## 3 Modelling Results  
The numerical modelling of the stability of headings located at different depths in the rock mass (1000 m b.g.l. and 1300 m b.g.l.) in the geological and mining conditions assumed for the LGCB mines confirmed the results in a three-stage work: \"Regulations on the selection of support systems for special-purpose room excavations in copper ore mines--Stage 1, Stage 2 and Stage 3\" [45; 46; 47]. The numerical simulations also demonstrated that:  
* The maximum range of the yielded rock mass (from 50% to 100%) in the roof (Table 8) of the headings located at the depth of 1000 m b.g.l. (load variant 1) was from 1.35 m to 1.54 m (Figures 3 and 4). For comparison, the maximum range of the yielded rock mass (from 50% to 100%) in the roof of the headings located at the depth of 1300 m b.g.l. (load variant 2) was from 1.97 m to 2.33 m (Figures 5 and 6). A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has thus caused the range of the yielded rock mass in the heading roof to increase from 0.43 m (heading 4) to 0.98 m (heading 2). The maximum range of the yielded rock mass in the roofs of all headings was greater than the 1.8 m range of the bolted zone. This fact indicates that in the LGCB mines, the heading depth in the rock mass may have a decisive impact on its stability. Problems with heading stability may occur when the yielded rock zone in the roof is larger than the bolted zone. * The surface of the yielded rock area around a group of headings increases together with an increase in the excavation depth (increase in primary stress in the rock mass); this phenomenon negatively influences the stability of mining excavations and is strictly related to the stress and strain parameters of the rock layers surrounding the excavations. * The maximum range of the yielded rock mass (from 50% to 100%) in the walls (Table 9) of the headings located at the depth of 1000 m b.g.l. was from 2.69 m to 3.02 m (Figures 3 and 4). For comparison, the maximum range of the yielded rock mass (from 50% to 100%) in the walls of the headings located at the depth of 1300 m b.g.l. was from 3.23 m to 3.47 m (Figures 5 and 6). A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has thus caused the range of the yielded rock mass in the walls to increase from 0.32 m (heading 4, left wall) to 0.62 m (heading 1, left wall). * A more complex formation mechanism of yielded rock mass was observed in the floors of the excavations. A change in the heading depth from 1000 m b.g.l. to 1300 m b.g.l. has caused the vertical range of the yielded rock mass in the floors to increase only to a limited degree in comparison to the change in the horizontal range. The maximum vertical range of the yielded rock mass (from 50% to 100%) in the floors of the headings  
Figure 2: Numerical model of the group of headings generated in the RS2 software, the central part of the model and region of dense finite elements. Legend: 1—anhydrite II–IV, 2—anhydrite I, 3—calcareous dolomite I–VIII, 4—dolomite-shale-sandstone formations, 5—quartz sandstone. (Table 10) was from 2.53 m to 2.58 m (for the depth of 1000 m b.g.l.) and from 2.92 m to 3.13 m (for the depth of 1300 m b.g.l.) A change in the heading depth caused the vertical range of the yielded rock mass to increase from 0.38 m (heading 1 and heading 4) to 0.60 m (heading 3). * The horizontal ranges of the yielded rock mass in the floors changed more significantly due to the change in the heading depth (Table 11). The maximum horizontal range of the yielded rock mass (from 50% to 100%) in the floors of the headings located at the depth of 1000 m b.g.l. was 5.80 m and was equal to the width of the heading at the floor. In the headings located at the depth of 1300 m b.g.l., the horizontal range of the yielded rock mass in the floors increased significantly and was from 9.52 m to 10.25 m. A change in the heading depth has thus caused the horizontal range of the yielded rock mass to increase from 3.72 m (heading 1) to 4.45 m (heading 2).