## 5 Application of the Developed Approach  
In order to verify the algorithm featured in Section 4, a series of analyses were performed involving a typical circular roadway of radius \(r_{w}=3\) m excavated at a depth of 1000 m, where the in situ hydrostatic stress equaled \(p_{z}=25\) MPa. Three cases considering rock mass classes with different mechanical properties were investigated for comparative purposes:  
* class I--competent rock mass,
* class II--fair rock mass,
* class III--weak rock mass. Input parameters for different rock mass classes were selected based on Polish Industrial Standard BN-78/0434-07 [14], which provides guidelines for the crude approximation of basic rock mass parameters such as an internal friction angle, cohesive strength, Young modulus, Poisson's ratio and critical longitudinal strain. These approximations are derived from the uniaxial compressive strength (UCS) of an intact rock and the Rock Quality Designation (RQD) of the rock mass. Input parameters selected for different rock mass class parameters are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Symbol**} & \multirow{2}{*}{**Unit**} & \multicolumn{3}{c}{**Rock Mass Class**} \\ \cline{3-6}  & & & **I** & **II** & **III** \\ \hline Cohesive strength of the rock mass & \(c\) & MPa & 6.39 & 5.18 & 2.65 \\ Internal friction angle of the rock mass & \(\phi\) & 0 & 38.67 & 33.73 & 29.30 \\ Rock mass Young modulus & \(E\) & MPa & 7667 & 5409 & 3338 \\ Rock mass Poisson’s ratio & \(\
u\) & - & 0.20 & 0.20 & 0.20 \\ Critical longitudinal strain of the rock mass & \(\varepsilon_{ng}\) & - & 0.0046 & 0.0051 & 0.0054 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters for exemplary calculation of GRC curves for different rock mass classes. The GRC curves for different rock mass classes were calculated based on the elasto-plastic-fractured model of the rock mass and the procedure featured in Section 4. The calculation results of basic GRC curves parameters are presented in Table 2.  
The results of the GRC calculations based on the proposed elasto-plasto-fractured model were compared with the typical elasto-plastic solution for the displacement of a circular roadway. GRC curves obtained for both the elasto-plasto-fractured and elasto-plastic model for different rock mass classes are depicted on Figures 3-5. Figure 4: GRC curves for the fair rock mass (class II). Figure 5: GRC curves for the weak rock mass (class III). The analysis of Figures 3-5 highlights the importance of the proper selection of the rock mass model used in geotechnical calculations. The initial portions of the GRC curves for both the elasto-plasto-fractured model and the elasto-plastic model were identical. According to the elasto-plasto-fractured model, once the fictitious pressure reached the theoretical value of the radial stress at the boundary between the fracture and plastic zone \(p_{o}\) (which is dependent on the value of the critical longitudinal strain of the rock mass \(\varepsilon_{ng}\)), a fracture zone began to develop in the vicinity of the roadway. Since the rock mass within the fracture zone lacked cohesion (and thus compressive strength), a portion of the GRC curve associated with the fractured rock mass exhibited a rapid displacement increase. Along with the decrease in rock mass strength, a simultaneous increase was observed in both the displacement of the rock mass and the values of deformational pressure occurring at the equilibrium state between the static and deformational pressures. In practice, the roadway support has to be installed before reaching an equilibrium point--especially in the case of fair and weak rock mass. Otherwise, excess displacement may lead to the dissipation of rock mass confinement, thereby allowing detrimental loosening and ultimately ground failure. Figure 6 illustrates the comparison of GRC (ground reaction curve) plots derived from the elasto-plasto-fractured model for different rock mass classes.