Abstract: In the unloading process of mined coal seam, it is damaged due to the continuous expansion of the original and new fractures, resulting in a sharp increase of permeability.The application scope of the classical stress-permeability model for coal reservoirs is limited to the elastic stage, which can not reflect the change law of the post-peak permeability.With the help of fractional derivative, which has unique advantages in describing nonlinear mechanical behavior, a two-parameter fractional derivative permeability model suitable for unloading fractured coal was used to describe the permeability variation characteristics of the whole process of unloading fractured coal.If the fractional derivative order is equal to zero, the established fractional derivative permeability model will degenerate into the S-D model, illustrating that the S-D model is a special case of the fractional derivative permeability model.If the fractional derivative order is equal to one, it will become a power function of the S-D model, characterizing the strongly nonlinear variation of the post-peak permeability.This new model extends the applicability of the classical S-D permeability model to the post-peak stage.However, the physical significance of the two-sparameter fractional permeability model parameters is not quite clear.Therefore, according to the improved Mazars damage criterion, the evolution of the damage variable is calculated, which helps us rebuild the relationship between the two parameters in the fractional derivative permeability model.Then the fractional permeability model with a damage parameter only is obtained.As a result, the static parameters in the model were modified to dynamic parameters, which is in line with the fact that the cleat compression coefficient changed constantly during the process of damage expansion.It makes up for the defect that the static parameters introduced in the existing stress-spermeability models are irrelevant to the damage variable.Thus, the physical background of the fractional derivative permeability model is relatively clear and this model can be more conveniently applied to numerical simulation and engineering practice.Then the fractional-order permeability model is applied to the numerical simulation of gas seepage law in backfill mining coal body, and the gas seepage law of backfill mining coal body is obtained.When the elastic foundation coefficient of the backfill body is increased, the risk of a gas outburst of this layer of coal will be intensified, and the gas concentration of the lower layer of coal floods into the upper seam will be reduced.Therefore, after the implementation of the backfilling method, there will be two sides of interest, especially for the gas outburst mine, it is necessary to strengthen the assessment of gas outburst risk before backfilling.