岩石声发射时间序列分析
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摘要
岩石是自然界较典型的非均质材料,力学性质复杂多变,其变形破坏过程实际上是内部微裂纹的萌生、扩展、聚合(即内部损伤的逐步积累)直至最终形成宏观裂纹而失去承载能力的过程。分形几何是研究在自相似意义下事物所具有的尺度不变性的数学分支。实验证明,岩石的声发射序列不仅在空间上是分形分布的,而且在时间上也具有分形特征。本论文采用关联维数来描述岩石声发射时间序列的分形特征,研究岩石损伤破坏过程的演化规律。
本文基于分形理论,利用matlab程序,通过对岩石声发射实验不同试样的时间序列进行计算分析,重点研究岩石不同破坏阶段分形关联维数的变化趋势,主要内容如下:
(1)介绍分形理论及分维数的算法,应用关联维数的计算,对岩石加载过程中的声发射时间序列进行分析。
(2)通过声发射实验,研究不同岩样(花岗岩、大理岩、砂岩、片麻岩)在单轴加载的方式下,声发射时间序列的分形特征。
(3)通过分析关联维数与声发射事件率的关系,研究声发射关联维数值的变化与岩石破碎失稳过程之间的联系。
(4)通过分析关联维数与最大破坏应力之间的关系,研究不同应力时关联维数的变化规律,在此基础上判断声发射时间序列关联维数对于预测预报冲击地压的参考价值。
Rock is a typical non-isotropic material, the mechanical properties is complicated and diversified, its deformation failure process is the internal micro cracks generates, pores, joints (i.e. internal damage accumulate gradually) so that forms macroscopic crack to lose the bearing capacity. Fractal geometry is about things have scale invariance in self-similar meaning, it is the mathematical branch. The experiment showed rock acoustic emission sequence not only has fractal distribution in space, but also has fractal feature in times. Therefore, describe the fractal feature of acoustic emission time sequence by correlation dimension and research the evolution law of rock damage and failure process.
Based on the fractal theory, using matlab program, calculate and analysis time sequence of different rock specimens acoustic emission, emphases on the trend of correlation dimension in various rock failure stages. There are following contents:
(1)Introducing the fractal theory and the algorithms of fractal dimensions, analyzing the rock acoustic emission time sequence in rock loading process by calculating correlation dimension.
(2)By acoustic emission experiment, studying the rock acoustic emission time sequence fractal features of different kinds of rock (granite, marble, sandstone and gneisses) in uniaxial loading.
(3)By analyzing the relation to correlation dimension and acoustic emission rate, studying the relation to the change of acoustic emission correlation dimension and rock failure instability process.
(4)By analyzing the relation to correlation dimension and maximum failure stress, studying the change regularity of correlation dimension ,which are under different stress in rock loading process. Based on above, estimating the reference value of rockburst predicating and forecasting which is about correlation dimension of rock acoustic emission time sequence.
本文基于分形理论,利用matlab程序,通过对岩石声发射实验不同试样的时间序列进行计算分析,重点研究岩石不同破坏阶段分形关联维数的变化趋势,主要内容如下:
(1)介绍分形理论及分维数的算法,应用关联维数的计算,对岩石加载过程中的声发射时间序列进行分析。
(2)通过声发射实验,研究不同岩样(花岗岩、大理岩、砂岩、片麻岩)在单轴加载的方式下,声发射时间序列的分形特征。
(3)通过分析关联维数与声发射事件率的关系,研究声发射关联维数值的变化与岩石破碎失稳过程之间的联系。
(4)通过分析关联维数与最大破坏应力之间的关系,研究不同应力时关联维数的变化规律,在此基础上判断声发射时间序列关联维数对于预测预报冲击地压的参考价值。
Rock is a typical non-isotropic material, the mechanical properties is complicated and diversified, its deformation failure process is the internal micro cracks generates, pores, joints (i.e. internal damage accumulate gradually) so that forms macroscopic crack to lose the bearing capacity. Fractal geometry is about things have scale invariance in self-similar meaning, it is the mathematical branch. The experiment showed rock acoustic emission sequence not only has fractal distribution in space, but also has fractal feature in times. Therefore, describe the fractal feature of acoustic emission time sequence by correlation dimension and research the evolution law of rock damage and failure process.
Based on the fractal theory, using matlab program, calculate and analysis time sequence of different rock specimens acoustic emission, emphases on the trend of correlation dimension in various rock failure stages. There are following contents:
(1)Introducing the fractal theory and the algorithms of fractal dimensions, analyzing the rock acoustic emission time sequence in rock loading process by calculating correlation dimension.
(2)By acoustic emission experiment, studying the rock acoustic emission time sequence fractal features of different kinds of rock (granite, marble, sandstone and gneisses) in uniaxial loading.
(3)By analyzing the relation to correlation dimension and acoustic emission rate, studying the relation to the change of acoustic emission correlation dimension and rock failure instability process.
(4)By analyzing the relation to correlation dimension and maximum failure stress, studying the change regularity of correlation dimension ,which are under different stress in rock loading process. Based on above, estimating the reference value of rockburst predicating and forecasting which is about correlation dimension of rock acoustic emission time sequence.
引文
[1]秦四清,李造鼎等.岩石声发射技术概论[M].成都:西南交通大学出版社,1993.
[2]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1988.
[3]谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.
[4]王振龙.时间序列分析.北京:中国统计出版社,2000.
[5]安鸿志,陈敏.非线性时间序列分析.上海:上海科学技术出版社,1998.
[6]杨叔子等.时间序列分析的工程应用[M].武汉:华中理工大学出版社,1991
[7]纪洪广.混凝土材料声发射性能研究与应用[M].北京:煤炭工业出版社,2004.
[8]陈顒,陈凌.分形几何学[M].北京:地震出版社,2005.
[9]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2005.
[10]Hirata T,Takashi Satoh,Keisuke Ito.Fractal structure of a spatial distribution of microfracturing in rock[J].Geophys J R Astar Soc,1987,90(2):369-374.
[11]陈顒,吴如山,陈凌等.地震从集的分形新方法:物理分形[J].中国地震,1997,13(2).
[12]茂木清夫.日本地震预报[M].北京:地震出版社,1984.
[13]傅征祥等.全球强震活动性的某些统计特征[J].地震学报,1986,8(2).
[14]尹贤刚,李庶林,唐海燕.岩石破坏声发射强度分形特征研究[J].岩石力学与工程学报,2005,VOL24:3512-3516.
[15]Lockner D.The role of acoustic emission in the study of rock fracture[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstract,1993,30(7):883-899.
[16]张晖辉,颜玉定,余怀忠等.循环载荷下大试件岩石破坏声发射实验—岩石破坏前兆的研究[J].岩石力学与工程学报,2004,23(21):3621-3628
[17]李元辉,赵兴东等.基于声发射实验岩石破坏前兆特征研究[J].金属矿山,2008,8.
[18]腾山邦久著,冯夏庭 译.声发射(AE)技术的应用[M].冶金工业出版社.1996.
[19]Kaiser E.J.A study of acoustic phenomena in tensile test[D].Technische Hochschule M(u|¨)nchen,1950.
[20]Goodman R.E.Sub audible noise during compression of rock[J].Geo.Soc.Am.Bull,1963,74:487-490.
[21]Kurita K.,N.Fujii.Stress memory of crystalline rocks in acoustic emission[J].Geophysical Research Letter,9-12,1979.
[22]Kanagawa T,Hayashi M and Nakasa H.Estimation of the spatial Geo-stress components in rock samples using the Kaiser Effect of acoustic emission[J].Tech.Report.,C.R.I.E.P.I.,E375004,1976.
[23]C.Li,E.Norlund.Experimental verification of the Kaiser effect in rock[J].Rock Mechanics and Rock Engineering,1993,26(4):333-351.
[24]Thomas Drouillard.Acoustic Emission-the First halfcentry[J].Progress in Acoustic Emission,the Japanese Society for NDT,1994.
[25]孙成栋.岩石声学测试[M].北京:地质出版社,1981.10.
[26]袁振明,马羽宽,何泽云.声发射技术及应用[M].北京:机械工业出版社,1985.
[27]张洪亭,王明赞.测试技术[M].沈阳:东北大学出版社,2005.02.
[28]T.Ozaki,H.Tong.On the fitting of nonstationary autoregressive models in time series analysis[J].Proc.8~(th) Hawaii Int.Conf.System Science,224-226,1975.
[29]G.Kitagawa,HAkaike.A procedure for the modeling of non-stationary time series[J].Ann.Inst.Satist.Math.30,Part B,351-363,1978.
[30]张治强,冯夏庭,杨成祥等.论非线性位移时间序列进化神经网络建模的适应性研究[J].岩土力学,1999,20(4):19-24.
[31]Nelder I.A,Mead R.A Simplex method for function minimization[J].Computer Journal,vol.7:308-373,1965.
[32]Gendzwill D.J.,Prugger A.F.Algorithms for microearthquake locations[J].Proc.4~(th) Symp.On Acoustic Emissions and Microseismicity,Penn State Uninversity,College Park,Pennsylvania,1985.
[33]张薇,薛嘉庆.最优化方法[M].沈阳:东北大学出版社,2004.09.
[34]L.Geiger.Probability method for the determination of earthquake epicenters from the arrival time only[J].Bulletin of St.Louis University,1912,vol8(1):56-71.
[35]Mandelbrot B.B.The Fractal Geometry of Nature[M].San Francisco,W.H.Freeman and Co.,1982.
[36]Falconer K.J.Fractal Geometry:Mathematical Foundation and Application[M].Wiley,New York,1990.
[37]Falconer K.J.The Geometry of Fractal Sets[M].Cambridge University Press,1985.
[38]Barnsley M.Fractals Everywhere[M].Academic Press Inc.,1988.
[39]Xie Heping,Fractals in Rock Mechanics[M].A.A.Balkema Press,1993.
[40]谢和平,薛秀谦.分形应用中的数学基础与方法[M].科学出版社,1997.03.
[41]Mandelbrot B.B.Self-affine fractal sets,in Fractals in Physics[M].PietroneroL.& Tosatti E.,Elseveri Sci.Publ.B.V.,1986
[42]Edgar G.A.Measure,Topology and Fractal Geometry[M].Berlin,spring-Verlag,1990.
[43]Hurst H.E.Long-term storage capacity of reservoirs[J].Trans.Am.Soc.Civ.Eng.,1965,116,770-808
[44]谢和平.岩石、混凝土损伤力学[M].中国矿业大学出版社,1990.
[45]Lajtal E.Z.Brittle Fracture in compression[J].Int.J.Fracture,1974.10,525-536.
[46]Costin I.S.A microcrack model for the deformation and failure of brittle rock[J].J.Geophys,Res.,1983,88,9485-9492.
[47]Botsis J.Kunin B.On Self-similarity of crack layer[J].Int.J.Fracture,1987,35,51-56.
[48]Main I.G.A modified Griffith for the evolution of damage with a fractal distribution of crack lengths:application to seismic event[J].Geohpys.J.Int.,1991,107,353-362.
[49]谢和平,高峰.岩石损伤过程中的分形描述[M].岩石力学与工程学报,1991,10,55-67.
[50]Robertson M.C.,Sammis C.G.et al.Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation[J].J.Geophys.Res.,1995,100,B1:609-620.
[2]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1988.
[3]谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.
[4]王振龙.时间序列分析.北京:中国统计出版社,2000.
[5]安鸿志,陈敏.非线性时间序列分析.上海:上海科学技术出版社,1998.
[6]杨叔子等.时间序列分析的工程应用[M].武汉:华中理工大学出版社,1991
[7]纪洪广.混凝土材料声发射性能研究与应用[M].北京:煤炭工业出版社,2004.
[8]陈顒,陈凌.分形几何学[M].北京:地震出版社,2005.
[9]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2005.
[10]Hirata T,Takashi Satoh,Keisuke Ito.Fractal structure of a spatial distribution of microfracturing in rock[J].Geophys J R Astar Soc,1987,90(2):369-374.
[11]陈顒,吴如山,陈凌等.地震从集的分形新方法:物理分形[J].中国地震,1997,13(2).
[12]茂木清夫.日本地震预报[M].北京:地震出版社,1984.
[13]傅征祥等.全球强震活动性的某些统计特征[J].地震学报,1986,8(2).
[14]尹贤刚,李庶林,唐海燕.岩石破坏声发射强度分形特征研究[J].岩石力学与工程学报,2005,VOL24:3512-3516.
[15]Lockner D.The role of acoustic emission in the study of rock fracture[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstract,1993,30(7):883-899.
[16]张晖辉,颜玉定,余怀忠等.循环载荷下大试件岩石破坏声发射实验—岩石破坏前兆的研究[J].岩石力学与工程学报,2004,23(21):3621-3628
[17]李元辉,赵兴东等.基于声发射实验岩石破坏前兆特征研究[J].金属矿山,2008,8.
[18]腾山邦久著,冯夏庭 译.声发射(AE)技术的应用[M].冶金工业出版社.1996.
[19]Kaiser E.J.A study of acoustic phenomena in tensile test[D].Technische Hochschule M(u|¨)nchen,1950.
[20]Goodman R.E.Sub audible noise during compression of rock[J].Geo.Soc.Am.Bull,1963,74:487-490.
[21]Kurita K.,N.Fujii.Stress memory of crystalline rocks in acoustic emission[J].Geophysical Research Letter,9-12,1979.
[22]Kanagawa T,Hayashi M and Nakasa H.Estimation of the spatial Geo-stress components in rock samples using the Kaiser Effect of acoustic emission[J].Tech.Report.,C.R.I.E.P.I.,E375004,1976.
[23]C.Li,E.Norlund.Experimental verification of the Kaiser effect in rock[J].Rock Mechanics and Rock Engineering,1993,26(4):333-351.
[24]Thomas Drouillard.Acoustic Emission-the First halfcentry[J].Progress in Acoustic Emission,the Japanese Society for NDT,1994.
[25]孙成栋.岩石声学测试[M].北京:地质出版社,1981.10.
[26]袁振明,马羽宽,何泽云.声发射技术及应用[M].北京:机械工业出版社,1985.
[27]张洪亭,王明赞.测试技术[M].沈阳:东北大学出版社,2005.02.
[28]T.Ozaki,H.Tong.On the fitting of nonstationary autoregressive models in time series analysis[J].Proc.8~(th) Hawaii Int.Conf.System Science,224-226,1975.
[29]G.Kitagawa,HAkaike.A procedure for the modeling of non-stationary time series[J].Ann.Inst.Satist.Math.30,Part B,351-363,1978.
[30]张治强,冯夏庭,杨成祥等.论非线性位移时间序列进化神经网络建模的适应性研究[J].岩土力学,1999,20(4):19-24.
[31]Nelder I.A,Mead R.A Simplex method for function minimization[J].Computer Journal,vol.7:308-373,1965.
[32]Gendzwill D.J.,Prugger A.F.Algorithms for microearthquake locations[J].Proc.4~(th) Symp.On Acoustic Emissions and Microseismicity,Penn State Uninversity,College Park,Pennsylvania,1985.
[33]张薇,薛嘉庆.最优化方法[M].沈阳:东北大学出版社,2004.09.
[34]L.Geiger.Probability method for the determination of earthquake epicenters from the arrival time only[J].Bulletin of St.Louis University,1912,vol8(1):56-71.
[35]Mandelbrot B.B.The Fractal Geometry of Nature[M].San Francisco,W.H.Freeman and Co.,1982.
[36]Falconer K.J.Fractal Geometry:Mathematical Foundation and Application[M].Wiley,New York,1990.
[37]Falconer K.J.The Geometry of Fractal Sets[M].Cambridge University Press,1985.
[38]Barnsley M.Fractals Everywhere[M].Academic Press Inc.,1988.
[39]Xie Heping,Fractals in Rock Mechanics[M].A.A.Balkema Press,1993.
[40]谢和平,薛秀谦.分形应用中的数学基础与方法[M].科学出版社,1997.03.
[41]Mandelbrot B.B.Self-affine fractal sets,in Fractals in Physics[M].PietroneroL.& Tosatti E.,Elseveri Sci.Publ.B.V.,1986
[42]Edgar G.A.Measure,Topology and Fractal Geometry[M].Berlin,spring-Verlag,1990.
[43]Hurst H.E.Long-term storage capacity of reservoirs[J].Trans.Am.Soc.Civ.Eng.,1965,116,770-808
[44]谢和平.岩石、混凝土损伤力学[M].中国矿业大学出版社,1990.
[45]Lajtal E.Z.Brittle Fracture in compression[J].Int.J.Fracture,1974.10,525-536.
[46]Costin I.S.A microcrack model for the deformation and failure of brittle rock[J].J.Geophys,Res.,1983,88,9485-9492.
[47]Botsis J.Kunin B.On Self-similarity of crack layer[J].Int.J.Fracture,1987,35,51-56.
[48]Main I.G.A modified Griffith for the evolution of damage with a fractal distribution of crack lengths:application to seismic event[J].Geohpys.J.Int.,1991,107,353-362.
[49]谢和平,高峰.岩石损伤过程中的分形描述[M].岩石力学与工程学报,1991,10,55-67.
[50]Robertson M.C.,Sammis C.G.et al.Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation[J].J.Geophys.Res.,1995,100,B1:609-620.