# Design of an Anthracite Creep Model Based on Fractional Order Theory: Experiments and Simulations
## 3 Results and Discussion
### Simulation Verification  
To verify the correctness and rationality of the NEG model, a secondary development of the FLAC3D software was carried out based on the Visual Studio 2010 platform. Based on the experimental samples of anthracite, the relevant numerical model was established. The model was divided into 8556 nodes and 8640 cells, and the vertical uniform load was applied at the top of the model, the \(Z\)-directional constraint force was applied at the bottom, and the fixed annular stress was applied laterally to simulate the surrounding pressure. The parameters related to Table 2 are written into the command program. The vertical displacement at the top of the model was recorded and converted to axial strain. Figure 7 shows the results of the numerical simulation compared with the creep experiments. According to the experimental and simulation comparison curves, the creep test curves were in closer agreement with the numerical simulation curves at low loading stress levels as well as short creep time conditions. This is due to the fact that, in the first four stages before the accelerated creep curve is reached, the model selected a phase-applicable plastic-viscoplastic-viscoelastic structure, which is more reasonably described by the model for transient deformation and isokinetic deformation. In the pseudo-acceleration-deceleration creep phase of the model, the inflection point of the combined fractional-order creep model curve was more obvious compared with the experimental creep curves at loading strengths up to 6 MPa and 7 MPa because the nodular development in the test samples has a certain influence on the strain of the experimental samples under loading conditions and the nodular fractured rock cannot be considered as a whole. In the combined fractional-order creep model, by considering the degradation effect of the nodal development on the sample, i.e., introducing the modifying variables of the nodal development in the pseudo-acceleration phase of the model, i.e., the parameters applicable to the parameter \(\eta_{1}\) and the Gramma function, the nonlinear variation characteristics of more decay phases can be characterized by changing the different orders. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Load** & \(\sigma_{s1}\) & \(\sigma_{s2}\) & \(\sigma_{s3}\) & \(G_{1}\) & \(\lambda_{1}\) & \(\eta_{1}\) & \(G_{2}\) & \(\lambda_{2}\) \\
**(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** \\ \hline
4.0 & 0.4 & 2.6 & 3.6 & 2.1831 & 8.414 & 74.92 & 1.5672 & 7.312 \\
5.0 & 0.5 & 3.25 & 4.5 & 1.0351 & 11.9874 & 34.481 & 1.3394 & 10.7845 \\
6.0 & 0.6 & 3.9 & 5.4 & 0.7841 & 17.5865 & 151.0281 & 1.9244 & 15.8056 \\
7.0 & 0.7 & 4.55 & 6.3 & 0.7539 & 28.9005 & 6.9049 & 1.0902 & 26.0005 \\
8.0 & 0.8 & 5.2 & 7.2 & 0.9228 & 43.616 & 8.023 & 1.5583 & 58.86 \\ \hline  & \(\eta_{2}\) (GPa/h) & \(\eta_{3}\) (GPa/h) & \(\lambda_{3}\) & \(\eta_{4}\) & \(\lambda_{4}\) & \(\alpha\) & \(\beta\) & \(\mathrm{R}^{2}\) \\ \hline
4.0 & 406.39 & 203.41 & 5.6094 & & & 0.6889 & & 0.9375 \\
5.0 & 530.69 & 58.742 & 7.9916 & & & 0.3183 & & 0.9620 \\
6.0 & 477.56 & 23.3648 & 11.7123 & & & 0.3785 & & 0.9904 \\
7.0 & 40.06 & 16.29 & 19.267 & & & 0.7699 & & 0.9911 \\
8.0 & 129.336 & 10.7724 & 65.43 & 20.98 & 87.23 & 0.2659 & 0.4216 & 0.9930 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameter fitting results of the creep model. The test was conducted at 8 MPa, and the late creep stage of the experimental sample, i.e., the model creep, reached the accelerated creep stage, at which the creep test curve at the early accelerated creep stage was in better agreement with the numerical simulation experimental curve.