逆冲断层地震主震的突变理论分析
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摘要
逆冲断层系统作准静态形变时的功、能量增量关系可以分解为关于体积应变能的功能增量关系和关于偏应力能的功能增量关系.采用突变理论方法对逆冲断层系统的偏应力功能量增量关系进行的分析表明:折迭突变模型展示的性状可对逆冲断层地震主震的发震条件、演化过程和若干震后特性作恰当描述.围岩的围压大,最大主应力大,逆冲潜断层面倾角小,围岩切向刚度与断层抗剪强度曲线软化段拐点处斜率的比值小,则震时围岩弹性能释放量大、震级高,断层破裂半错距大,围岩端面位移振幅也大.断层岩体破裂扩容和震时围岩体积应变能释放,增强了前述效应.
The relationship between work and energy increment of thrust fault system with quasi-static deformation can be decomposed into two parts,i.e.the relationship between work and energy increment of volume strain energy and that of deviation stress energy, which was analyzed by using method of catastrophe theory. The research indicates that the characteristics displayed by fold catastrophe model can appropriately describe the earthquake generation condition,the evolvement process of main shock of thrust fault earthquake and some important earthquake effects as well.The bigger the surrounding press of surrounding rock is,the bigger the maximum principal stress is. The smaller the incidences of the potential thrust fault surface are,the smaller the rate between the tangential stiffness of surrounding rock and the slope is,which is at inflexion point on the softened zone of fault shearing strength curve.Thus when earthquake occurrs,the larger the elastic energy releasing amount of surrounding rock is,i.e.the larger the intensity of earthquake is.The larger the half distance of fault dislocation is. The larger the displacement amplitude of surrounding rock end face is.Fracturing,expanding of the fault rock body and releasing of volume strain energy of surrounding rock while earthquake occurrs enhance the foregoing earthquake effects together.
The relationship between work and energy increment of thrust fault system with quasi-static deformation can be decomposed into two parts,i.e.the relationship between work and energy increment of volume strain energy and that of deviation stress energy, which was analyzed by using method of catastrophe theory. The research indicates that the characteristics displayed by fold catastrophe model can appropriately describe the earthquake generation condition,the evolvement process of main shock of thrust fault earthquake and some important earthquake effects as well.The bigger the surrounding press of surrounding rock is,the bigger the maximum principal stress is. The smaller the incidences of the potential thrust fault surface are,the smaller the rate between the tangential stiffness of surrounding rock and the slope is,which is at inflexion point on the softened zone of fault shearing strength curve.Thus when earthquake occurrs,the larger the elastic energy releasing amount of surrounding rock is,i.e.the larger the intensity of earthquake is.The larger the half distance of fault dislocation is. The larger the displacement amplitude of surrounding rock end face is.Fracturing,expanding of the fault rock body and releasing of volume strain energy of surrounding rock while earthquake occurrs enhance the foregoing earthquake effects together.
引文
[1]Jeger J C,Cook G W.Fundamentals of Rock Mechanics[M].London:Chapman and Hall Press,1979:466-470.
[2]Rice J R.New perspectives in crack and fault dynamics[C]//Aref H,Phillips J W.Mechanics for a New Millennium(Proceedings of the20th International Congress of Theoretical and Applied Mechanics,27Aug—2Sept2000).Chicago:Kluwer Academic Publishers,2001:1-23.
[3]殷有泉,郑顾团.断层地震的尖角型突变模型[J].地球物理学报,1988,31(6):657-664.(YIN You-quan,ZHENG Gu-tuan.A cusp type catastrophic model of fault earthquake[J].Acta Geophysica Sinica,1988,31(6):657-664.(in Chinese))
[4]杨修信,殷有泉,康仲远,刘光勋,王廷韫,陈沅俊,张彦山.压扭性断层地震的Cusp型突变分析[J].中国科学(B辑),1994,24(6):656-663.(YONG Xiu-xin,YIN You-quan,KANG Zhong-yuan,LIU Guang-xun,WANG Ting-yun,CHEN Yuan-jun,ZHANG Yan-shan.The cusp type catas-trophe analyses of compresso-shear fault earthquake[J].Science in China(Series B),1994,24(6):656-663.(in Chinese))
[5]潘岳,李爱武.走滑式断层地震的折迭突变模型[J].应用数学和力学,2010,31(3):324-336.(PAN Yue,LI Ai-wu.Fold catastrophe model of strike-slip fault earthquake[J].Applied Mathematics and Mechanics(English Edition),2010,31(3):324-336.(in Chinese))
[6]何宏林,孙昭民,王世元,王纪强,董绍鹏.汶川M s 8.0地震地表破裂带[J].地震地质,2008,30(2):359-362(HE Hong-lin,SUN Zhao-min,WANG Shi-yuan,WANG Ji-qiang,DONG Shao-peng.Rupture of the M s 8.0Wenchuan earthquakes[J].Seismology and Geology,2008,30(2):359-362.(in Chinese))
[7]Massimo C,Concetta N,Ekstrm G.Static stress changes and fault interaction during the1997Um-bria-Marche earthquake sequence[J].J Seismology,2000,4(4):501-506.
[8]Ben-zion Y.Dynamic rupture in recent models of earthquake faults[J].J Mech Phys Solids,2001,49(9):2209-2244.
[9]LIN Jian,Stein R S.Stress triggering in thrust and subduction earthquakes and stress interaction be-tween the southern San Andreas and nearby thrust and strike-slip faults[J].J Geophys Res,2004,109(B02303):1-19.
[10]Jaime O H,Diane I D,Russell R,Stress changes induced by earthquakes and secular stress accumula-tion in the Buller Region,south island,New Zealand(1929-2002)[J].Pure and Applied Geophysics,2005,162(2):291-310.
[11]卡恰诺夫L M.塑性理论基础[M].周承侗译.北京:人民教育出版社,1982:147-148.(Kacha-nov L M.Fundamentals of Plastic Theory[M].Translated by ZHOU Sheng-tong.Beijing:People’s Education Press,1982:147-148.(in Chinese)).
[12]Karcinovic D.Statistical aspects of the continuous damage theory[J].Int J Solids Structures,1982,18(3):551-562.
[13]凌复华.突变理论──历史、现状和展望[J].力学进展,1984,14(4):289-403.(LING Fu-hua.History,present and advances of the catastrophe theory[J].Advances in Mechanics,1984,14(4):289-403.(in Chinese))
[14]Cook N G W.The failure of rock[J].Int J Rock Mech Min Sci,1965,2(3):389-403.
[15]陈顒.地壳岩石的力学性能[M].北京:地震出版社,1988.(CHEN Yong.Mechanical Properties of Crustal Rock[M].Beijing:Earthquake Press,1988.(in Chinese))
[16]Stuart W D.Quasi-static earthquake mechanics[J].Reviews of Geophysics and Space Physics,1979,17(6):1115-1120.
[2]Rice J R.New perspectives in crack and fault dynamics[C]//Aref H,Phillips J W.Mechanics for a New Millennium(Proceedings of the20th International Congress of Theoretical and Applied Mechanics,27Aug—2Sept2000).Chicago:Kluwer Academic Publishers,2001:1-23.
[3]殷有泉,郑顾团.断层地震的尖角型突变模型[J].地球物理学报,1988,31(6):657-664.(YIN You-quan,ZHENG Gu-tuan.A cusp type catastrophic model of fault earthquake[J].Acta Geophysica Sinica,1988,31(6):657-664.(in Chinese))
[4]杨修信,殷有泉,康仲远,刘光勋,王廷韫,陈沅俊,张彦山.压扭性断层地震的Cusp型突变分析[J].中国科学(B辑),1994,24(6):656-663.(YONG Xiu-xin,YIN You-quan,KANG Zhong-yuan,LIU Guang-xun,WANG Ting-yun,CHEN Yuan-jun,ZHANG Yan-shan.The cusp type catas-trophe analyses of compresso-shear fault earthquake[J].Science in China(Series B),1994,24(6):656-663.(in Chinese))
[5]潘岳,李爱武.走滑式断层地震的折迭突变模型[J].应用数学和力学,2010,31(3):324-336.(PAN Yue,LI Ai-wu.Fold catastrophe model of strike-slip fault earthquake[J].Applied Mathematics and Mechanics(English Edition),2010,31(3):324-336.(in Chinese))
[6]何宏林,孙昭民,王世元,王纪强,董绍鹏.汶川M s 8.0地震地表破裂带[J].地震地质,2008,30(2):359-362(HE Hong-lin,SUN Zhao-min,WANG Shi-yuan,WANG Ji-qiang,DONG Shao-peng.Rupture of the M s 8.0Wenchuan earthquakes[J].Seismology and Geology,2008,30(2):359-362.(in Chinese))
[7]Massimo C,Concetta N,Ekstrm G.Static stress changes and fault interaction during the1997Um-bria-Marche earthquake sequence[J].J Seismology,2000,4(4):501-506.
[8]Ben-zion Y.Dynamic rupture in recent models of earthquake faults[J].J Mech Phys Solids,2001,49(9):2209-2244.
[9]LIN Jian,Stein R S.Stress triggering in thrust and subduction earthquakes and stress interaction be-tween the southern San Andreas and nearby thrust and strike-slip faults[J].J Geophys Res,2004,109(B02303):1-19.
[10]Jaime O H,Diane I D,Russell R,Stress changes induced by earthquakes and secular stress accumula-tion in the Buller Region,south island,New Zealand(1929-2002)[J].Pure and Applied Geophysics,2005,162(2):291-310.
[11]卡恰诺夫L M.塑性理论基础[M].周承侗译.北京:人民教育出版社,1982:147-148.(Kacha-nov L M.Fundamentals of Plastic Theory[M].Translated by ZHOU Sheng-tong.Beijing:People’s Education Press,1982:147-148.(in Chinese)).
[12]Karcinovic D.Statistical aspects of the continuous damage theory[J].Int J Solids Structures,1982,18(3):551-562.
[13]凌复华.突变理论──历史、现状和展望[J].力学进展,1984,14(4):289-403.(LING Fu-hua.History,present and advances of the catastrophe theory[J].Advances in Mechanics,1984,14(4):289-403.(in Chinese))
[14]Cook N G W.The failure of rock[J].Int J Rock Mech Min Sci,1965,2(3):389-403.
[15]陈顒.地壳岩石的力学性能[M].北京:地震出版社,1988.(CHEN Yong.Mechanical Properties of Crustal Rock[M].Beijing:Earthquake Press,1988.(in Chinese))
[16]Stuart W D.Quasi-static earthquake mechanics[J].Reviews of Geophysics and Space Physics,1979,17(6):1115-1120.
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