硬岩矿柱失稳及时间相依性研究
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摘要
在房柱式开采中,随着采矿工作的向前推进,采场的稳定性问题变得突出,而矿柱是决定采场稳定状态的重要结构单元,对采空区起支撑作用,不但维护着采场项板及围岩的稳定性,而且稳定的矿柱对矿石回采率的提高有极大的潜在作用。目前国内外地下开采厚大矿体,多向高阶段、高分段、大型化、无轨化方向发展,使得采场的控项高度相应提高,矿柱高宽比相应增大,其横向的整体稳定性显著下降。此外,由于矿柱的几何形状不规则,而矿柱中岩体又含有各种缺陷,它们对矿柱的稳定性产生很大影响,降低了矿柱的承载能力。矿柱的失稳破坏通常是在亚临界裂纹扩展到一定程度后发生的,导致矿柱的失稳与岩石裂纹扩展的时间相关。针对上述问题,作者结合国家自然科学基金项目“超高硬岩矿柱地压显现及时间相依性研究”,对硬岩矿柱的失稳及时间相依性进行了深入系统的研究。本文主要研究内容如下:
在矿柱失稳的非线性分析方面,针对矿柱在不同开挖条件下的结构建立了相应的力学模型,基于能量原理及突变理论导出了相应的失稳充要力学条件判据、矿柱变形突跳量和能量释放量的表达式,为定量研究其失稳问题奠定了基础。讨论了外界扰动力的临界行为,探讨了临界状态下微小扰动诱发矿柱失稳的形成机理,揭示了矿柱失稳的本质。
考虑矿柱失稳的初始条件方面,针对具有初始几何缺陷的超高矿柱的稳定性问题建立了一个简化的力学模型,根据初始挠度的形状、岩石的应力-应变关系、应变-曲率关系及静力平衡关系对具有初始挠度的矿柱的弹性和弹塑性稳定性进行了探讨,分析了超高矿柱稳定性对初始几何缺陷的依从关系,确定了具有初始几何缺陷的超高矿柱的弹塑性失稳的极限载荷。以裂隙张量为基础,将岩体中的裂隙看作初始损伤,对含随机分布裂隙的矿柱岩体特性进行了分析,推求了裂隙岩体的等效变形模量和等效泊松比,并探讨了初始地质缺陷对矿柱稳定性的影响。
利用Instron1342型电液伺服材料试验机,采用双扭常位移松弛法对矿石、二辉橄榄岩、大理岩、花岗岩四种岩石的试件进行了亚临界
The stability of stope is more important with the mining progress in room-pillar mining. Pillar is a pivotal stope unit and it supports stope, so, it not only ensures stability of roof beam and wall rock, but also stability pillar increases the mining rate of ore body obviously. At present, underground mining is developing toward high stage, high subsection, large scale, trackless in the world, consequently, the height of controlling roof increases. The holistic steady behavior of pillar debases markedly with the ratio of height to width increasing. Furthermore, the geometrical shape of pillar is irregular, and rock mass contains various flaws, which influence on the stability of pillar obviously, and the load-carrying capacity decreases of consequently. Usually, the pillar instability occurs when subcritical crack growth reaches to some extent, which results in time dependence of pillar instability. As mentioned above, the author carried out the research deeply and systematically on instability and time dependence of pillar in hard rock, combining with the item "study on the behavior and time dependence of deformation and failure for ultra high pillars in hard rock mass" , supported by National Natural Science Foundation of China. The main content of the dissertation is as follows:Firstly, simplified mechanical models of pillar were established under different mining conditions and instabilities of the systems were discussed by means of potential energy principle and cusp catastrophe theory. The necessary-sufficient condition of instability and the jump value of displacement of pillar and the released energy expressions were derived, which laid foundation for quantifying of the pillar instability. The critical behavior and the forming mechanism of pillar instability were discussed by external disturbance under critical conditions according to nonlinear theory. The essence of pillar instability is revealed consequently.Secondly, a simplified mechanical model of ultra high pillar with initial geometrical imperfection was established and the stability of the system was discussed by means of initial flexibility function, the
stress-strain relation of rock, the strain-curvature relation and static balance at elastic stage and at elastic- plastic stage. The compliance relations between the stability of ultra high pillar and initial geometrical imperfections were discussed and limit loads of ultra high pillar with initial geometrical imperfections were obtained at elasticity- plasticity stage. On the basis of crack tensor, the behavior of pillar rock mass containing a random distribution cracks is discussed by regarding cracks as initial damage. The equivalent modulus and the equivalent Poisson's ratio were derived and the effect of initial geological flaws on the stability of pillar was discussed.Thirdly, subcritical crack growth of double torsion specimens made of ore, lherzolite, marble and granite was tested using Instronl342 type electro hydraulic servo test machine. The relations between the mode-I stress intensity factor Kj and the subcritical crack growth velocity V and the fracture toughness KIC were obtained by the double torsion constant displacement load relaxation method. The behavior of subcritical crack growth was analysed in different rocks. The testing results provide basis data for the study of time-dependency of pillar stability.Finally, based on testing results of subcritical crack growth, according to the relations of the mode-I stress intensity factor Ki versus the subcritical crack growth velocity V (Ki-V curve) and geometrical parameters of cracks, the time-dependency of pillar stability was discussed.In short, the research of this dissertation, which is based on the frontal of the subject, applying the newest mathematical and mechanical methods and advanced experiment means to study on instability and time dependence of pillar in hard rock, is of theoretical significance and engineering application values to the safe, economical, and reasonable mining of the underground mineral resources.
在矿柱失稳的非线性分析方面,针对矿柱在不同开挖条件下的结构建立了相应的力学模型,基于能量原理及突变理论导出了相应的失稳充要力学条件判据、矿柱变形突跳量和能量释放量的表达式,为定量研究其失稳问题奠定了基础。讨论了外界扰动力的临界行为,探讨了临界状态下微小扰动诱发矿柱失稳的形成机理,揭示了矿柱失稳的本质。
考虑矿柱失稳的初始条件方面,针对具有初始几何缺陷的超高矿柱的稳定性问题建立了一个简化的力学模型,根据初始挠度的形状、岩石的应力-应变关系、应变-曲率关系及静力平衡关系对具有初始挠度的矿柱的弹性和弹塑性稳定性进行了探讨,分析了超高矿柱稳定性对初始几何缺陷的依从关系,确定了具有初始几何缺陷的超高矿柱的弹塑性失稳的极限载荷。以裂隙张量为基础,将岩体中的裂隙看作初始损伤,对含随机分布裂隙的矿柱岩体特性进行了分析,推求了裂隙岩体的等效变形模量和等效泊松比,并探讨了初始地质缺陷对矿柱稳定性的影响。
利用Instron1342型电液伺服材料试验机,采用双扭常位移松弛法对矿石、二辉橄榄岩、大理岩、花岗岩四种岩石的试件进行了亚临界
The stability of stope is more important with the mining progress in room-pillar mining. Pillar is a pivotal stope unit and it supports stope, so, it not only ensures stability of roof beam and wall rock, but also stability pillar increases the mining rate of ore body obviously. At present, underground mining is developing toward high stage, high subsection, large scale, trackless in the world, consequently, the height of controlling roof increases. The holistic steady behavior of pillar debases markedly with the ratio of height to width increasing. Furthermore, the geometrical shape of pillar is irregular, and rock mass contains various flaws, which influence on the stability of pillar obviously, and the load-carrying capacity decreases of consequently. Usually, the pillar instability occurs when subcritical crack growth reaches to some extent, which results in time dependence of pillar instability. As mentioned above, the author carried out the research deeply and systematically on instability and time dependence of pillar in hard rock, combining with the item "study on the behavior and time dependence of deformation and failure for ultra high pillars in hard rock mass" , supported by National Natural Science Foundation of China. The main content of the dissertation is as follows:Firstly, simplified mechanical models of pillar were established under different mining conditions and instabilities of the systems were discussed by means of potential energy principle and cusp catastrophe theory. The necessary-sufficient condition of instability and the jump value of displacement of pillar and the released energy expressions were derived, which laid foundation for quantifying of the pillar instability. The critical behavior and the forming mechanism of pillar instability were discussed by external disturbance under critical conditions according to nonlinear theory. The essence of pillar instability is revealed consequently.Secondly, a simplified mechanical model of ultra high pillar with initial geometrical imperfection was established and the stability of the system was discussed by means of initial flexibility function, the
stress-strain relation of rock, the strain-curvature relation and static balance at elastic stage and at elastic- plastic stage. The compliance relations between the stability of ultra high pillar and initial geometrical imperfections were discussed and limit loads of ultra high pillar with initial geometrical imperfections were obtained at elasticity- plasticity stage. On the basis of crack tensor, the behavior of pillar rock mass containing a random distribution cracks is discussed by regarding cracks as initial damage. The equivalent modulus and the equivalent Poisson's ratio were derived and the effect of initial geological flaws on the stability of pillar was discussed.Thirdly, subcritical crack growth of double torsion specimens made of ore, lherzolite, marble and granite was tested using Instronl342 type electro hydraulic servo test machine. The relations between the mode-I stress intensity factor Kj and the subcritical crack growth velocity V and the fracture toughness KIC were obtained by the double torsion constant displacement load relaxation method. The behavior of subcritical crack growth was analysed in different rocks. The testing results provide basis data for the study of time-dependency of pillar stability.Finally, based on testing results of subcritical crack growth, according to the relations of the mode-I stress intensity factor Ki versus the subcritical crack growth velocity V (Ki-V curve) and geometrical parameters of cracks, the time-dependency of pillar stability was discussed.In short, the research of this dissertation, which is based on the frontal of the subject, applying the newest mathematical and mechanical methods and advanced experiment means to study on instability and time dependence of pillar in hard rock, is of theoretical significance and engineering application values to the safe, economical, and reasonable mining of the underground mineral resources.
引文
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