# A Fractional-Order Creep Model of Water-Immersed Coal
## 2 Experimental Methods
### Results of Creep Deformation  
All the measured data of creep strain versus time is plotted in Figure 4. Each loading stage, as shown in the subfigure in Figure 4, experienced instantaneous creep deformation, as well as decelerating, steady, and accelerating creep at the last loading stage. As announced by [32], under the axial load, the coal sample experiences an instantaneous elastic strain, during which the internal pores of the coal are compacted, resulting in significant deformation. Subsequently, the sample enters the decelerating creep deformation, characterized by a convex creep curve, indicating an increase in strain with a decreasing creep rate as the internal pores continue to be compacted. Once the creep rate reaches a certain level, it remains constant, known as the steady creep stage, where creep strain exhibits a proportional relationship with time. Finally, the sample enters the accelerating creep stage, which occurs for a short period, and the creep strain increases approximately exponentially with time.  
Figure 4: Strain–time curves of experimental specimen.  
Figure 3: Facilities of creep experiment.  
As shown in Figure 4, a significant difference can be seen from the strain versus time curves of the coal samples with different immersion times. Under the same stress level, the longer the immersion time of the sample, the more severe the deformation. This indicates that the water immersion has a softening effect on the strength of the coal. In addition, it can be found that for the same experimental coal sample, when the horizontal stress rises, the deformation generated by the coal sample becomes more obvious and the creep stress changes greatly. This indicates that the increase in stress has a promoting effect on the creep of coal, which can accelerate the creep of coal. When the load is greater than the yield strength of coal and rock, the internal pores and cracks of the material will have a large range of penetration and the coal and rock will fail after the deformation reaches a certain value. This stage can be called the accelerated creep stage or plastic failure stage. Immersed samples D, C, and B enter the accelerated creep stage according to the length of the immersion time when the loading stress is 13 MPa, while the non-immersed sample A enters the accelerated creep stage when the loading stress is 15 MPa, indicating that the coal rock has a softening effect after immersion.  
To investigate the influence of immersion time on the creep behavior, the time-strain curve of the coal sample under different immersion durations is compared in Figure 4. The deformation of the soaked coal sample is significantly greater than that of the non-soaked coal sample and the rate enters the plastic failure stage first. Moreover, the longer the soaking time of the coal sample, the greater the creep strain generated. This indicates that immersion has a significant impact on the mechanical properties of the coal sample, leading to significant differences in the creep stages of the tested coal sample. As announced by [44], water has a softening effect on coal via mineral dissolution, Rhebinder-effect-induced cohesion deduction, chemical bond-breakage-induced crack propagation, etc. In order to further study the creep performance of immersed coal, the evolution of elasticity, creep strength, and creep rate have been analyzed in the following subsections.