# 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
### Figure Evolution of Coal Mass Under Different Confining Pressures  
The variation in the number of fissures in the jointed coal mass at confining pressures of 0.2 MPa, 0.5 MPa, 1.0 MPa, 2.0 MPa, 4.0 MPa, and 8.0 MPa is depicted in Figure 10. With the increase in the confining pressure, the total number of fissures under the same strain decreased significantly, and the proportion of matrix fissures increased significantly, which indicated that the increase in the confining pressure would reduce the development rate of  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fissure Degree** & **Fitting Formula with Confining Pressure** & \(R^{2}\) & \(\sigma_{3}\) **(MPa)** &
\begin{tabular}{c} **Fitting Formula with** \\ **Fissure Degree** \\ \end{tabular} & \(R^{2}\) \\ \hline
33.04 & \(y=55.72(x+1)^{-0.22}\) & 0.9810 & 0.5 & \(y=32.33(x+1)^{-0.26}\) & 0.9975 \\
14.68 & \(y=1.95x+14.68\) & 0.9570 & 1.0 & \(y=34.88(x+1)^{-0.26}\) & 0.9910 \\
8.26 & \(y=2.19x+17.01\) & 0.9835 & 2.0 & \(y=38.24(x+1)^{-0.25}\) & 0.9140 \\
5.28 & \(y=2.50x+18.22\) & 0.9707 & 4.0 & \(y=44.31(x+1)^{-0.23}\) & 0.9971 \\
3.67 & \(y=2.55x+20.28\) & 0.9840 & 8.0 & \(y=55.72(x+1)^{-0.22}\) & 0.9869 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Summary of fitting formulas for the peak value of deviatoric, fissure degree, and confining pressure.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fissure Degree** & \multicolumn{5}{c}{**The Peak Value of Deviatoric Stress (MPa)**} \\ \cline{2-5}
**(m\({}^{-1}\))** & \(\sigma_{3}\) **= 8.0 MPa** & \(\sigma_{3}\) **= 0.5 MPa** & \(\sigma_{3}\) **= 1.0 MPa** & \(\sigma_{3}\) **= 2.0 MPa** & \(\sigma_{3}\) **= 4.0 MPa** \\ \hline
33.04 & 12.78 & 13.92 & 16.12 & 19.63 & 26.12 \\
14.68 & 16.03 & 16.94 & 19.25 & 24.01 & 29.27 \\
8.26 & 17.88 & 19.68 & 22.21 & 26.57 & 33.84 \\
5.28 & 20.02 & 21.69 & 23.77 & 29.24 & 37.39 \\
3.67 & 21.61 & 23.22 & 26.64 & 30.95 & 40.08 \\ \hline \hline \end{tabular}  
fissues in the coal mass, and had a significant restriction effect on the failure of the joints. Taking the coal mass model with \(K_{Y}\) = 8.26 m\({}^{-1}\) as an example, the total number of fissures at 0.75% axial strain with a confining pressure of 0.5 MPa (3933) was much larger than that with a confining pressure of 8.0 MPa (1712). The total number of fissures at an axial strain of 1.5% with a confining pressure of 4.0 MPa (4641) was 1.53 times that with a confining pressure of 8.0 MPa (3035), suggesting that an increase in the confining pressure can inhibit the development of microscopic fissures in coal mass under the same deformation. In the peak bearing stage, the proportion of joint-failure-induced fissures under each confining pressure was 84.96%, 81.63%, 79.23%, 73.67%, and 67.18%, respectively, with a maximum decrease of 20.93%. The summary of the total number of fissures and the proportion of joint-failure-induced fissures is shown in Tables 7 and 8. The results indicated that, although joint-dominated microscopic fissure failure prevailed in the coal mass under a high confining pressure, the proportion of matrix fissures in the coal mass continued to increase as the confining pressure rose. Consequently, the failure mode shifted from joint failure to matrix failure.