## 6 Engineering Application--Ventilating a Roadway in the \"Knurow\" Coal Mine  
The \"Knurow\" coal mine is located in the western part of the Upper Silesian Coal Basin in Poland. An elasto-plasto-fractured model of the rock mass was employed for the initial support design of a ventilating roadway situated near the \"Antioki\" ventilation shaft. This roadway is to be excavated at a depth of 474 m using the conventional \"drill and blast\" method. The roadway has a horseshoe shape with a maximum height of approximately 6.05 m and a width of approximately 6.09 m, corresponding to a circular geometry with a radius of 3.13 m (Figure 11). According to the geological survey, the roadway will be excavated in a thick layer of claystone characterized by an uniaxial compressive strength (UCS) of at least 21.98 MPa. Other geotechnical parameters of the rock mass, such as its cohesive strength, internal friction angle, and Young's modulus, were determined using the guidelines provided by the Polish Industrial standard BN-78/0434-07 [14]. The input parameters and basic calculation results of the Ground Reaction Curve (GRC), utilized in the initial design of the roadway support structure, are listed in Table 4.  
Figure 10: SCC curve coupled with GRC curve for the weak rock mass (class III). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & **Value** \\ \hline \multicolumn{4}{c}{Input Parameters} \\ \hline Excavation radius & \(r_{w}\) & m & 3.13 \\ In situ hydrostatic stress & \(p_{z}\) & MPa & 11.39 \\ Cohesive strength of the rock mass & \(c\) & MPa & 2.65 \\ Internal friction angle of the rock mass & \(\phi\) & \({}^{\circ}\) & 29.30 \\ Rock mass Young’s modulus & \(E\) & MPa & 3347.83 \\ Rock mass Poisson’s ratio & \(\
u\) & - & 0.24 \\ Critical longitudinal strain of the rock mass & \(\varepsilon_{ng}\) & - & 0.0054 \\ \hline \multicolumn{4}{c}{Results} \\ \hline Compressive strength of the rock mass within the elastic zone & \(R_{cg}\) & MPa & 9.05 \\ Compressive strength of the rock mass within the plastic zone & \(R^{\prime}_{cg}\) & MPa & 3.62 \\ Computational factor & \(\beta\) & - & 1.92 \\ Radial stress on the boundary between plastic and elastic zone & \(p_{g}\) & MPa & 3.504 \\ Radial stress on the boundary between fracture and plastic zone & \(p_{o}\) & MPa & 1.103 \\ Deformational pressure at the equilibrium state & \(p_{a_{q}}\) & MPa & 0.143 \\ Fracture zone radius at the equilibrium state & \(r_{a_{q}}\) & m & 9.09 \\ Plastic zone radius at the equilibrium state & \(r_{l_{q}}\) & m & 12.35 \\ Rock mass displacement at the equilibrium state & \(u\Big{(}p_{a_{q}}\Big{)}\) & m & 0.210 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input parameters for the calculation of the GRC curve for the ventilating roadway in the “Knuów” coal mine. Figure 11: Cross-section of the ventilating roadway in the “Knuów” coal mine. The support structure of the roadway under consideration consists of yielding steel arches made from V36 profiles, spaced 0.50 m apart. After reaching an equilibrium point between the rock mass and steel yielding support, additional steel arches shall be embedded in fiber-reinforced shotcrete (Figure 12). The input parameters and basic calculation results of SCC curve for the designed support structure are listed in Table 5.  
The SCC curve coupled with the GRC curve calculated for the geological conditions of the ventilation roadway in the \"Knurow\" coal mine is depicted in Figure 13.  
As a result of the application of the convergence-confinement method and the employment of the elasto-plasto-fractured rock mass model, the initial choice of the support scheme--consisting of yielding steel arches made from V36 profiles with a spacing of 0.50 m--was confirmed to be correct. The factors of safety for the roadway support (\(F_{sup}=5.39\)) and the rock mass (\(F_{srm}=1.78\)) indicate that the designed support structure can be successfully employed in a ventilation roadway under the given geological conditions.