# Numerical Modeling of Engineering-Scale Jointed Coal Mass and Confining Pressure Effect
## 4 Effect of Confining Pressure on Jointed Coal Mass Under Different Joint Distributions
### Failure Modes and Mechanism of Coal Mass Under Different Confining Pressures  
The strain corresponding to the end point of the linear elastic phase of the stress-strain curve for the coal mass increased significantly when the confining pressure gradually increased, which indicated that the elastic limit of the coal mass under a high confining pressure was greater. Taking the coal mass model with \(K_{Y}\) = 8.26 m\({}^{-1}\) as an example, when the stress difference reached the peak, the corresponding axial strains under each confining pressure were 0.86%, 0.94%, 0.94%, 1.02%, 1.24%, and 1.79%, which increased rapidly with the increase in the confining pressure. Meanwhile, due to the reinforcing effect of the confining pressure on the residual strength, the load-bearing capacity of the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fissure Degree (m\({}^{-1}\))**} & \multicolumn{6}{c}{**The Number of Fissures**} \\ \cline{2-6}  & \(\sigma_{3}\) = 0.5 MPa & \(\sigma_{3}\) = 1.0 MPa & \(\sigma_{3}\) = 2.0 MPa & \(\sigma_{3}\) = 4.0 MPa & \(\sigma_{3}\) = 8.0 MPa \\ \hline
33.04 & 3897 & 3881 & 5277 & 6880 & 8061 \\
14.68 & 2638 & 3580 & 3860 & 5088 & 6872 \\
8.26 & 2467 & 2548 & 2609 & 3232 & 4162 \\
5.28 & 1428 & 2670 & 1559 & 3227 & 3559 \\
3.67 & 1525 & 1483 & 1779 & 2233 & 4419 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of the number of fissures corresponding to the peak load under different fissure degrees and confining pressures. Figure 10: Evolution rules of fissures under different fissure degrees and confining pressures (for the proportion of joint fissures, the solid line with corresponding color represents joint fissures, while the dashed line represents matrix fissures). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fissure Degree (m\({}^{-1}\))**} & \multicolumn{6}{c}{**Proportion of Joint-Failure-Induced Fissures (\%)**} \\ \cline{2-6}  & \(\sigma_{3}\) = 0.5 MPa & \(\sigma_{3}\) = 1.0 MPa & \(\sigma_{3}\) = 2.0 MPa & \(\sigma_{3}\) = 4.0 MPa & \(\sigma_{3}\) = 8.0 MPa \\ \hline
33.04 & 92.33 & 91.06 & 86.98 & 83.14 & 73.06 \\
14.68 & 89.99 & 85.36 & 82.00 & 74.98 & 62.06 \\
8.26 & 84.96 & 81.63 & 79.23 & 73.67 & 67.18 \\
5.28 & 87.05 & 73.48 & 80.31 & 64.92 & 59.27 \\
3.67 & 76.92 & 74.11 & 67.29 & 61.85 & 44.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Proportion of joint fissures corresponding to peak load under different fissure degrees and confining pressures. coal mass would not drop abruptly when it reached the peak, and its stress reduction rate gradually decreased with the increase in the confining pressure, which indicated that the coal mass failure under the confining pressure was transformed from elastic-brittle failure to elastic-plastic failure. The post-peak failure modes of the coal mass under different fissure degrees and confining pressures are plotted in Figure 11. It was observed that the angles of the main fissure in the failed models under different fissure degrees were all above 70\({}^{\circ}\) for the smaller confining pressure (0.5 MPa). Vertical splitting failure fissures were occasionally observed in the model, and the local aperture of the fissures was obviously larger, and the macroscopic fissure development pattern was similar to that of the uniaxial compression test. The angle of the main fissure gradually decreased when the confining pressure increased to 0.5-1 MPa. The failure mode was gradually transformed from longitudinal splitting failure to oblique winging failure, and the main fissure planes failed along the joints were further reduced. As the confining pressure continued to increase, the longitudinal splitting failure mode basically disappeared. The model failure shifted to the shear-stress-dominated single-shear rupture plane mode, and the wing fissures were reduced, while the coal mass model with a higher fissure degree was less sensitive to the increase in the confining pressure.