## 3 Materials and Methods
### Simulation Results
The distribution of vertical and horizontal displacements along the monitoring lines is shown in Figure 12. These graphs indicate that, within the goaf, across the fractured zone and caved zone, irregular vertical displacements are observed. The maximum vertical displacements occurred in the goaf of the number 817 longwall panel (Figure 12a). Above the ventilation roadway of the number 817 longwall, vertical displacements decreased. After that, they increased again in the goaf of the number 815 longwall. The maximum inflection of the vertical displacements curve was observed along monitoring line 2. Along monitoring line 3, the inflection of the vertical displacement curve decreased, reflecting a general stabilization trend. At the aquifer level (monitoring line 1), vertical displacements stabilized, and no inflection of the curve was observed. Above the goaf of the 817 longwall panel, horizontal displacements reached their maximum values (Figure 12b). Horizontal displacements represent tensile deformations, as they have a positive sign. The maximum horizontal displacement reaches 16 cm along  
Figure 12: Vertical (**a**) and horizontal (**b**) displacements along the monitoring lines: 1—monitoring line 1; 2—monitoring line 2; and 3—monitoring line 3.  
the monitoring line 2. Along the monitoring line 3, horizontal displacements decrease, and, at the aquifer level, they stabilize, aligning in magnitude with the horizontal displacements over the coal seam near the edge of the 817 longwall. Thus, the vertical and horizontal displacement analysis highlights two potentially hazardous zones:  
* The center of the goaf of the 817 longwall panel, where maximum vertical and horizontal displacements are observed;
* The edge of the 817 longwall panel, where significant horizontal deformations occur. However, the analysis also indicates that, at the aquifer level, vertical and horizontal deformations vary smoothly and without any abrupt changes. The stress distribution analysis along the monitoring lines is shown in Figure 13. At the conveyor roadway level, the vertical stresses in the rock mass are equal to the lithological ones (Figure 13a). To the right of the conveyor roadway (toward the seam), vertical stresses increase within the abutment pressure zone and stabilize at a distance of 150-200 m.  
Figure 13: Vertical (**a**) and horizontal (**b**) stresses along the monitoring lines: 1—monitoring line 1; 2—monitoring line 2; 3—monitoring line 3. The maximum vertical stress concentration factor was observed along monitoring line 2, with a peak stress value of 24.3 MPa. The maximum stress zone was shifted toward the coal seam. Vertical stresses at the aquifer level reached 18.6 MPa. The safety factor (SF) by stress at the aquifer level is  
\[\text{Safety Factor}(\text{Stress})=\frac{[\sigma]}{\sigma_{max}}=\frac{21.5}{18. 6}=1.15 \tag{4}\]  
where \(\sigma_{max}\)--Maximum stress, MPa; \([\sigma]\)--Uniaxial Compressive Strength (UCS) of rock mass, MPa. The safety factor 1.15, based on the stress parameter, indicates a conditionally stable state (SF = 1.1-1.3) of rock mass near the aquifer zone, according to Hubble [32]. In the goaf of the 817 longwall panel, a stress relief zone was observed, with a minimum stress of \(-10\) MPa. Stress stabilized in the goaf of the 815 longwall panel as a result of compaction. Horizontal stresses are maximal along monitoring line 3 (Figure 13b). In the goaf of the 817 longwall panel, the same stress variation pattern was observed as in the case of vertical stress distribution. However, at the aquifer level (monitoring line 1), horizontal stress fluctuations are insignificant, unlike the vertical stress fluctuations. From a risk assessment perspective, the most hazardous zone is in the surrounding rock of the conveyor roadway of the 817 longwall panel at the coal seam side, where the stress peak was observed.