## 4 Discussion  
The numerical simulations allowed an optimal selection of the roof bolting design for headings driven at different depths in the rock mass in the conditions of the LGCB mines. For safety reasons, the simulations were based on an assumption that the bolted zone in the roof must be larger by at least 0.25 m than the maximum range of the yielded zone (yield from 50% to 100%). In the case of the headings driven at the depth of 1000 m b.g.l, the selection of 1.8 m long RM-18 grouted bolts in the 1.5 \(\times\) 1.5 m grid (bolt distance) was proven correct. However, in the case of headings driven at 1300 m b.g.l., the range of the bolting zone should be increased. The selected bolts were 2.6 m long RM-18 grouted bolts in the 1.5 \(\times\) 1.5 m grid (bolt distance). The analysis of the results of numerical simulations also confirmed that a change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. caused the range of the yielded rock mass in the walls to increase. In actual mining conditions, the stability of the walls may be thus compromised. Observations in the LGCB mines indicate that in such cases, the walls may be effectively reinforced with the use of bolts not shorter than 1.6 m and installed in the 1.5 m \(\times\) 1.5 m bolting grid (bolt spacing), with the bottom row of the bolts situated at a distance approximately 1.8 m from the floor. In justified cases, the walls may be reinforced with so-called deep bolts (longer than 2.6 m), e.g., cable bolts. A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. caused a limited increase in the vertical range and a significant increase in the horizontal range of the yielded rock mass in the floors. In situ observations in the LGCB mines indicate that in the case of deep headings (located more than 1000 m b.g.l), the floor is uplifted more frequently than in the case of headings located at smaller depths. This phenomenon is also influenced by the low values of strength and deformation parameters of sandstones present in the floors of the headings. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Excavation**} & \multicolumn{2}{c}{**Yield Range in the Floor [m]**} & \multicolumn{2}{c}{**Increase in Yield Range in the Floor**} \\ \cline{2-5}  & **Load Variant 1** & **Load Variant 2** & **[m]** & **[\%]** \\ \hline
1 & 2.54 & 2.92 & 0.38 & 14.96 \\
2 & 2.58 & 2.97 & 0.39 & 15.12 \\
3 & 2.53 & 3.13 & 0.60 & 23.72 \\
4 & 2.58 & 2.96 & 0.38 & 14.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Yielded rock mass range in the floors of the analysed excavations (yield and 100%). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Excavation**} & \multicolumn{2}{c}{**Horizontal Range of Yielded Rock**} & \multicolumn{2}{c}{**Increase in Horizontal Yield Range**} \\ \cline{2-5}  & **Mass in the Floor [m]** & **in the Floor** \\ \cline{2-5}  & **Load Variant 1** & **Load Variant 2** & **[m]** & **[\%]** \\ \hline
1 & 5.80 & 9.52 & 3.72 & 64.14 \\
2 & 5.80 & 10.25 & 4.45 & 76.72 \\
3 & 5.80 & 9.98 & 4.18 & 72.07 \\
4 & 5.80 & 9.71 & 3.91 & 67.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Horizontal range of yielded rock mass in the floors of the analysed excavations (yield between 50% and 100%). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Excavation**} & \multicolumn{2}{c}{**Yield Range in the Wall [m]**} & \multicolumn{2}{c}{**Increase in Yield Range in the Wall**} \\ \cline{2-5}  & **Load Variant 1** & **Load Variant 2** & **[m]** & **[\%]** \\ \hline
3 (right wall) & 2.78 & 3.24 & 0.46 & 16.55 \\
4 (left wall) & 3.02 & 3.34 & 0.32 & 10.60 \\
4 (right wall) & 2.73 & 3.25 & 0.52 & 19.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._In situ studies performed in the LGCB mines confirm that in the geological and mining conditions of the Polish copper ore mines, the stability of the heading is affected by its depth in the rock mass.