基于动力系统结构稳定性的共轭剪切破裂-地震复合模型
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摘要
地壳中岩体破坏、断层形成与地震诱发具有成因联系,其中"X"型共轭剪切破裂与地震发生关系密切。为此,基于动力系统结构稳定性理论和孔洞岩体蝶形破坏理论,构建了"X"型共轭剪切破裂-地震复合模型,推导了破裂尺寸计算公式,给出了地震释放能量的计算方法。用动力系统理论解释了破裂扩展尺寸与地震能量释放存在的定量对应关系,从理论上完整阐述"X"型、"V"型和"Y"型共轭破裂特征的生成及演化力学机理,推演出共轭剪切破裂扩展和伴随地震发生的重要物理力学现象及规律。研究结果表明:在高偏差应力场作用下的地下软弱异性体周围岩体满足摩尔-库仑剪切破坏条件发生破坏,形成蝶形破坏区,即花瓣形破坏区,随着蝶形破坏区的扩展,会形成以软弱异性体为中心的显性或隐性X型共轭剪切破裂;软弱异性体周围岩体强度特征变化,使得共轭破裂表现出"X","V","Y"型共轭特征;在一定地应力和围岩环境中,地壳软弱异性体及其周围岩体构成的非线性动力系统,对于地应力和地层强度的变化具有敏感依赖性,即共轭剪切破裂的扩展尺寸和地震释放的能量具有相互伴生的指数型变化特征,相同的应力扰动在不同的构造应力场作用下引发共轭剪切破裂一次性扩展的尺度不同,会引发不同级别的地震,存在着非敏感依赖区域向敏感依赖区转化的特征拐点。
Rock mass failure and fault formation in the earth crust are related to the genesis of induced seismicity,in which the X-typed conjugate shear fracture is closely related to zones which are frequently subjected to earthquakes.Based on the stability theory of dynamic system and butterfly failure theory about rock masses around holes,a X-shaped conjugate shear fracture-seismic composite model was established. The calculation formula of fracture size was derived,and the calculation method of seismic energy was presented.The authors used the dynamical system theory to explain a quantitative correspondence between the size of fracture expansion and the energy release of earthquake,and fully elaborated the formation and evolution mechanics of X-type,V-type and Y-type conjugate fractures.The important physical mechanics phenomena and laws associated with the conjugate shear fractures and earthquakes were deduced.The research result indicated that the failure of rock mass around the underground soft anisotropic body under the action of high deviation stress field was in accordance with the Mohr-Coulomb shear failure condition,and formed a butterfly-shaped failure zone which can also be called as the petal-shaped damage zone.With the expansion of the butterfly-shaped failure zone,the dominant or recessive X-type conjugate shear fracture centered on the soft anisotropic body was formed.The change of strength characteristics of the rock mass around the soft anisotropic body made the conjugate fracture exhibit X-type,V-type and Y-type characteristics.Under certain in-situ stress and surrounding rock environment,the non-linear dynamic system comprised of soft anisotropic bodies in the earth's crust and surrounding rock mass showed sensitivity to,and dependence on,the in situ stress and formation strength.The extended size of conjugate shear fracture and the energy released by the earthquake had mutual associated exponential variation characteristics.The same stress increment triggered different one-time extension scales of conjugate fractures under different tectonic stress fields to thus induce different magnitudes of earthquake,and there existed a characteristic inflection point from non-sensitive dependence region to sensitive dependence region.
Rock mass failure and fault formation in the earth crust are related to the genesis of induced seismicity,in which the X-typed conjugate shear fracture is closely related to zones which are frequently subjected to earthquakes.Based on the stability theory of dynamic system and butterfly failure theory about rock masses around holes,a X-shaped conjugate shear fracture-seismic composite model was established. The calculation formula of fracture size was derived,and the calculation method of seismic energy was presented.The authors used the dynamical system theory to explain a quantitative correspondence between the size of fracture expansion and the energy release of earthquake,and fully elaborated the formation and evolution mechanics of X-type,V-type and Y-type conjugate fractures.The important physical mechanics phenomena and laws associated with the conjugate shear fractures and earthquakes were deduced.The research result indicated that the failure of rock mass around the underground soft anisotropic body under the action of high deviation stress field was in accordance with the Mohr-Coulomb shear failure condition,and formed a butterfly-shaped failure zone which can also be called as the petal-shaped damage zone.With the expansion of the butterfly-shaped failure zone,the dominant or recessive X-type conjugate shear fracture centered on the soft anisotropic body was formed.The change of strength characteristics of the rock mass around the soft anisotropic body made the conjugate fracture exhibit X-type,V-type and Y-type characteristics.Under certain in-situ stress and surrounding rock environment,the non-linear dynamic system comprised of soft anisotropic bodies in the earth's crust and surrounding rock mass showed sensitivity to,and dependence on,the in situ stress and formation strength.The extended size of conjugate shear fracture and the energy released by the earthquake had mutual associated exponential variation characteristics.The same stress increment triggered different one-time extension scales of conjugate fractures under different tectonic stress fields to thus induce different magnitudes of earthquake,and there existed a characteristic inflection point from non-sensitive dependence region to sensitive dependence region.
引文
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[25]燕乃玲,李辉,申重阳.丽江地震前后重力场变化的有限矩形位错模型分析[J].地震学报,2003,25(2):172-181.YAN Nailing,LI Hui,SHEN Chongyang. Analyses on gravity variation before and after the Lijiang earthquake based on a finite rectangular dislocation model[J]. Acta Seismologica Sinica,2003,25(2):172-181.
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[29]马念杰,李季,赵志强.圆形巷道围岩偏应力场及塑性区分布规律研究[J].中国矿业大学学报,2015,44(2):206-213.MA Nianjie,LI Ji,ZHAO Zhiqiang. Distribution of the deviatoric stress field and plastic zone in circular roadway surrounding rock[J].Journal of China University of Mining and Technology,2015,44(2):206-213.
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[31]郭晓菲,马念杰,赵希栋,等.圆形巷道围岩塑性区的一般形态及其判定准则[J].煤炭学报,2016,41(8):1871-1877.GUO Xiaofei,MA Nianjie,ZHAO Xidong,et al. General shapes and criterion for surrounding rock mass plastic zone of round roadway[J].Journal of China Coal Society,2016,41(8):1871-1877.
[32]马念杰,郭晓菲,赵志强,等.均质圆形巷道蝶型冲击地压发生机理及其判定准则[J].煤炭学报,2016,41(11):2679-2688.MA Nianjie,GUO Xiaofei,ZHAO Zhiqiang,et al.Occurrence mechanisms and judging criterion on circular tunnel butterfly rock burst in homogeneous medium[J]. Journal of China Coal Society,2016,41(11),2679-2688.
[33]赵志强,马念杰,郭晓菲,等.煤层巷道蝶型冲击地压发生机理猜想[J].煤炭学报,2016,41(11):2689-2697.ZHAO Zhiqiang,MA Nianjie,GUO Xiaofei,et al. Mechanism conjecture of butterfly rock burst in coal seam roadway[J]. Journal of China Coal Society,2016,41(11):2689-2697.
[34]马念杰,赵希栋,赵志强,等.掘进巷道蝶型煤与瓦斯突出机理猜想[J].矿业科学学报,2017,40(4):137-149.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al. Conjecture about mechanism of butterfly-shape coal and gas outburst in excavation roadway[J]. Journal of Mining Science and Technology,2017,40(4):137-149.
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