# Research on Mechanical Properties and Damage Constitutive Model of Water-Bearing Coal
## 6 Conclusions  
The main conclusions are summarized as follows:  
* The full stress-strain curve of coal under uniaxial compression has a nearly horizontal step before the elastic stage, which is described as the pore compaction stage in this article. The interval length of this stage is positively correlated with the water content, and this stage will only emerge with the stress-strain curve of water-bearing coal with high porosity and permeability. * With increasing water content, the interval between the fracture compaction stage and the coal sample pore compaction stage increases, the elastic deformation stage interval decreases, the plastic failure stage is more obvious, and the multistage stress drop platform appears in the post-peak failure stage. * The loading rate does not change the type of the fitting function between the mechanical parameters (uniaxial compression strength, Young's modulus, and peak strain) \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Index**} & \multicolumn{3}{c}{\(\omega=0\%\)} & \multicolumn{3}{c}{\(\omega=3.31\%\)} & \multicolumn{3}{c}{\(\omega=7.06\%\)} & \multicolumn{3}{c}{\(\omega=10.34\%\)} & \multicolumn{3}{c}{\(\omega=13.14\%\)} \\  & \multicolumn{1}{c}{**The Authors’**} & \multicolumn{1}{c}{**The Comparison**} & \multicolumn{1}{c}{**The Authors’**} & \multicolumn{1}{c}{**The Comparison**} & \multicolumn{1}{c}{**The Authors’**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The The**} \\  & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** \\ \hline MAE & 0.282 & 0.761 & 0.834 & 0.949 & 0.231 & 0.556 & 0.688 & 0.496 & 0.345 & 0.792 \\ MSE & 0.563 & 1.840 & 4.838 & 1.949 & 0.187 & 1.067 & 1.450 & 0.538 & 1.229 & 1.203 \\ RMSE & 0.751 & 1.357 & 2.200 & 1.396 & 0.432 & 1.033 & 1.204 & 0.733 & 1.108 & 1.097 \\ R\({}^{2}\) & 0.89 & 0.64 & 0.73 & 0.89 & 0.98 & 0.89 & 0.73 & 0.90 & 0.76 & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The fitting effect evaluation index values of the two models based on the experimental data in test group 3. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Index**} & \multicolumn{3}{c}{\(\omega=0\%\)} & \multicolumn{3}{c}{\(\omega=3.31\%\)} & \multicolumn{3}{c}{\(\omega=7.06\%\)} & \multicolumn{3}{c}{\(\omega=10.34\%\)} & \multicolumn{3}{c}{\(\omega=13.14\%\)} \\  & \multicolumn{1}{c}{**The The Authors’**} & \multicolumn{1}{c}{**The Comparison**} & \multicolumn{1}{c}{**The The Authors’**} & \multicolumn{1}{c}{**The Comparison**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The The**} & \multicolumn{1}{c}{**The The**} \\  & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** & **Model** \\ \hline MAE & 0.120 & 0.620 & 0.876 & 0.639 & 0.727 & 0.756 & 0.296 & 0.588 & 0.311 & 0.374 \\ MSE & 0.058 & 0.739 & 2.827 & 1.443 & 2.650 & 0.881 & 0.365 & 0.590 & 0.225 & 0.299 \\ RMSE & 0.240 & 0.860 & 1.681 & 1.201 & 1.628 & 0.939 & 0.604 & 0.768 & 0.475 & 0.547 \\ R\({}^{2}\) & 0.99 & 0.86 & 0.77 & 0.88 & 0.61 & 0.87 & 0.90 & 0.84 & 0.93 & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The fitting effect evaluation index values of the two models based on the experimental data in test group 4.  
of coal samples and their moisture content. The mechanical parameters of the coal samples in each parallel test group can be fitted as the same function as their moisture content, and all have good fitting results. * The three-stage damage constitutive model of water-bearing coal is derived, and the statistical indicators (MAE, MSE, RMSE, and R\({}^{2}\)) are introduced to scientifically evaluate the fitting effect of the model. This model improves the shortcomings of the traditional continuous fitting curve and the two-stage fitting curve.