. And,a reasonable meshing was carried out. In addition,the constitutive models and physical and mechanical parameters of different material components were determined. Initially,the numerical simulation of uniaxial compression was carried out to qualitatively study the damage evolution and failure mechanism of coal samples using displacement controlling loading. Furthermore,on the basis of numerical simulation of uniaxial compression,the triaxial numerical simulations of coal samples under five different confining pressure conditions were carried out by applying different circumferential stresses to the coal sample. The damage evolution of deep coal under triaxial compression was qualitatively analyzed from the aspects of stress-strain curve,fracture morphology and fracture angle of coal sample.The results show that the stress-strain curve and damage evolution characteristics obtained by the numerical simulation of uniaxial compression are in good agreement with the results obtained by CT real-time scanning experiment. With the increase of axial stress,the meso-damage evolution of coal sample occurs in four stages:the zero damage stage,the local damage generation stage,the damage linear and nonlinear steady growth stage and the accelerated damage growth stage. When the specimen is destroyed,its maximum shear strain rate region and plastic zone are approximately parallel or perpendicular to the interface between the coal matrix and the coal inclusion,and the two main damage surfaces are perpendicular to each other. The coal sample mainly undergoes tensile failure during uniaxial compression,and the shear failure occurs after the yield stress due to the uneven deformation. The damage evolution characteristics under triaxial compression obtained by numerical simulation based on CT reconstruction can be well matched with the six classical stages of rock damage evolution. The coal sample mainly undergoes shear failure. With the increase of confining pressure,the peak strength,the stress at the expansion point and the residual strength of coal all increase. The rupture angle decreases with the increasing confining pressure,and displays an approximately negatively linearly curve with the confining pressure. In this paper,the numerical simulation was optimized for meshing,establishment of geometric model,determination of material parameters and constitutive models and calculating method of stress and strain,and had achieved some good results of damage evolution. The numerical simulation method also can eliminate the influence of the difference of experimental samples,and can qualitatively describe the damage evolution law under uniaxial and triaxial compression intuitively and accurately.
In order to study the damage evolution characteristics and failure mechanism of deep coal under different stress conditions,the coal at the No.17220 working face of the Ji-15 coal seam in No.12 Pingdingshan Coal Mine was sampled for this study. The CT real-time testing of uniaxial compression was carried out. Combining with the meso-statistical damage mechanics,a method of defining the damage variable based on the gray value of CT images was proposed to quantitatively analyze the damage evolution characteristics during the uniaxial compression of coal samples.Based on CT scanning experiment,mercury intrusion experiment and indoor basic mechanics experiment,a three-dimensional numerical geometric model of deep heterogeneous coal sample was established to reflect the distribution of solid matrix. And,a reasonable meshing was carried out. In addition,the constitutive models and physical and mechanical parameters of different material components were determined. Initially,the numerical simulation of uniaxial compression was carried out to qualitatively study the damage evolution and failure mechanism of coal samples using displacement controlling loading. Furthermore,on the basis of numerical simulation of uniaxial compression,the triaxial numerical simulations of coal samples under five different confining pressure conditions were carried out by applying different circumferential stresses to the coal sample. The damage evolution of deep coal under triaxial compression was qualitatively analyzed from the aspects of stress-strain curve,fracture morphology and fracture angle of coal sample.The results show that the stress-strain curve and damage evolution characteristics obtained by the numerical simulation of uniaxial compression are in good agreement with the results obtained by CT real-time scanning experiment. With the increase of axial stress,the meso-damage evolution of coal sample occurs in four stages:the zero damage stage,the local damage generation stage,the damage linear and nonlinear steady growth stage and the accelerated damage growth stage. When the specimen is destroyed,its maximum shear strain rate region and plastic zone are approximately parallel or perpendicular to the interface between the coal matrix and the coal inclusion,and the two main damage surfaces are perpendicular to each other. The coal sample mainly undergoes tensile failure during uniaxial compression,and the shear failure occurs after the yield stress due to the uneven deformation. The damage evolution characteristics under triaxial compression obtained by numerical simulation based on CT reconstruction can be well matched with the six classical stages of rock damage evolution. The coal sample mainly undergoes shear failure. With the increase of confining pressure,the peak strength,the stress at the expansion point and the residual strength of coal all increase. The rupture angle decreases with the increasing confining pressure,and displays an approximately negatively linearly curve with the confining pressure. In this paper,the numerical simulation was optimized for meshing,establishment of geometric model,determination of material parameters and constitutive models and calculating method of stress and strain,and had achieved some good results of damage evolution. The numerical simulation method also can eliminate the influence of the difference of experimental samples,and can qualitatively describe the damage evolution law under uniaxial and triaxial compression intuitively and accurately.
引文
[1]谢和平,高峰,鞠杨.深部岩体力学研究与探索[J].岩石力学与工程学报,2015,34(11):2161-2178.XIE Heping,GAO Feng,JU Yang.Research and development of rock mechanics in deep ground engineering[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2161-2178.
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[3]ZHANG R,AI T,LI H G,et al.3D reconstruction method and connectivity rules of fracture networks generated under different mining layouts[J].International Journal of Mining Science and Technology,2013,23(6):863-871.
[4]谢和平,周宏伟,薛东杰,等.煤炭深部开采与极限开采深度的研究与思考[J].煤炭学报,2012,37(4):535-542.XIE Heping,ZHOU Hongwei,XUE Dongjie,et al.Research and consideration on deep coal mining and critical mining depth[J].Journal of China Coal Society,2013,37(4):535-542.
[5]谢和平,高峰,鞠杨,等.深部开采的定量界定与分析[J].煤炭学报,2015,40(1):1-10.XIE Heping,GAO Feng,JU Yang,et al.Quantitative definition and investigation of deep mining[J].Journal of China Coal Society,2015,40(1):1-10.
[6]HOU P,JU Y,GAO F,et al.Simulation and visualization of the displacement between CO2and formation fluids at pore-scale levels and its application to the recovery of shale gas[J].International Journal of Coal Science&Technology,2016,3(4):351-369.
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[8]杨更社,谢定义,张长庆,等.岩石损伤扩展力学特性的CT分析[J].岩石力学与工程学报,1999,18(3):250-254.YANG Gengshe,XIE Dingyi,ZHANG Changqing,et al.CT analysis on damage mechanic characteristics of propagation of rock[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(3):250-254.
[9]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.
[10]仵彦卿,丁卫华,蒲毅彬,等.压缩条件下岩石密度损伤增量的CT动态观测[J].自然科学进展,2000,10(9):830-835.WU Yanqing,DING Weihua,PU Yibin,et al.Dynamic observation of density damage increment for rock under compression conditions by CT technology[J].Process in Nature Science,2000,10(9):830-835.
[11]任建喜,葛修润.单轴压缩岩石损伤演化细观机理及其本构模型研究[J].岩石力学与工程学报,2001,20(4):425-431.REN Jianxi,GE Xiurun.Study of rock meso-damage evolution law and its constitutive model under uniaxial compression loading[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(4):425-431.
[12]ZHAO Y X,LIU S M,ZHAO G F,et al.Failure mechanisms in coal:Dependence on strain rate and microstructure[J].Journal of Geophysical Research:Solid Earth,2014,119(9):6924-6935.
[13]ZHOU H W,ZHONG J C,REN W G,et al.Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-rayμCT and a fractal method[J].International Journal of Coal Geology,2018,189:35-49
[14]于庆磊,杨天鸿,唐世斌,等.基于CT的准脆性材料三维结构重建及应用研究[J].工程力学,2015,32(11):51-62.YU Qinglei,YANG Tianhong,TANG Shibin,et al.The 3D reconstruction method for quasi-brittle material structure and application[J].Engineering Mechanics,2015,32(11):51-62.
[15]王刚,杨鑫祥,张孝强,等.基于CT三维重建的煤层气非达西渗流数值模拟[J].煤炭学报,2016,41(4):931-940.WANG Gang,YANG Xinxiang,ZHANG Xiaoqiang,et al.Numerical simulation on non-Darcy seepage of CBM by means of 3D reconstruction based on computed tomography[J].Journal of China Coal Society,2016,41(4):931-940.
[16]岳中琦.岩土细观介质空间分布数字表述和相关力学数值分析的方法、应用和进展[J].岩石力学与工程学报,2006,25(5):875-888.YUE Zhongqi.Digital representation of meso-geomaterial spatial distribution and associated numerical analysis of geomechanics:Methods,applications and developments[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):875-888.
[17]陈永强,郑小平,姚振汉.三维非均匀脆性材料破坏过程的数值模拟[J].力学学报,2002,34(3):351-361.CHEN Yongqiang,ZHENG Xiaoping,YAO Zhenhan.Numerical simulation of failure process in 3-D heterogeneous brittle material[J].Acta Mechanica Sinica,2002,34(3):351-361.
[18]谢和平,周宏伟,王金安,等.FLAC在煤矿开采沉陷预测中的应用及对比分析[J].岩石力学与工程学报,1999,18(4):29-33.XIE Heping,ZHOU Hongwei,WANG Jin’an,et al.Application of FLAC to predict ground surface displacements due to coal extraction and its comparative analysis[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(4):29-33.
[19]TAN X.Hydro-mechanical coupled behavior of brittle rocks:Laboratory experiments and numerical simulations[D].Freiberg:Geotechnical Institute of TU Bergakademie Freiberg,2013.
[20]郭依宝,周宏伟,荣腾龙,等.采动应力路径下深部煤体扰动特征研究[J].煤炭学报,2018,43(11):3072-3079.GUO Yibao,ZHOU Hongwei,RONG Tenglong,et al.Study on the disturbance characteristics of deep coal mass under the mining stress path[J].Journal of China Coal Society,2018,43(11):3072-3079.
[21]赵星光,蔡明,蔡美峰.岩石剪胀角模型与验证[J].岩石力学与工程学报,2010,29(5):970-981.ZHAO Xingguang,CAI Ming,CAI Meifeng.A rock dilation angle model and its verification[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):970-981.
[22]钟江城,周宏伟,任伟光,等.基于CT图像灰度分布的含杂质煤体三值化方法[J].力学与实践,2018,40(2):140-147.ZHONG Jiangcheng,ZHOU Hongwei,REN Weiguang,et al.A three-value-segmentation method of coal containing inclusion based on gray distribution of computed tomography image[J].Mechanics in Engineering,2018,40(2):140-147.
[23]MAHABADI O K,RANDALL N X,ZONG Z,et al.A novel approach for micro-scale characterization and modeling of geomaterials incorporating actual material heterogeneity[J].Geophysical Research Letters,2012,39(1):1303.
[24]RANDALL N X,VANDAMME M,UlM F J.Nanoindentation analysis as a two-dimensional tool for mapping the mechanical properties of complex surfaces[J].Journal of Materials Research,2009,24(3):679-690.
[25]王桂华,程远方,梁何生.岩屑显微硬度法确定地层力学参数[J].石油钻探技术,2003,31(3):7-9.WANG Guihua,CHENG Yuanfang,LIANG Hesheng.A new method to determine the formation mechanical properties with cuttings microhardness[J].Petroleum Drilling Techniques,2003,31(3):7-9.
[26]田威,党发宁,陈厚群.单轴压缩条件下混凝土细观损伤演化机理的CT试验研究[J].实验力学,2011,26(1):54-60.TIAN Wei,DANG Faning,CHEN Houqun.Experimental study of concrete meso-damage evolution mechanism based on uniaxial compression CT method[J].Experiment Mechanics,2011,26(1):54-60.
[27]蔡明,赵星光,KAISER P K.论完整岩体的现场强度[J].岩石力学与工程学报,2014,33(1):1-13.CAI Ming,ZHAO Xingguang,KAISER P K.On field strength of massive rocks[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):1-13.
[2]XUE J H,WANG H P,ZHOU W,et al.Experimental research on overlying strata movement and fracture evolution in pillarless stressrelief mining[J].International Journal of Coal Science&Technology,2015,2(1):38-45.
[3]ZHANG R,AI T,LI H G,et al.3D reconstruction method and connectivity rules of fracture networks generated under different mining layouts[J].International Journal of Mining Science and Technology,2013,23(6):863-871.
[4]谢和平,周宏伟,薛东杰,等.煤炭深部开采与极限开采深度的研究与思考[J].煤炭学报,2012,37(4):535-542.XIE Heping,ZHOU Hongwei,XUE Dongjie,et al.Research and consideration on deep coal mining and critical mining depth[J].Journal of China Coal Society,2013,37(4):535-542.
[5]谢和平,高峰,鞠杨,等.深部开采的定量界定与分析[J].煤炭学报,2015,40(1):1-10.XIE Heping,GAO Feng,JU Yang,et al.Quantitative definition and investigation of deep mining[J].Journal of China Coal Society,2015,40(1):1-10.
[6]HOU P,JU Y,GAO F,et al.Simulation and visualization of the displacement between CO2and formation fluids at pore-scale levels and its application to the recovery of shale gas[J].International Journal of Coal Science&Technology,2016,3(4):351-369.
[7]KAWAKATA H,CHO A,YANAGIDANI T,et al.The observations of faulting in westerly granite under triaxial compression by X-ray CTscan[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(3-4):151-162.
[8]杨更社,谢定义,张长庆,等.岩石损伤扩展力学特性的CT分析[J].岩石力学与工程学报,1999,18(3):250-254.YANG Gengshe,XIE Dingyi,ZHANG Changqing,et al.CT analysis on damage mechanic characteristics of propagation of rock[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(3):250-254.
[9]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.
[10]仵彦卿,丁卫华,蒲毅彬,等.压缩条件下岩石密度损伤增量的CT动态观测[J].自然科学进展,2000,10(9):830-835.WU Yanqing,DING Weihua,PU Yibin,et al.Dynamic observation of density damage increment for rock under compression conditions by CT technology[J].Process in Nature Science,2000,10(9):830-835.
[11]任建喜,葛修润.单轴压缩岩石损伤演化细观机理及其本构模型研究[J].岩石力学与工程学报,2001,20(4):425-431.REN Jianxi,GE Xiurun.Study of rock meso-damage evolution law and its constitutive model under uniaxial compression loading[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(4):425-431.
[12]ZHAO Y X,LIU S M,ZHAO G F,et al.Failure mechanisms in coal:Dependence on strain rate and microstructure[J].Journal of Geophysical Research:Solid Earth,2014,119(9):6924-6935.
[13]ZHOU H W,ZHONG J C,REN W G,et al.Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-rayμCT and a fractal method[J].International Journal of Coal Geology,2018,189:35-49
[14]于庆磊,杨天鸿,唐世斌,等.基于CT的准脆性材料三维结构重建及应用研究[J].工程力学,2015,32(11):51-62.YU Qinglei,YANG Tianhong,TANG Shibin,et al.The 3D reconstruction method for quasi-brittle material structure and application[J].Engineering Mechanics,2015,32(11):51-62.
[15]王刚,杨鑫祥,张孝强,等.基于CT三维重建的煤层气非达西渗流数值模拟[J].煤炭学报,2016,41(4):931-940.WANG Gang,YANG Xinxiang,ZHANG Xiaoqiang,et al.Numerical simulation on non-Darcy seepage of CBM by means of 3D reconstruction based on computed tomography[J].Journal of China Coal Society,2016,41(4):931-940.
[16]岳中琦.岩土细观介质空间分布数字表述和相关力学数值分析的方法、应用和进展[J].岩石力学与工程学报,2006,25(5):875-888.YUE Zhongqi.Digital representation of meso-geomaterial spatial distribution and associated numerical analysis of geomechanics:Methods,applications and developments[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(5):875-888.
[17]陈永强,郑小平,姚振汉.三维非均匀脆性材料破坏过程的数值模拟[J].力学学报,2002,34(3):351-361.CHEN Yongqiang,ZHENG Xiaoping,YAO Zhenhan.Numerical simulation of failure process in 3-D heterogeneous brittle material[J].Acta Mechanica Sinica,2002,34(3):351-361.
[18]谢和平,周宏伟,王金安,等.FLAC在煤矿开采沉陷预测中的应用及对比分析[J].岩石力学与工程学报,1999,18(4):29-33.XIE Heping,ZHOU Hongwei,WANG Jin’an,et al.Application of FLAC to predict ground surface displacements due to coal extraction and its comparative analysis[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(4):29-33.
[19]TAN X.Hydro-mechanical coupled behavior of brittle rocks:Laboratory experiments and numerical simulations[D].Freiberg:Geotechnical Institute of TU Bergakademie Freiberg,2013.
[20]郭依宝,周宏伟,荣腾龙,等.采动应力路径下深部煤体扰动特征研究[J].煤炭学报,2018,43(11):3072-3079.GUO Yibao,ZHOU Hongwei,RONG Tenglong,et al.Study on the disturbance characteristics of deep coal mass under the mining stress path[J].Journal of China Coal Society,2018,43(11):3072-3079.
[21]赵星光,蔡明,蔡美峰.岩石剪胀角模型与验证[J].岩石力学与工程学报,2010,29(5):970-981.ZHAO Xingguang,CAI Ming,CAI Meifeng.A rock dilation angle model and its verification[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):970-981.
[22]钟江城,周宏伟,任伟光,等.基于CT图像灰度分布的含杂质煤体三值化方法[J].力学与实践,2018,40(2):140-147.ZHONG Jiangcheng,ZHOU Hongwei,REN Weiguang,et al.A three-value-segmentation method of coal containing inclusion based on gray distribution of computed tomography image[J].Mechanics in Engineering,2018,40(2):140-147.
[23]MAHABADI O K,RANDALL N X,ZONG Z,et al.A novel approach for micro-scale characterization and modeling of geomaterials incorporating actual material heterogeneity[J].Geophysical Research Letters,2012,39(1):1303.
[24]RANDALL N X,VANDAMME M,UlM F J.Nanoindentation analysis as a two-dimensional tool for mapping the mechanical properties of complex surfaces[J].Journal of Materials Research,2009,24(3):679-690.
[25]王桂华,程远方,梁何生.岩屑显微硬度法确定地层力学参数[J].石油钻探技术,2003,31(3):7-9.WANG Guihua,CHENG Yuanfang,LIANG Hesheng.A new method to determine the formation mechanical properties with cuttings microhardness[J].Petroleum Drilling Techniques,2003,31(3):7-9.
[26]田威,党发宁,陈厚群.单轴压缩条件下混凝土细观损伤演化机理的CT试验研究[J].实验力学,2011,26(1):54-60.TIAN Wei,DANG Faning,CHEN Houqun.Experimental study of concrete meso-damage evolution mechanism based on uniaxial compression CT method[J].Experiment Mechanics,2011,26(1):54-60.
[27]蔡明,赵星光,KAISER P K.论完整岩体的现场强度[J].岩石力学与工程学报,2014,33(1):1-13.CAI Ming,ZHAO Xingguang,KAISER P K.On field strength of massive rocks[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(1):1-13.
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