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

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 pres- sure 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 load- ing conditions. In the permeability-volume strain space under mining stress,when the volume strain reaches the dila- tion point,the permeability shows a process of decreasing,steady-state and increasing with the volume strain transfor- ming 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 equa- tion of coal derived from fractional calculus theory is substituted into the developed permeability equation,and the per- meability function with axial strain as independent variable is obtained. It is verified that through the existing experi- mental 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.