# 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
### Characteristics of Loading Strength Change in Coal Mass  
Based on the simulation of the uniaxial compression test, the confining pressure was simulated by servo-loading the walls set on both sides of the model. The deviatoric stress  
Figure 5: Calculation of fissure degrees in different directions.  
Figure 6: Coal model sampling lines and description of fissure degree.  
(\(\Delta\sigma=\sigma_{1}-\sigma_{3}\)) versus the axial strain, compressive strength, and residual stress difference for the jointed coal mass at different confining pressures of 0.2 MPa, 0.5 MPa, 1.0 MPa, 2.0 MPa, 4.0 MPa, and 8.0 MPa are illustrated in Figure 8.  
As the confining pressure gradually increased from 0.2 MPa to 8 MPa, the peak value of the \(\Delta\sigma\) (\(\Delta\sigma_{\text{max}}\)) jointed coal mass under varying confining pressures gradually increased. The \(\Delta\sigma_{\text{max}}\) under different fissure degrees and confining pressures are summarized in Table 5. According to Figure 8, the \(\Delta\sigma\) with the confining pressure was plotted in Figure 9a. It was observed from the scatter plot distribution that the deviatoric stress increased linearly with the increasing confining pressure, and the \(R^{2}\) values of the fitted relationships were above 0.95 for all groups. When the fissure degree decreased from 33.04 m\({}^{-1}\) to 3.67 m\({}^{-1}\), the slopes were 1.87, 1.95, 2.19, 2.50, and 2.55, respectively. The results indicated that as the fissure degree decreased, the rate of change in the \(\Delta\sigma\) with the increasing confining pressure accelerated. The presence of internal joints weakened the reinforcing effect of the confining pressure on its load-bearing capacity. In addition, the \(\Delta\sigma\) at \(K_{Y}=8.26\) m\({}^{-1}\) and a confining pressure of 0 MPa was 17.01 MPa, while the error between it and the average value of 15.86 MPa during the uniaxial strength calibration of the coal mass was only 6.76%, which demonstrates that a linear fitting could accurately describe the relationship between the deviatoric stress and the confining pressure.  
Figure 8: Biaxial loading stress curve of models with different fissure degrees.  
The variations in \(\Delta\sigma\) with the fissure degree are plotted in Figure 9b. It was observed from the scatter plot distribution that the \(\Delta\sigma\) followed a multiplicative power relationship with the fissure degree. As the confining pressure increased from 0.5 MPa to 8.0 MPa, the corresponding power indices were \(-0.26\), \(-0.26\), \(-0.25\), \(-0.23\), and \(-0.22\), respectively (as shown in Table 6). As the confining pressure increased, the strength of the coal mass decreased under the same change in the fissure degree, indicating that the weakening effect of the joint was diminished under high confining pressures. The \(R^{2}\) values of the fitted relationships were above 0.95 for all groups, which confirmed that the multiplicative power fitting could well describe the relationship between the deviatoric stress and the fissure degree. This fitting equation could be applied to quickly estimate the peak strength of the coal mass under various joint distributions.