基于岩石破坏全过程能量特征改进的能量跌落系数
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摘要
合理而准确地评价岩石的脆性是评估岩爆风险、油气储层可压裂性等工程实践的前提。针对表征脆性岩石破坏过程的能量跌落系数,详细分析了其适用性和局限性。为更加有效地评价岩石的脆性,基于岩石破坏全过程的应力-应变曲线,在能量跌落系数的基础上,进一步考虑峰前总能量中可释放弹性能的占比,提出一种改进的能量跌落系数,认为脆性是岩石内部可释放弹性能在峰前阶段大量储存并于峰后阶段快速释放的综合表现。通过对不同围压下大理岩和花岗岩试验数据进行分析和对比,结果表明改进后的能量跌落系数不仅能反映同种岩石不同围压下的脆-延转化行为,还能有效评价相同围压下不同岩石的脆性强弱。同时讨论了泊松比、损伤变量对岩石脆性评价的影响,发现随着泊松比增大,各围压下花岗岩的脆性强于大理岩的性质不改变;随着损伤变量增大,花岗岩的脆性由强于大理岩转变为弱于大理岩,且围压越高,现象越明显。试验结果验证了改进后能量跌落系数的可靠性,研究成果有望对岩石脆性评价提供参考。
Reasonable and accurate evaluation of rock brittleness is the precondition of engineering practices, such as the assessment of rock burst risk and fracturing of oil and gas reservoir. In this paper, the applicability and limitation of energy drop coefficient for characterizing the failure process of brittle rock are analyzed in detail. In order to evaluate the brittleness of rocks more effectively, based on the stress-strain curve of the whole process of rock failure and the energy drop coefficient, a revised energy drop coefficient is developed by considering the ratio of released elastic energy in the total energy of the pre-peak stage. It is considered that brittleness is a comprehensive manifestation of releasable elastic energy stored in large quantities in the pre-peak stage and released rapidly in the post-peak stage. The experimental data of marble and granite under different confining pressures are analyzed and compared. It is found that the revised energy drop coefficient can not only reflect the brittle-ductile behavior of same rock under different confining pressures, but also effectively evaluate the degree of brittleness of different rocks under same confining pressure. In addition, the influences of Poisson's ratio and damage variable on rock brittleness evaluation are discussed, the brittleness of granite is found greater than that of marble under each confining pressure with the increase of Poisson's ratio; and with the increase of damage variable, the brittleness of granite is firstly greater than that of marble and then less than. The test results verify the reliability of revised energy drop coefficient, which may be expected to provide some references for rock brittleness evaluation.
Reasonable and accurate evaluation of rock brittleness is the precondition of engineering practices, such as the assessment of rock burst risk and fracturing of oil and gas reservoir. In this paper, the applicability and limitation of energy drop coefficient for characterizing the failure process of brittle rock are analyzed in detail. In order to evaluate the brittleness of rocks more effectively, based on the stress-strain curve of the whole process of rock failure and the energy drop coefficient, a revised energy drop coefficient is developed by considering the ratio of released elastic energy in the total energy of the pre-peak stage. It is considered that brittleness is a comprehensive manifestation of releasable elastic energy stored in large quantities in the pre-peak stage and released rapidly in the post-peak stage. The experimental data of marble and granite under different confining pressures are analyzed and compared. It is found that the revised energy drop coefficient can not only reflect the brittle-ductile behavior of same rock under different confining pressures, but also effectively evaluate the degree of brittleness of different rocks under same confining pressure. In addition, the influences of Poisson's ratio and damage variable on rock brittleness evaluation are discussed, the brittleness of granite is found greater than that of marble under each confining pressure with the increase of Poisson's ratio; and with the increase of damage variable, the brittleness of granite is firstly greater than that of marble and then less than. The test results verify the reliability of revised energy drop coefficient, which may be expected to provide some references for rock brittleness evaluation.
引文
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[4]李庆辉,陈勉,金衍,等.页岩脆性的室内评价方法及改进[J].岩石力学与工程学报,2012,31(8):1680-1685.LI Qing-hui,CHEN Mian,JIN Yan,et al.Indoor evaluation method for shale brittleness and improvement[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(8):1680-1685.
[5]周辉,孟凡震,张传庆,等.基于应力-应变曲线的岩石脆性特征定量评价方法[J].岩石力学与工程学报,2014,33(6):1114-1122.ZHOU Hui,MENG Fan-zhen,ZHANG Chuan-qing,et al.Quantitative evaluation of rock brittleness based on stress-strain curve[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(6):1114-1122.
[6]夏英杰,李连崇,唐春安,等.基于峰后应力跌落速率及能量比的岩体脆性特征评价方法[J].岩石力学与工程学报,2016,35(6):1141-1154.XIA Ying-jie,LI Lian-chong,TANG Chun-an,et al.Rock brittleness evaluation based on stress dropping rate after peak stress and energy ratio[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(6):1141-1154.
[7]HNODA H,SANADA Y.Hardness of coal[J].Fuel,1956,35(4):451-461.
[8]LAWN B R,MARSHALL D B.Hardness,toughness,and brittleness:an indentation analysis[J].Journal of the American Ceramic Society,1979,62(7-8):347-350.
[9]QUINN J B,QUINN G D.Indentation brittleness of ceramics:a fresh approach[J].Journal of Materials Science,1997,32(16):4331-4346.
[10]RICKMAN R,MULLEN M J,PETRE J E,et al.Apractical use of shale petrophysics for stimulation design optimization:all shale plays are not clones of the Barnett shale[R].Colorado:Society of Petroleum Engineers,2008.
[11]HUCKA V,DAS B.Brittleness determination of rocks by different methods[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1974,11(10):389-392.
[12]ALTINDAG R.Correlation of specific energy with rock brittleness concepts on rock cutting[J].Journal of South African Institute of Mining and Metallurgy,2003,103(3):163-171.
[13]BISHOP A W.Progressive failure with special reference to the mechanism causing it[C]//Proceedings of the Geotechnical Conference on Shear Strength Properties of Natural Soils and Rocks.Oslo:Norwegian Geotechnical Institute,1967,2:142-150.
[14]HAJIABDOLMAJID V,KAISER P K,MARTIN C D.Modelling brittle failure of rock[J].International Journal of Rock Mechanics and Mining Sciences,2002,39(6):731-741.
[15]HAJIABDOLMAJID V,KAISER P K.Brittleness of rock and stability assessment in hard rock tunneling[J].Tunnelling and Underground Space Technology,2003,18(1):35-48.
[16]BARON L I.Determination of properties of rocks[M].[S.l.]:Gozgotekhizdat,1962:231-233.
[17]KIDYBINSKI A.Bursting liability indices of coal[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1981,18(4):295-304.
[18]谢和平,彭瑞东,鞠杨.岩石变形破坏过程中的能量耗散分析[J].岩石力学与工程学报,2004,23(21):3565-3570.XIE He-ping,PENG Rui-dong,JU Yang.Energy dissipation of rock deformation and fracture[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3565-3570.
[19]谢和平,鞠杨,黎立云.基于能量耗散与释放原理的岩石强度与整体破坏准则[J].岩石力学与工程学报,2005,24(17):3003-3010.XIE He-ping,JU Yang,LI Li-yun.Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3003-3010.
[20]TARASOV B,POTVIN Y.Universal criteria for rock brittleness estimation under triaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,2013,59(4):57-69.
[21]左建平,黄亚明,熊国军,等.脆性岩石破坏的能量跌落系数研究[J].岩土力学,2014,35(2):321-327.ZUO Jian-ping,HUANG Ya-ming,XIONG Guo-jun,et al.Study of energy-drop coefficient of brittle rock failure[J].Rock and Soil Mechanics,2014,35(2):321-327.
[22]GRIGGS D T,HANDIN J.Chapter 13:observations on fracture and a hypothesis of earthquakes[J].Geological Society of America Memoirs,1960,79:347-364.
[23]SOLECKI R,CONANT R J.Advanced mechanics of materials[M].London:Oxford University Press,2003.
[24]陈子全,李天斌,陈国庆,等.不同应力路径下砂岩能耗变化规律试验研究[J].工程力学,2016,33(6):120-128.CHEN Zi-quan,LI Tian-bin,CHEN Guo-qing,et al.Experimental study on energy evolution of sandstone under different stress paths[J].Engineering Mechanics,2016,33(6):120-128.
[25]朱泽奇,盛谦,肖培伟,等.岩石卸围压破坏过程的能量耗散分析[J].岩石力学与工程学报,2011,30(增刊1):2675-2681.ZHU Ze-qi,SHENG Qian,XIAO Pei-wei,et al.Analysis of energy dissipation in process of unloading confining pressure failure of rocks[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2675-2681.
[26]史贵才.脆塑性岩石破坏后区力学特性的面向对象有限元与无界元耦合模拟研究[D].武汉:中国科学院武汉岩土力学研究所,2005.SHI Gui-cai.Research on post-failure mechanical properties of brittle-plastic rocks by OOFEM coupled with IEM[D].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Science,2005.
[27]黄达,黄润秋,张永兴.三轴加卸载下花岗岩脆性破坏及应力跌落规律[J].土木建筑与环境工程,2011,33(2):1-6.HUANG Da,HUANG Run-qiu,ZHANG Yong-xing.Characteristics of brittle failure and stress drop under triaxial loading and unloading[J].Journal of Civil,Architectural and Environmental Engineering,2011,33(2):1-6.
[28]鞠杨,谢和平.基于应变等效性假说的损伤定义的适用条件[J].应用力学学报,1998,15(1):43-49.JU Yang,XIE He-ping.A variable condition of the damage description based on hypothesis of strain equivalence[J].Chinese Journal of Applied Mechanics,1998,15(1):43-49.
[2]张镜剑,傅冰骏.岩爆及其判据和防治[J].岩石力学与工程学报,2008,27(10):2034-2042.ZHANG Jing-jian,FU Bing-jun.Rock burst and its criteria and control[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(10):2034-2042.
[3]袁俊亮,邓金根,张定宇,等.页岩气储层可压裂性评价技术[J].石油学报,2013,34(3):523-527.YUAN Jun-liang,DENG Jin-gen,ZHANG Ding-yu,et al.Friability evaluation of shale-gas reservoirs[J].Acta Petrolei Sinica,2013,34(3):523-527.
[4]李庆辉,陈勉,金衍,等.页岩脆性的室内评价方法及改进[J].岩石力学与工程学报,2012,31(8):1680-1685.LI Qing-hui,CHEN Mian,JIN Yan,et al.Indoor evaluation method for shale brittleness and improvement[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(8):1680-1685.
[5]周辉,孟凡震,张传庆,等.基于应力-应变曲线的岩石脆性特征定量评价方法[J].岩石力学与工程学报,2014,33(6):1114-1122.ZHOU Hui,MENG Fan-zhen,ZHANG Chuan-qing,et al.Quantitative evaluation of rock brittleness based on stress-strain curve[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(6):1114-1122.
[6]夏英杰,李连崇,唐春安,等.基于峰后应力跌落速率及能量比的岩体脆性特征评价方法[J].岩石力学与工程学报,2016,35(6):1141-1154.XIA Ying-jie,LI Lian-chong,TANG Chun-an,et al.Rock brittleness evaluation based on stress dropping rate after peak stress and energy ratio[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(6):1141-1154.
[7]HNODA H,SANADA Y.Hardness of coal[J].Fuel,1956,35(4):451-461.
[8]LAWN B R,MARSHALL D B.Hardness,toughness,and brittleness:an indentation analysis[J].Journal of the American Ceramic Society,1979,62(7-8):347-350.
[9]QUINN J B,QUINN G D.Indentation brittleness of ceramics:a fresh approach[J].Journal of Materials Science,1997,32(16):4331-4346.
[10]RICKMAN R,MULLEN M J,PETRE J E,et al.Apractical use of shale petrophysics for stimulation design optimization:all shale plays are not clones of the Barnett shale[R].Colorado:Society of Petroleum Engineers,2008.
[11]HUCKA V,DAS B.Brittleness determination of rocks by different methods[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1974,11(10):389-392.
[12]ALTINDAG R.Correlation of specific energy with rock brittleness concepts on rock cutting[J].Journal of South African Institute of Mining and Metallurgy,2003,103(3):163-171.
[13]BISHOP A W.Progressive failure with special reference to the mechanism causing it[C]//Proceedings of the Geotechnical Conference on Shear Strength Properties of Natural Soils and Rocks.Oslo:Norwegian Geotechnical Institute,1967,2:142-150.
[14]HAJIABDOLMAJID V,KAISER P K,MARTIN C D.Modelling brittle failure of rock[J].International Journal of Rock Mechanics and Mining Sciences,2002,39(6):731-741.
[15]HAJIABDOLMAJID V,KAISER P K.Brittleness of rock and stability assessment in hard rock tunneling[J].Tunnelling and Underground Space Technology,2003,18(1):35-48.
[16]BARON L I.Determination of properties of rocks[M].[S.l.]:Gozgotekhizdat,1962:231-233.
[17]KIDYBINSKI A.Bursting liability indices of coal[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1981,18(4):295-304.
[18]谢和平,彭瑞东,鞠杨.岩石变形破坏过程中的能量耗散分析[J].岩石力学与工程学报,2004,23(21):3565-3570.XIE He-ping,PENG Rui-dong,JU Yang.Energy dissipation of rock deformation and fracture[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(21):3565-3570.
[19]谢和平,鞠杨,黎立云.基于能量耗散与释放原理的岩石强度与整体破坏准则[J].岩石力学与工程学报,2005,24(17):3003-3010.XIE He-ping,JU Yang,LI Li-yun.Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3003-3010.
[20]TARASOV B,POTVIN Y.Universal criteria for rock brittleness estimation under triaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,2013,59(4):57-69.
[21]左建平,黄亚明,熊国军,等.脆性岩石破坏的能量跌落系数研究[J].岩土力学,2014,35(2):321-327.ZUO Jian-ping,HUANG Ya-ming,XIONG Guo-jun,et al.Study of energy-drop coefficient of brittle rock failure[J].Rock and Soil Mechanics,2014,35(2):321-327.
[22]GRIGGS D T,HANDIN J.Chapter 13:observations on fracture and a hypothesis of earthquakes[J].Geological Society of America Memoirs,1960,79:347-364.
[23]SOLECKI R,CONANT R J.Advanced mechanics of materials[M].London:Oxford University Press,2003.
[24]陈子全,李天斌,陈国庆,等.不同应力路径下砂岩能耗变化规律试验研究[J].工程力学,2016,33(6):120-128.CHEN Zi-quan,LI Tian-bin,CHEN Guo-qing,et al.Experimental study on energy evolution of sandstone under different stress paths[J].Engineering Mechanics,2016,33(6):120-128.
[25]朱泽奇,盛谦,肖培伟,等.岩石卸围压破坏过程的能量耗散分析[J].岩石力学与工程学报,2011,30(增刊1):2675-2681.ZHU Ze-qi,SHENG Qian,XIAO Pei-wei,et al.Analysis of energy dissipation in process of unloading confining pressure failure of rocks[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2675-2681.
[26]史贵才.脆塑性岩石破坏后区力学特性的面向对象有限元与无界元耦合模拟研究[D].武汉:中国科学院武汉岩土力学研究所,2005.SHI Gui-cai.Research on post-failure mechanical properties of brittle-plastic rocks by OOFEM coupled with IEM[D].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Science,2005.
[27]黄达,黄润秋,张永兴.三轴加卸载下花岗岩脆性破坏及应力跌落规律[J].土木建筑与环境工程,2011,33(2):1-6.HUANG Da,HUANG Run-qiu,ZHANG Yong-xing.Characteristics of brittle failure and stress drop under triaxial loading and unloading[J].Journal of Civil,Architectural and Environmental Engineering,2011,33(2):1-6.
[28]鞠杨,谢和平.基于应变等效性假说的损伤定义的适用条件[J].应用力学学报,1998,15(1):43-49.JU Yang,XIE He-ping.A variable condition of the damage description based on hypothesis of strain equivalence[J].Chinese Journal of Applied Mechanics,1998,15(1):43-49.