## 3 Results and Discussion
### Numerical Simulation of Stress-Relief Groove Utility Analysis
#### 3.1.2 Grooving of the Floor-Side Corner for Stress-Relief  
(i) Concentration of stress in the surrounding rock  
The stress-relief grooving analysis at the floor-side corner follows a similar approach to central grooving. With a groove width of 1 m and varying depth, stress concentration results are illustrated in Figure 12. Horizontal stress contours show three stress concentration zones 5 m below the floor before grooving. As depth increases, central stress concentration decreases while sidewall concentrations persist, shifting towards the far roadway. Vertical stress contours reveal a similar trend: initial stress concentration at the roof height shifts downward with increased groove depth, with stress concentrations below the floor spreading away. Post-grooving, asymmetry is observed, with more pronounced stress concentration on the ungrooved sidewall.  
Figure 13 shows the peak horizontal and vertical stress points and their distances. As groove depth increases, peak horizontal stress rises, with the vertical distance from the floor remaining nearly constant, and the horizontal distance from the roadway centerline increasing. Specifically, peak horizontal stress is 43.00 MPa without grooving and 46.21 MPa at 2 m depth, with a 1.65 m shift from the centerline. For vertical stress, the peak value rises with groove depth, showing a 29.28 MPa peak without grooving and 30.48 MPa at 2 m depth, with a 1.03 m shift from the centerline. These trends align with the central grooving results, with central grooving proving more effective in stress transfer compared to floor-side corner grooving.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Depth (m)** & **Width (m)** & **1** & **1.5** & **2** & **2.5** \\ \hline
**1** & 54.428 & 50.558 & 39.894 & 32.406 \\
**1.5** & 68.130 & 50.923 & 56.271 & 51.295 \\
**2** & 37.379 & 40.459 & 11.844 & 20.554 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Volume of plastic zone per meter (62.26 m\({}^{3}\) ungrooved).  
Figure 12: Stress-relief effect of floor-side corners grooving.  
2. Trends in perimeter surrounding rock displacement  
Tables 8 and 9 present the maximum displacements of the roadway floor and sidewalls. The results show that as groove depth and width increase, the maximum floor deformation decreases, with depth having a more pronounced effect. In contrast, the maximum sidewall displacement increases slightly with greater groove width and depth, reaching 0.394 m. The grooved side shows a 0.08 m increase compared to the ungrooved state. Unlike central grooving, floor-side corner grooving reduces control over sidewall rock. Overall, floor-side corner grooving is marginally less effective in controlling floor deformation and increases the exposed height of the coal rib, leading to greater sidewall deformation.  
configurations. At a groove depth of 2 m, plastic zone volumes ranged from 11 to 41 m\({}^{3}\), with the 2 m \(\times\) 2 m groove showing the lowest volume of 11.824 m\({}^{3}\). At a depth of 1.5 m, the plastic zone volume was the largest, though still reduced compared to the ungrooved state. The 1 m \(\times\) 1.5 m groove produced a larger volume than the ungrooved state.