冲击地压的非线性岩梁混沌动力学分析
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摘要
发生在许多煤矿井下开采中的冲击地压问题是岩石力学面对的长期悬而未决的最困难的难题之一。国内外学者对此进行了长期研究,取得了大量的成果。由于该问题的复杂性,目前对于冲击地压的发生机理和条件仍不是十分清楚,距离彻底解决冲击地压问题仍有相当的距离。本文利用混沌动力学的方法对顶板系统的失稳规律进行了定量分析,为冲击地压的研究提供新的思路和方法,为冲击地压的预测与防治提供一定的理论基础。本文的主要研究方法和成果如下：
(1)通过建立夹支、固支和悬臂梁体力学模型,并应用三次非线弹性本构关系近似模拟峰后软化效应,建立了模型的非线性控制方程。采用Galerkin法对控制方程进行离散,得到微分动力系统,利用Melnikov函数法求得了无扰动系统非稳定平衡态的条件,包围中心的闭周期轨道和扰动系统进入Smale马蹄混沌的条件,并计算得系统通过次谐分岔进入混沌状态；
(2)基于混沌理论求得了夹支梁、固支梁和悬臂梁型顶板煤层型或顶板型冲击地压发生的失稳判据及失稳的扰动条件,认为顶板型冲击地压的发生都具有随机性和初值敏感性的特点；
(3)顶板系统非稳定平衡态的条件就可以成为顶板煤层型或顶板型冲击地压发生的判据。与顶板破断的极限跨距做对比,建立了动静结合的判断顶板稳定性的双重判据；
(4)顶板稳定性主要受拉应力控制,通过对固支梁与悬臂梁判断顶板稳定性双重判据的分析发现顶板的冲击危险性与其抗拉强度密切相关,抗拉强度越小,其冲击危险性越小；
(5)冲击地压多发生在地质构造带,本文通过对轴向力的分析发现,当存在轴向力时,岩梁的失稳跨距明显减小,且轴向力越大,失稳跨距越小；
(6)认为应用强度理论计算的顶板破断的极限跨距失效的原因主要有两个：一是煤岩材料简化为线弹性模型,只考虑峰值强度,未考虑峰后的软化效应；二是计算中只考虑横向载荷下的纯弯曲,未考虑轴向力下的复合弯曲；
(7)根据失稳理论思想,利用Hamilton表述方法,求得了系统的势能函数,是对失稳理论的进一步认识和发展。因此应用混沌动力学方法研究冲击地压问题是可行的。
Rock burst is one of the most common and difficult hazard in mining engineering. Domestic and foreign experts have studied it for a long time, until now, the essential reasons of this hazard have not been thoroughly understood due to the complexity of the hazard. This paper quantitatively analysis instability criterion of the burst hazard in chaos dynamics theory, presents the new research thinking and method, and provides the theory foundation for rock bust prevention and cure. The research methods and achievements of this paper are as follows:
(1) The mechanical model of folder-type, clamped-clamped and cantilever rock beam was established to analyze the roof with disturbance. The cubic nonlinear elastic constitutive law was used to describe the strain-softening characteristics of rock. By using of Galerkin method, differential dynamic system was obtained and the condition of dynamic instability critical state and disturbance criterion for the instability were determined by Melnikov method, and calculated the system through sub-harmonic bifurcation into chaos;
(2) The mechanical instability criterion and disturbance criterion which used to judge the roof rock burst occurred were obtained by the chaos theory. This paper thought the roof rock beam has the characteristics of chaotic system, namely randomness and sensitivity to initial conditions;
(3) The condition estimated unstable equilibrium station of roof system could as the criterion of roof rock burst. The dual criterion is established for the stability control of roof with burst hazard through the comparison between instable span and limited span;
(4) Rock burst hazard for roof and tensile strength is closely related through the analysis of dual criterion, the smaller the tensile strength, the less the rock burst hazard;
(5) Rock burst occurred geological structure belt more, this paper analyzed the horizontal tectonic load, and the instability criterion is influenced distinctly by horizontal tectonic load, the larger horizontal tectonic load, the smaller the instable span;
(6) There were two reasons that the limit span calculated in strength theory was failure: first, coal simplified linear elastic material model, considering only the peak intensity, did not consider the post-peak softening effect; second calculation considered only the pure bending under transverse load, does not consider the composite bending under axial force;
(7) This paper, according to the instability theory, got the potential energy function of system through Hamilton method; obtained the mechanical condition and disturbance criterion which quantitatively judged the roof instability. This paper thought roof could be dynamic buckling when it failed to reach the strength and it is a further understands and development for instability theory.
(1)通过建立夹支、固支和悬臂梁体力学模型,并应用三次非线弹性本构关系近似模拟峰后软化效应,建立了模型的非线性控制方程。采用Galerkin法对控制方程进行离散,得到微分动力系统,利用Melnikov函数法求得了无扰动系统非稳定平衡态的条件,包围中心的闭周期轨道和扰动系统进入Smale马蹄混沌的条件,并计算得系统通过次谐分岔进入混沌状态；
(2)基于混沌理论求得了夹支梁、固支梁和悬臂梁型顶板煤层型或顶板型冲击地压发生的失稳判据及失稳的扰动条件,认为顶板型冲击地压的发生都具有随机性和初值敏感性的特点；
(3)顶板系统非稳定平衡态的条件就可以成为顶板煤层型或顶板型冲击地压发生的判据。与顶板破断的极限跨距做对比,建立了动静结合的判断顶板稳定性的双重判据；
(4)顶板稳定性主要受拉应力控制,通过对固支梁与悬臂梁判断顶板稳定性双重判据的分析发现顶板的冲击危险性与其抗拉强度密切相关,抗拉强度越小,其冲击危险性越小；
(5)冲击地压多发生在地质构造带,本文通过对轴向力的分析发现,当存在轴向力时,岩梁的失稳跨距明显减小,且轴向力越大,失稳跨距越小；
(6)认为应用强度理论计算的顶板破断的极限跨距失效的原因主要有两个：一是煤岩材料简化为线弹性模型,只考虑峰值强度,未考虑峰后的软化效应；二是计算中只考虑横向载荷下的纯弯曲,未考虑轴向力下的复合弯曲；
(7)根据失稳理论思想,利用Hamilton表述方法,求得了系统的势能函数,是对失稳理论的进一步认识和发展。因此应用混沌动力学方法研究冲击地压问题是可行的。
Rock burst is one of the most common and difficult hazard in mining engineering. Domestic and foreign experts have studied it for a long time, until now, the essential reasons of this hazard have not been thoroughly understood due to the complexity of the hazard. This paper quantitatively analysis instability criterion of the burst hazard in chaos dynamics theory, presents the new research thinking and method, and provides the theory foundation for rock bust prevention and cure. The research methods and achievements of this paper are as follows:
(1) The mechanical model of folder-type, clamped-clamped and cantilever rock beam was established to analyze the roof with disturbance. The cubic nonlinear elastic constitutive law was used to describe the strain-softening characteristics of rock. By using of Galerkin method, differential dynamic system was obtained and the condition of dynamic instability critical state and disturbance criterion for the instability were determined by Melnikov method, and calculated the system through sub-harmonic bifurcation into chaos;
(2) The mechanical instability criterion and disturbance criterion which used to judge the roof rock burst occurred were obtained by the chaos theory. This paper thought the roof rock beam has the characteristics of chaotic system, namely randomness and sensitivity to initial conditions;
(3) The condition estimated unstable equilibrium station of roof system could as the criterion of roof rock burst. The dual criterion is established for the stability control of roof with burst hazard through the comparison between instable span and limited span;
(4) Rock burst hazard for roof and tensile strength is closely related through the analysis of dual criterion, the smaller the tensile strength, the less the rock burst hazard;
(5) Rock burst occurred geological structure belt more, this paper analyzed the horizontal tectonic load, and the instability criterion is influenced distinctly by horizontal tectonic load, the larger horizontal tectonic load, the smaller the instable span;
(6) There were two reasons that the limit span calculated in strength theory was failure: first, coal simplified linear elastic material model, considering only the peak intensity, did not consider the post-peak softening effect; second calculation considered only the pure bending under transverse load, does not consider the composite bending under axial force;
(7) This paper, according to the instability theory, got the potential energy function of system through Hamilton method; obtained the mechanical condition and disturbance criterion which quantitatively judged the roof instability. This paper thought roof could be dynamic buckling when it failed to reach the strength and it is a further understands and development for instability theory.
引文
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