煤层变形与瓦斯运移耦合系统动力学研究
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摘要
煤与瓦斯突出是煤矿安全生产的重大隐患,其突出机理是目前采矿学界研究的热点问题,同时也是一直没有解决的问题。研究煤层变形与瓦斯在煤层中运移之间的耦合作用、探索耦合运动计算方法以及分析系统的结构稳定性和运动稳定性,对于解释突出机理、预防和治理煤与瓦斯突出灾害具有重要的意义。
煤炭资源的开采破坏了煤层及其围岩的原始平衡,开采后煤层及其围岩的变形状态与瓦斯的运移形式发生急剧变化,并可能导致运动失稳或结构失稳。瓦斯在煤层中的运动(吸附/解吸、扩散、渗流)受到煤层变形状态的影响,反过来瓦斯含量、压力的变化引起煤层孔隙度、变形状态、位移、速度、加速度、应变率、应变和应力的变化,因此,煤层的变形运动与瓦斯的运移之间存在着复杂的耦合作用。
本文从时变边界系统动力学的角度,综合利用理论分析、试验和数值计算等手段研究煤层变形与瓦斯运移耦合系统的动力学行为,得到以下主要创新性结论:
(1)对低瓦斯矿、高瓦斯非突出矿和高瓦斯且突出矿的煤样进行的应力-应变全程的非Darcy流渗透特性试验,结果表明,低瓦斯矿煤样的渗透率在峰后随应变单调增加;高瓦斯非突出矿煤样在峰后的渗透率变化幅度很小;高瓦斯且突出矿煤样的渗透率在ε=1.4%处出现谷值、在ε=2.7%处剧增,其他点起伏不大;在相同应变下,低瓦斯矿煤样的渗透率大于高瓦斯非突出矿煤样的渗透率,高瓦斯非突出矿煤样的渗透率大于高瓦斯且突出矿煤样的渗透率;煤样的非Darcy流β因子和加速度系数随应变的变化趋势与渗透率相反;破碎煤样渗透试验结果表明,渗透率、非Darcy流β因子与孔隙度的关系可以用幂函数来拟合。
(2)在讨论了煤层的破坏形式和变形状态、剪切屈服和拉伸破坏后的流动法则及变形状态的转换条件、瓦斯压力对D-P准则和Lagrange准则材料常数的影响的基础上构建了煤层的本构关系。
(3)以煤层孔隙度和瓦斯压力为桥梁建立煤层变形运动与瓦斯在煤层中运移之间的耦合关系,构建了一种煤层变形与瓦斯运移耦合动力学模型,该模型考虑了煤层变形的三种变形状态(弹性变形、剪切屈服和拉伸破坏)和瓦斯的三种运移形式(吸附/解吸、扩散、渗流)。
(4)采用显式快速Lagrange算法构造了煤层变形与瓦斯运移耦合动力学响应的计算方法。其中,瓦斯压力、扩散速度和煤层孔隙度在节点和单元上都要定义。
(5)基于显式快速Lagrange算法,利用Fortran语言编制了煤层变形与瓦斯运移耦合动力学响应计算程序,以大兴矿、崔家沟矿和祁南矿煤层及瓦斯的力学性质为控制参量分别计算了三类煤层(低瓦斯煤层、高瓦斯非突出煤层和高瓦斯且突出煤层)开采后的动力学响应,给出了煤层变形状态、渗透率、非Darcy流β因子、加速度系数的曲面图和瓦斯涌出量的时间历程曲线,以及煤层变形状态的转换。
该论文有图71幅,表10个,参考文献133篇。
Coal and gas outburst is one of the serious hidden dangers in coal mining. The outburst mechanism is a popular issue in the mining field, and peoples have not made a thorough study about it. It is of great importance to study the interaction between coal seam deformation and gas migration in coal seam, to explore effective computational method of coal seam deformation and gas migration coupling system, and to analyze the structural stability and Lyapunov’s stability of the system.
The initial state of coal seam and its surrounding rock was disturbed by mining, and violent change in both the deformation state of coal seam and the motion state of gas migration follows. At the same time, Lyapunov’s instability or structural instability would occur. Gas migration (adsorption/desorption, diffusion and seepage) is effected by the deformation state of coal seam; and the change of porosity, deformation state, displacement, velocity, acceleration, strain and stress of coal seam were effected by the change of gas content and gas pressure. So the interaction between coal seam deformation and gas migration in coal seam is of extreme complication.
The behaviors of dynamic system were researched by using theory, experiments and numerical calculation from the point of view of Dynamics of Systems with Variable Boundaries (DSVB). The main innovative results are listed as follows
(1) Permeability parameters of coal samples in complete stress-strain process were obtained by experiments, those samples came from a low gas mine, a high gas mine and an outburst mine, respectively. The result shows that the permeability of coal sample from low gas mine monotonously increase with strain after failure. The permeability of coal sample from high gas mine does not fluctuate drastically after failure. The permeability of coal sample from outburst mine has a valley atε=1.4%, and leaps fromε=2.7%. The permeability of sample from low gas coal mine is larger than that of sample from high gas mine, and the later is higher than that of sample from outburst mine under a same strain. The non-Darcy-flowβfactor and acceleration coefficient change in a contrary manner to permeability.Permeability parameters of granular coal sampled from a low gas mine, a high gas mine and an outburst mine are obtained by test, respectively. The test results show that the permeability, non-Darcy-flowβfactor and acceleration coefficient can all be expressed by power function of porosity.
(2) The failure modes and deformation states of coal seam were discussed, flow rules after both shear yielding and tensile failure were studied, the conversion condition of deformation states were presented, and the effect of gas pressure on material constants in both D-P criterion and Lagrange criterion was considered. Based on all these, the constitutive relation of coal seam was constructed.
(3) The relationship between coal seam deformation and gas migration is connected by porosity and gas pressure. A dynamic system, coal seam deformation and gas migration coupling system, was modeled. In the establishment of dynamic model, three deformation state (elastic deformation, shear yielding, tensile failure) and three gas migration (adsorption/desorption, diffusion and seepage) were involved.
(4) A numerical method for calculation of the response of the dynamic system is constructed by Fast Explicit Finite Difference Method based on Lagrangian description. Gas pressure, diffusion velocity and porosity of coal seam need to be defined on both nodes and elements.
(5) A algorithm program for calculation of response of the dynamic system was programmed by Fortran. The mechanical properties of Daxing Coal Mine, Cuijiagou Coal Mine, and Qinan Coal Mine are used as control parameters to calculate the dynamic response of low gas coal seam, high gas coal seam and outburst coal seam, respectively. The deformation state of coal seam, permeability, non-Darcy-flowβfactor and acceleration coefficient are given by surface. The time history plot of gas emission was also given, and the state transition of deformation was obtained.
煤炭资源的开采破坏了煤层及其围岩的原始平衡,开采后煤层及其围岩的变形状态与瓦斯的运移形式发生急剧变化,并可能导致运动失稳或结构失稳。瓦斯在煤层中的运动(吸附/解吸、扩散、渗流)受到煤层变形状态的影响,反过来瓦斯含量、压力的变化引起煤层孔隙度、变形状态、位移、速度、加速度、应变率、应变和应力的变化,因此,煤层的变形运动与瓦斯的运移之间存在着复杂的耦合作用。
本文从时变边界系统动力学的角度,综合利用理论分析、试验和数值计算等手段研究煤层变形与瓦斯运移耦合系统的动力学行为,得到以下主要创新性结论:
(1)对低瓦斯矿、高瓦斯非突出矿和高瓦斯且突出矿的煤样进行的应力-应变全程的非Darcy流渗透特性试验,结果表明,低瓦斯矿煤样的渗透率在峰后随应变单调增加;高瓦斯非突出矿煤样在峰后的渗透率变化幅度很小;高瓦斯且突出矿煤样的渗透率在ε=1.4%处出现谷值、在ε=2.7%处剧增,其他点起伏不大;在相同应变下,低瓦斯矿煤样的渗透率大于高瓦斯非突出矿煤样的渗透率,高瓦斯非突出矿煤样的渗透率大于高瓦斯且突出矿煤样的渗透率;煤样的非Darcy流β因子和加速度系数随应变的变化趋势与渗透率相反;破碎煤样渗透试验结果表明,渗透率、非Darcy流β因子与孔隙度的关系可以用幂函数来拟合。
(2)在讨论了煤层的破坏形式和变形状态、剪切屈服和拉伸破坏后的流动法则及变形状态的转换条件、瓦斯压力对D-P准则和Lagrange准则材料常数的影响的基础上构建了煤层的本构关系。
(3)以煤层孔隙度和瓦斯压力为桥梁建立煤层变形运动与瓦斯在煤层中运移之间的耦合关系,构建了一种煤层变形与瓦斯运移耦合动力学模型,该模型考虑了煤层变形的三种变形状态(弹性变形、剪切屈服和拉伸破坏)和瓦斯的三种运移形式(吸附/解吸、扩散、渗流)。
(4)采用显式快速Lagrange算法构造了煤层变形与瓦斯运移耦合动力学响应的计算方法。其中,瓦斯压力、扩散速度和煤层孔隙度在节点和单元上都要定义。
(5)基于显式快速Lagrange算法,利用Fortran语言编制了煤层变形与瓦斯运移耦合动力学响应计算程序,以大兴矿、崔家沟矿和祁南矿煤层及瓦斯的力学性质为控制参量分别计算了三类煤层(低瓦斯煤层、高瓦斯非突出煤层和高瓦斯且突出煤层)开采后的动力学响应,给出了煤层变形状态、渗透率、非Darcy流β因子、加速度系数的曲面图和瓦斯涌出量的时间历程曲线,以及煤层变形状态的转换。
该论文有图71幅,表10个,参考文献133篇。
Coal and gas outburst is one of the serious hidden dangers in coal mining. The outburst mechanism is a popular issue in the mining field, and peoples have not made a thorough study about it. It is of great importance to study the interaction between coal seam deformation and gas migration in coal seam, to explore effective computational method of coal seam deformation and gas migration coupling system, and to analyze the structural stability and Lyapunov’s stability of the system.
The initial state of coal seam and its surrounding rock was disturbed by mining, and violent change in both the deformation state of coal seam and the motion state of gas migration follows. At the same time, Lyapunov’s instability or structural instability would occur. Gas migration (adsorption/desorption, diffusion and seepage) is effected by the deformation state of coal seam; and the change of porosity, deformation state, displacement, velocity, acceleration, strain and stress of coal seam were effected by the change of gas content and gas pressure. So the interaction between coal seam deformation and gas migration in coal seam is of extreme complication.
The behaviors of dynamic system were researched by using theory, experiments and numerical calculation from the point of view of Dynamics of Systems with Variable Boundaries (DSVB). The main innovative results are listed as follows
(1) Permeability parameters of coal samples in complete stress-strain process were obtained by experiments, those samples came from a low gas mine, a high gas mine and an outburst mine, respectively. The result shows that the permeability of coal sample from low gas mine monotonously increase with strain after failure. The permeability of coal sample from high gas mine does not fluctuate drastically after failure. The permeability of coal sample from outburst mine has a valley atε=1.4%, and leaps fromε=2.7%. The permeability of sample from low gas coal mine is larger than that of sample from high gas mine, and the later is higher than that of sample from outburst mine under a same strain. The non-Darcy-flowβfactor and acceleration coefficient change in a contrary manner to permeability.Permeability parameters of granular coal sampled from a low gas mine, a high gas mine and an outburst mine are obtained by test, respectively. The test results show that the permeability, non-Darcy-flowβfactor and acceleration coefficient can all be expressed by power function of porosity.
(2) The failure modes and deformation states of coal seam were discussed, flow rules after both shear yielding and tensile failure were studied, the conversion condition of deformation states were presented, and the effect of gas pressure on material constants in both D-P criterion and Lagrange criterion was considered. Based on all these, the constitutive relation of coal seam was constructed.
(3) The relationship between coal seam deformation and gas migration is connected by porosity and gas pressure. A dynamic system, coal seam deformation and gas migration coupling system, was modeled. In the establishment of dynamic model, three deformation state (elastic deformation, shear yielding, tensile failure) and three gas migration (adsorption/desorption, diffusion and seepage) were involved.
(4) A numerical method for calculation of the response of the dynamic system is constructed by Fast Explicit Finite Difference Method based on Lagrangian description. Gas pressure, diffusion velocity and porosity of coal seam need to be defined on both nodes and elements.
(5) A algorithm program for calculation of response of the dynamic system was programmed by Fortran. The mechanical properties of Daxing Coal Mine, Cuijiagou Coal Mine, and Qinan Coal Mine are used as control parameters to calculate the dynamic response of low gas coal seam, high gas coal seam and outburst coal seam, respectively. The deformation state of coal seam, permeability, non-Darcy-flowβfactor and acceleration coefficient are given by surface. The time history plot of gas emission was also given, and the state transition of deformation was obtained.
引文
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