# Design of an Anthracite Creep Model Based on Fractional Order Theory: Experiments and Simulations
## 1 Introduction  
Coal resources are the main energy source in China [1, 2]. The consumption of coal resources is increasing year by year, and the mining depth of coal resources is gradually shifting from shallow to deep with the consumption of the shallow resources [3, 4]. During deep mining in mines, most hard rocks exhibit the characteristics of soft rocks [5, 6]. Due to the influence of \"three highs and one disturbance\", strong dynamic pressure disturbances and soft fractures keep appearing in surrounding roadways [7, 8, 9, 10, 11]. The stability and safety of the roadway are challenged due to extrusion creep deformation [12, 13] due to the surrounding rocks of the roadway exhibiting creep behavior [14, 15, 16, 17]. In natural conditions, the creep behavior of the rock is subtle, but its rheological deformation constantly affects the stability of the roadway [18, 19, 20, 21, 22]. To study the rheological deformation characteristics of the coal rock mass, a large number of uniaxial and triaxial compression experiments have been used to determine the creep characteristics of the coal rock mass. For example, [PERSON] et al. conducted triaxial compression experiments on coal samples at different depths and revealed the rule that the internal fracture size of coal samples decreases with increasing depth [23]. [PERSON] et al. developed a damage model based on the theory of minimum energy consumption [24]. [PERSON] et al. obtained the relevant data from creep tests based on a hydraulic servo test system and calculated the relevant parameters in the creep process based on fractionalorder calculus fitting [25]. [PERSON] et al. studied the permeability change of clastic rocks in creep experiments and revealed the effect of surrounding pressure on the permeability of the material [26]. [PERSON] et al. revealed the effect of rock expansion and fracture on the creep process through creep experiments with cyclic loading and unloading [27]. According to the different creep properties of coal rock bodies, creep models of coal rock bodies under various geological conditions have been studied and classified. At present, creep models are classified as linear and nonlinear creep models. According to existing studies and applications, to describe the various stages of the creep process, the linear model was modified by incorporating rock fracture damage theory. For example, [PERSON] et al. modified the Nishihara model and the intrinsic equation to describe the accelerated creep phase of granite [28]. [PERSON] et al. developed the creep equation for water content based on the Burgers model [29]. [PERSON] et al. developed a modified Nishihara model by conducting shear creep experiments on mudstone [30][PERSON] Most of the intrinsic relationships of coal rock material show strong temporal properties, i.e., the intrinsic relationships of rock materials will change with time. The creep of the coal rock body, on the other hand, exhibits complex characteristics of nonlinear mechanics, and the linear model cannot express the nonlinear creep of the rock no matter what form the combination takes, i.e., the accelerated creep phase of the rock cannot be simulated, so the linear model has certain application limitations in expressing the creep phase of the coal rock body. Some researchers have recently introduced fractional order theory into the nonlinear model. For example, [PERSON] et al. combined the viscous unit of the Kelvin unit in the Nishihara model with the Abel damper (a linear component improved to a nonlinear component) to establish a constitutive equation [31]. [PERSON] et al. proposed a new nonlinear viscous unit in combination with the Nishihara model, which can better respond to the accelerated creep phase of soft rocks [32]. [PERSON] et al. established a quadratic creep model that can describe the creep of soft rocks based on fractional-order calculus theory and [PERSON]'s dampers, combined with the special function of H-Fox [33]. At this stage, some researchers have added damage to the study of creep models.