## 2 Ontological Modeling of Damage in Coal-Rock Combination
### Numerical Simulation of Coal-Rock Combination with Different Surrounding Pressures  
After loading the constitutive model, verify its calculation results and experimental results. The height and diameter of the rock and coal established by numerical simulation are both 50 mm, as shown in Figure 2. The loaded surrounding rock pressures are 5 MPa and 10 MPa, respectively, and the axial the loading velocity is \(1\times 10^{-7}\) mm/step. The parameters F0, and m are based on Table 1. The physical and mechanical parameters of the rock selected for the simulation test are consistent with the test, as shown in Table 2.  
Figure 1: Custom constitutive model FLAC3D running program. Figure 2: Conventional triaxial numerical calculation model and loading. The arrow in the figure represents the direction of stress action. In view of the space to insert a figure as an example, Figure 3 shows the stress distribution cloud and the stress-strain curve of the coal-rock combination when the surrounding pressure is 10 MPa, while Figure 4 shows the fitting results of the custom principal structure testing under different surrounding pressure conditions. As shown in Figure 3, it can be seen that the stress distribution of the coal-rock combination using the Mohr-Coulomb constitutive model is relatively uniform, while the stresses of the custom constitutive model clearly tend to decrease in subregions, and there are \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surrounding Rock** & **\(\mathbf{\xi}\)** & \
\begin{tabular}{c} **Micro-Element Intensity** \\ **Weibull Distribution** \\ **Parameters F\({}_{0}\)** \\ \end{tabular} &
\begin{tabular}{c} **Micro-Element Intensity** \\ **Weibull Distribution** \\ **Parameters m** \\ \end{tabular} & **Goodness of Fit R\({}^{2}\)** \\ \hline \multirow{4}{*}{5 MPa} & 0.33 & 14.7538 & 3.2466 & 0.944 \\  & 0.5 & 13.5508 & 5.9780 & 0.906 \\  & 0.67 & 14.7134 & 3.9261 & 0.946 \\  & 0.75 & 12.7565 & 4.9362 & 0.961 \\ \hline \multirow{4}{*}{10 MPa} & 0.33 & 21.9997 & 5.8555 & 0.901 \\  & 0.5 & 25.6579 & 3.8349 & 0.893 \\ \cline{1-1}  & 0.67 & 27.1918 & 4.5514 & 0.875 \\ \cline{1-1}  & 0.75 & 20.4382 & 3.8718 & 0.853 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated values of damage nonlinear model parameters. Figure 4: Fitting of the customization constitutive model and the Mohr-Coulomb and test curve with 10 MPa of surrounding rock pressure (experimental data cited from [PERSON] [38]). Figure 3: Deformation and stress-strain trend of the model under 10 MPa surrounding rock pressure. obvious low-stress regions in the coal body. This is because the stress in the custom constitutive model decays gradually with loading after the material reaches yield, which is also reflected in its stress and strain curves. It can be seen in Figure 4 that the coal-rock combination is kept in a linear elastic state initially with a constant stress-strain ratio when the Mohr-Coulomb constitutive simulation is used. The stress remains constant and the strain keeps increasing when the plastic state is reached, as the Mohr-Coulomb is an ideal elastic-plastic model that maintains ideal plastic flow characteristics after the peak stress is reached, which differs greatly from the actual stress-strain relationship of the rock. Moreover, the peak stresses and strains of the coal-rock combination calculated with the Mohr-Coulomb model were 17.98 MPa, 0.006 and 33.97 MPa, 0.012 for the two surrounding rock pressures, respectively; while the peak stresses and strains of the custom constitutive model were 15.82 MPa, 0.00507 and 28.73 MPa, 0.00895, respectively. The difference between the calculated results of the Mohr-Coulomb model and the experimental values is large, with a maximum difference of 13.5% in peak stress and 15.05% in peak strain, while the maximum differences between the corresponding peak stress and strain of the custom constitutive model are 4.3% and 3.7%.