冲击地压粘滑失稳的混沌特性
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摘要
为探讨冲击地压发生的非线性特征,在分析断层型或构造型冲击地压粘滑失稳的原因和特点基础上,引入了模拟粘滑失稳的双滑块模型。理论分析表明,双滑块模型在对称情况下,完全相同的2个滑块可以造成空间上不相同的滑块运动,但其动力学行为只表现出周期性的特点;在非对称的情况下,滑块的粘滑失稳表现出复杂的混沌行为。通过适当考虑模型参数物理意义以及对参数值进行选取,该模型可用于解释断层型或构造型冲击地压粘滑失稳机理,描述其动力学行为复杂的非线性混沌特性。
Two types of rock bursts,strain rock bursts and fault-slip rock bursts,are defined briefly in terms of their instability mechanisms.Justification for stick-slip instability to account for a fault-slip rock burst is presented.A model we call spring-and-two-slider is introduced to simulate the behavior of stick slip that rock bursts exhibit.Theoretical analysis demonstrates that the stick-slip motions of two identical sliders are periodic,although they have their own spatial motions.Their behaviors,however,are characterized by chaos for different sliders.The results show that fault-slip rock bursts could be explained satisfactorily by stick-slip motion,the chaotic behavior of which implies the dynamic system of rock bursts is deterministic instead of stochastic.
Two types of rock bursts,strain rock bursts and fault-slip rock bursts,are defined briefly in terms of their instability mechanisms.Justification for stick-slip instability to account for a fault-slip rock burst is presented.A model we call spring-and-two-slider is introduced to simulate the behavior of stick slip that rock bursts exhibit.Theoretical analysis demonstrates that the stick-slip motions of two identical sliders are periodic,although they have their own spatial motions.Their behaviors,however,are characterized by chaos for different sliders.The results show that fault-slip rock bursts could be explained satisfactorily by stick-slip motion,the chaotic behavior of which implies the dynamic system of rock bursts is deterministic instead of stochastic.
引文
[1]谢和平.分形-岩石力学导轮[M].北京:科学出版社,1996.
[2]SLAWOMIR JERZY GIBOWICZ,ANDRZEI KIJKO.矿山地震学引论[M].修济刚,徐平,杨心平,译.北京:地震出版社,1998.
[3]郑捷.研究地震和岩石破裂现象的非线性科学方法[J].地球物理学进展,1992,7(1):20-35.ZHENG JIE.Nonlinear scientific methods applied torock rupture and earthquake phenomena[J].Progressin Geophysics,1992,7(1):20-35.
[4]TURCOTTE D L.Fractals in geology and geophysics[J].Pure and Appl Geophys,1989,131:1-2.
[5]KAGAN Y Y,KNOPOFF Z.Spatial distribution ofearthquakes:the two-point correlation function,Geophys[J].J R astr Soc,1980,62:303-320.
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[7]代高飞,尹光志.采场顶板来压的分形预报[J].矿山压力与顶板管理,2000(4):8-10.DAI GAO-FEI,YIN GUANG-ZHI.The fractalprediction of roof weighting around working face[J].Ground Pressure and Strata Control,2000(4):8-10.
[8]章梦涛.矿震的粘滑失稳理论[D].阜新:阜新矿业学院,1993.
[12]代高飞,尹光志,皮文丽,等.用滑块模型对冲击地压的研究[J].岩土力学,2004,25(8):1263-1266.DAI GAO-FEI,YIN GUANG-ZHI,PI WEN-LI,et al.Study on rockburst using stick slip model[J].Rock and Soil Mechanics,2004,25(8):1263-1266.
[13]齐庆新,毛德兵,王永秀.冲击地压的非线性非连续特征[J].岩土力学,2003,24(增):575-579.QI QING-XIN,MAO DE-BING,WANG YONG-XIU.A study of nonlinear and discontinuous characters ofrockburst[J].Rock and Soil Mechanics,2003,24(supplement):575-579.
[14]BRACE W F,BYERLEE J D.Stick-slip as amechanism for earthquake[J].Science,1966,153(3739):990-992.
[15]BRACE W F.Laboratory studies of stick-slip and theirapplication to earthquake[J].Tectono-physics,1972,14(3):189-200.
[16]HUANG J,TURCOTTE D L.Evidence for chaoticfault interaction in the seismicity of the San Andreasfault and Nakai trough[J].Nature,1990,348:234-6.
[17]TURCOTTE D L.分形与混沌—在地质学和地球物理学中的应用[M].陈顒,郑捷,季颖,译.北京:地震出版社,1993.
[18]TAKENS F.Detecting strange attractors in fluidturbulence[J].Lecture Notes in Mathematics,1981,366-381.
[19]代高飞.岩石非线性动力学特征及冲击地压的研究[D].[博士学位论文].重庆:重庆大学,2002.
[2]SLAWOMIR JERZY GIBOWICZ,ANDRZEI KIJKO.矿山地震学引论[M].修济刚,徐平,杨心平,译.北京:地震出版社,1998.
[3]郑捷.研究地震和岩石破裂现象的非线性科学方法[J].地球物理学进展,1992,7(1):20-35.ZHENG JIE.Nonlinear scientific methods applied torock rupture and earthquake phenomena[J].Progressin Geophysics,1992,7(1):20-35.
[4]TURCOTTE D L.Fractals in geology and geophysics[J].Pure and Appl Geophys,1989,131:1-2.
[5]KAGAN Y Y,KNOPOFF Z.Spatial distribution ofearthquakes:the two-point correlation function,Geophys[J].J R astr Soc,1980,62:303-320.
[6]尹光志,鲜学福,代高飞.岩石非线性动力学理论及其应用[M].重庆:重庆大学出版社,2004.
[7]代高飞,尹光志.采场顶板来压的分形预报[J].矿山压力与顶板管理,2000(4):8-10.DAI GAO-FEI,YIN GUANG-ZHI.The fractalprediction of roof weighting around working face[J].Ground Pressure and Strata Control,2000(4):8-10.
[8]章梦涛.矿震的粘滑失稳理论[D].阜新:阜新矿业学院,1993.
[12]代高飞,尹光志,皮文丽,等.用滑块模型对冲击地压的研究[J].岩土力学,2004,25(8):1263-1266.DAI GAO-FEI,YIN GUANG-ZHI,PI WEN-LI,et al.Study on rockburst using stick slip model[J].Rock and Soil Mechanics,2004,25(8):1263-1266.
[13]齐庆新,毛德兵,王永秀.冲击地压的非线性非连续特征[J].岩土力学,2003,24(增):575-579.QI QING-XIN,MAO DE-BING,WANG YONG-XIU.A study of nonlinear and discontinuous characters ofrockburst[J].Rock and Soil Mechanics,2003,24(supplement):575-579.
[14]BRACE W F,BYERLEE J D.Stick-slip as amechanism for earthquake[J].Science,1966,153(3739):990-992.
[15]BRACE W F.Laboratory studies of stick-slip and theirapplication to earthquake[J].Tectono-physics,1972,14(3):189-200.
[16]HUANG J,TURCOTTE D L.Evidence for chaoticfault interaction in the seismicity of the San Andreasfault and Nakai trough[J].Nature,1990,348:234-6.
[17]TURCOTTE D L.分形与混沌—在地质学和地球物理学中的应用[M].陈顒,郑捷,季颖,译.北京:地震出版社,1993.
[18]TAKENS F.Detecting strange attractors in fluidturbulence[J].Lecture Notes in Mathematics,1981,366-381.
[19]代高飞.岩石非线性动力学特征及冲击地压的研究[D].[博士学位论文].重庆:重庆大学,2002.
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