## 2 Predictions of the Stability of Headings in the LGCB Mines
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Location** & **Rock Type** & \(\mathbf{c}\) & \(\mathbf{\varphi}\) & \(\mathbf{\sigma_{t}}\) & \(\mathbf{E_{rm}}\) \\  & & [MPa] & [\({}^{\circ}\)] & [MPa] & [MPa] \\ \hline \multirow{8}{*}{Roof} & Anhydrite I & 9.914 & 38.66 & 1.061 & 31,085.97 \\  & Anhydrite II & 8.801 & 38.66 & 0.942 & 28,022.81 \\  & Anhydrite III & 7.324 & 38.66 & 0.784 & 29,752.25 \\  & Anhydrite IV & 6.505 & 38.66 & 0.696 & 28,066.78 \\  & Dolomite I & 16.040 & 39.00 & 3.893 & 60,215.79 \\  & Dolomite II & 14.248 & 39.00 & 3.458 & 41,631.65 \\  & Dolomite III & 17.715 & 39.00 & 4.299 & 79,055.23 \\  & Dolomite IV & 17.020 & 39.00 & 4.131 & 72,232.54 \\  & Dolomite V & 15.113 & 39.00 & 3.668 & 57,266.63 \\  & Dolomite VI & 11.574 & 39.00 & 2.809 & 20,600.14 \\  & Dolomite VII & 17.229 & 39.00 & 4.182 & 74,301.36 \\  & Dolomite VIII & 10.803 & 39.00 & 2.622 & 34,465.62 \\ \hline \multirow{2}{*}{Walls} & Dolomite IX & 7.579 & 37.69 & 1.442 & 22,180.23 \\  & Dolomite shale & 6.447 & 30.41 & 1.327 & 18,250.37 \\  & Sandstone I & 3.589 & 40.54 & 0.180 & 10,701.33 \\ \hline Floor & Sandstone II & 2.520 & 39.06 & 0.093 & 7072.00 \\ \hline \hline \end{tabular} The symbols used in the above table are as follows: \(c\)—cohesion, \(\varphi\)—internal friction angle, \(\sigma_{t}\)—uniaxial tensile strength of the rock mass, \(E_{rm}\)—rock mass modulus of elasticity.  
\end{table} 
Table 3: Rock mass parameters determined with the RocLab 1.0 software—the Jm-15/H-173 borehole and the Jm-15-460 borehole. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Bar diameter [mm] & 18.2 \\ Bar length [m] & 1.8 \\ Bar material & steel \\ Young’s modulus [MPa] & 210,000.0 \\ Real load-capacity [kN] & 170.0 \\ Residual load-capacity [kN] & 17.0 \\ Pretension [kN] & 30.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the RM-18 grouted rockbolts [43]. Figure 1: Heading protected with full-length-grouted rockbolts in the 1.5 m \(\times\) 1.5 m bolting grid; legend: 1—domolite I–VIII, 2—domolite-shale-sandstone formations, 3—sandstone. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Location** & **Rock Type** & \(\mathbf{h}\) & \(\mathbf{E_{g}}\) & \(\mathbf{\
u}\) & \(\mathbf{\sigma_{t}}\) & \(\mathbf{\varphi}\) & \(\mathbf{c}\) & \(\delta\) & \(\mathbf{\varphi_{res}}\) & \(\mathbf{c_{res}}\) \\  & **[m]** & **[MPa]** & **[–]** & **[MPa]** & **[\({}^{\circ}\)]** & **[MPa]** & **[\({}^{\circ}\)]** & **[\({}^{\circ}\)]** & **[\({}^{\circ}\)]** & **[MPa]** \\ \hline \multirow{3}{*}{Roof} & Anhydrite I-III & 5.50 & 29,356.00 & 0.24 & 0.871 & 38.66 & 8.137 & 2.00 & 36.73 & 1.627 \\  & Anhydrite IV & 9.30 & 28,066.78 & 0.24 & 0.696 & 38.66 & 6.505 & 2.00 & 36.73 & 1.301 \\  & Dolomite I-VIII & 7.20 & 52,975.30 & 0.25 & 3.611 & 39.00 & 14.879 & 2.00 & 37.05 & 2.976 \\ \hline \multirow{3}{*}{Walls} & Dolomite—sandstone formations & \multirow{3}{*}{3.50} & \multirow{3}{*}{17,435.35} & \multirow{3}{*}{0.20} & \multirow{3}{*}{0.976} & \multirow{3}{*}{37.41} & \multirow{3}{*}{5.971} & \multirow{3}{*}{2.00} & \multirow{3}{*}{35.54} & \multirow{3}{*}{1.194} \\ \cline{1-1} \cline{5-12} Floor & Sandstone & & & & & & & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline \end{tabular}
\end{table} 
Table 4: Rock mass parameters adopted for the numerical modelling in the elastic-plastic medium with softening (the roof and the walls) and in the elastic-plastic medium (the floor), for the Coulomb–Mohr criterion. The stress values were identified from the GG-1 shaft profile as per PN-G-05016:1997 [44]. The calculations included the porosity and water-logging of the rock layers. Table 7 shows the calculated primary stress values for two heading depths: 1000 m b.g.l. and 1300 m b.g.l. Owing to the deposit depth, the hydrostatic state of stress was assumed in the numerical models:  
\[\sigma_{z}=\sigma_{x}=\sigma_{y}, \tag{5}\]  
where:  
\(\sigma_{z}\)--vertical stresses,  
\(\sigma_{x}\) and \(\sigma_{y}\)--horizontal stresses.