Characterization of multi-step creep behavior and fractional derivative modeling for a water-saturated coal

The long-term stability of coal pillars affected by cyclic dry-saturation state faces serious challenge in the normal operation of underground reservoirs in coal mines. The time-dependent deformation of coal is often controlled by the combined effects of mining disturbance, pressure- relief, dry and saturated cycles, etc. Tri-axial creep tests of coal samples were performed under stepped deviatoric stress paths including increasing axial pressure (AP) and decreasing confining pressure (CP). In addition, a fractional derivative creep model considering long-term strength is proposed to describe multi-step creep deformation. It was found that the saturation state has little effect on the peak deviatoric stress in the CP-unloading creep. In analyzing the creep strain, the tangent method can accurately distinguish transition boundary between the deceleration creep and the constant-velocity creep, and the statistical averaging method provides a large time scale for grasping the whole behavior of creep deformation. Finally, the long-term strengths of dry-saturated coal are obtained by the isochronous deviatoric stress–circumferential strain curve cluster. The proposed fractional derivative creep model is suitable for the CP-unloading creep test and can describe the multi-step creep deformation and the transient deformation in stepped stages.