## 2 The Project of Roadways Maintained behind the Longwall Face
### Numerical Models  
The numerical model was a rectangular shield with dimensions of 100 m \(\times\) 80 m in a plane strain. A Coulomb-Mohr elastic-plastic model was adopted for all layers. The model was built according to the geological profile, with rock bed properties shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Roadway**} & \multirow{2}{*}{**Rock Bed**} & \multirow{2}{*}{\begin{tabular}{c} **Unit Weight** \\ \(\gamma\) **[kN/m\({}^{3}\)]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Young** \\ **Modulus** \\ **E [GPa]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson** \\ **Ratio** \\ **v [-]** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **UCS** \\ **[MPa]** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Tensile** \\ **Strength** \\ **[MPa]** \\ \end{tabular} } \\ \hline \multirow{3}{*}{Bw-4} & shale & 26.42–26.61 & 7.88–9.52 & 0.21–0.22 & 25–35 & 1.6–2.58 \\ \cline{2-7}  & sandstone & 24.71 & 9.12 & 0.22 & 37.3 & 2.49 \\ \cline{2-7}  & coal & 12.62 & 1.77 & 0.30 & 20.9 & 0.33 \\ \hline \multirow{3}{*}{PW-1} & shale & 25.1–26.1 & 4.81–6.27 & 0.26 & 25.7–32.7 & 1.93–2.42 \\ \cline{2-7}  & mudstone & 26.3 & 6.73 & 0.22 & 36.3 & 2.83 \\ \cline{1-1} \cline{2-7}  & sandstone & 26.1 & 9.99 & 0.20 & 42.6 & 2.84 \\ \cline{1-1} \cline{2-7}  & coal & 12.2 & 2.10 & 0.30 & 7.2 & 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geomechanical rock properties. Figure 2: Rock mass displacement zones around the roadway: 1—collapse zone, 2—fracture zone, 3—continuous displacement zone. Structural beam elements of the \"liner\" type were used to model the support system. A contact plane was assumed between the support elements and the rock mass, with parameters corresponding to the mechanical (cement bond) lining parameters. Structural \"cable\" elements were used to model the rock bolt support system, with load capacities according to technical specifications. The Finite Difference Method (FDM) was applied to the calculations, and discretization was performed using FLAC 7.0 software. The computational grid was densified around the excavation to approximately 25 cm \(\times\) 20 cm. Stress states were analysed, ahead and behind the longwall face, and the results were presented as maps, illustrating the distribution of vertical stresses in the rock mass and the range of plastic zones. The analysis revealed that in Bw-4, the maximum values of vertical compressive stresses ahead of the longwall face occur in the coal sidewalls and reach a value of 45 MPa (Figure 3a). Additionally, areas of tensile stresses can be observed, particularly in the floor. The destressed zone in the roof extends to approximately 2 m and to approximately 3.5 m in the floor, but complete rock damage does not occur here. Figure 3b illustrates the extent of plastic zones (cracks) around Bw-4. Particular attention should be paid to indicators of plastic changes (interpreted here as cracking). Shear and volumetric changes are shown in red, while damage due to tension is in purple. High tensions occur only in the roadway's floor. The fracture range includes the seam and the overlying clay shales up to 1.5 m above the sidewall. For the next step, a goal was modelled behind the longwall face, and separated from Bw-4 by a wooden crib, taking into account the stress state ahead of the longwall face. A wooden crib filled with aggregate with external dimensions of 1.2 \(\times\) 1.2 m was designed at the sections of the steel arch support from the goaf side. It was assumed that the actual bearing capacity of this support would be no less than 8 MN. The results of the calculations showed that maximum values of vertical compressive stresses occur in the coal sidewall behind the steel arch support and reach 42 MPa (Figure 4a), which is slightly lower than ahead of the longwall face. Stresses in the area of the wooden crib reach 48 MPa. The range of the plastic zone is significantly more comprehensive than ahead of the longwall face.