In the past decades, many permeability models have been
proposed
to characterize the coal permeability evolution in the elastic state.
Considering that the coal near the mining working face is often in
the plastic or post-peak failure state, it is significant to characterize
the coal permeability evolution in the plastic and post-peak failure
stages for safe mining. In this study, two permeability models are
developed using a variable-order fractional derivative to characterize
the coal permeability evolution during the whole process of elastic,
plastic, and post-peak failure stages. The results indicate that both
models have the ability to better describe the coal permeability evolution
during the whole process in areas near the mining working face. In
addition, the physical and mechanical interpretation of the variable-order
function is given as an indicator of fracture development, indicating
the sensitivity of stress variation to coal fracture development.
Moreover, the relationships among the effective stress, damage variable,
and post-peak permeability of coal are discussed.