深部煤体采动应力下双曲函数型渗透率模型

Hyperbolic function-based permeability model of coal under mining stress at deep mine

深部资源开采中,采动应力下煤体渗透率演化规律成为煤炭开采理论研究的热点之一。通过对煤体常规三轴渗流实验和采动应力路径下渗流实验对比分析,发现深部含瓦斯煤体在采动应力路径下其渗透率-体积应变异于常规三轴渗透实验。煤体常规三轴实验主要以三向应力加载为路径,而煤体在不断采出过程中其应力路径主要表现为特定方向加载其他方向卸荷的过程,可凝练为加轴压卸围压的应力路径,而应力-应变分析的起始点为静水压力状态,这必然引起煤体力学物理性质异于三向加载条件的行为。在采动应力条件下的渗透率-体应变空间内,以煤体体应变扩容点为界,当体应变达到扩容点后,随着体应变从压缩变形转换为膨胀变形,渗透率呈现出降低、稳态、增加的过程。为了定量地描述深部煤体渗透率在采动破坏或流变失稳过程中先减小后增大的行为,基于在体积应变空间内真实渗透网络是所有可能渗透网络中最优演化形式的假设,建立以渗透率、体积应变为变量的泛函关系,从而得出由体积应变表示的渗透率表达式。考虑深部煤体流变过程,将分数阶微积分理论推导的煤体体积蠕变方程代入渗透率函数中,得出以轴向应变为自变量的渗透率表达式。根据已有的实验数据对渗透率模型进行验证,结果表明:基于最优渗透网络得出的渗透率模型能很好地描述煤体渗透率在破坏过程中的演化规律,同时也可拟合流变过程中渗透率的变化趋势。

In the exploitation of deep resources,the permeability evolution of coal under mining stress has become one of the fundamental research topics in coal mining theory.It is found that through the comparative analysis of two kinds of seepage tests under different stress paths the permeability evolution with volumetric strain under mining stress path is different from that of conventional triaxial seepage test in deep gas-infiltrated coal.To the contrast of conventional triaxial compression test,the stress path of coal in the process of continuous mining is mainly the unloading process of a specific direction and loading at other directions.It can be simplified as the stress path of unloading confining pressure meanwhile loading axial stress,thus making hydrostatic pressure state as the starting point of stress-strain analysis and inevitably resulting in the behavior of the mechanical and physical properties of coal body different from the loading conditions.In the permeability-volume strain space under mining stress,when the volume strain reaches the dilation point,the permeability shows a process of decreasing,steady-state and increasing with the volume strain transforming from compression deformation to expansion deformation.In order to quantitatively describe the process that the permeability first decreases and then increases in the process of mining failure or rheological instability,based on the hypothesis that real permeable network is the best evolution form of all possible permeable networks in volume strain space,the permeability is expressed by volumetric strain through building the functional relationship with permeability and volumetric strain as variables.Considering the volume rheological process of deep coal,the volumetric creep equation of coal derived from fractional calculus theory is substituted into the developed permeability equation,and the permeability function with axial strain as independent variable is obtained.It is verified that through the existing experimental data the permeability model based on the hypothesis of the optimal permeable network can well describe the permeability evolution of deep coal in the process of failure or creep.