## 5 Application of the Developed Approach
It is evident that with decreases in the mechanical parameters of the rock mass, there was an increase in rock mass displacement observed at consistent values of fictitious pressure. Regardless of the rock mass class under consideration, along with the reduction in fictitious pressure, the radius of the fracture and the plastic zones--and thereby the value of the displacement--tended to infinity, thereby indicating the need for support installation. This feature of the GRC curve based on the elasto-plasto-fractured model  
Figure 6: Comparison of GRC curves for different rock mass classes. distinguishes it from a typical elasto-plastic GRC curve. In the latter, there is always a theoretical equilibrium point where the fictitious pressure equals zero, while the radius of the plastic zone and the value of ground displacement reach their maximum value (in most cases, in practical applications, before such an equilibrium point is reached, excessive displacements may lead to detrimental loosening and ground failure). In the subsequent stage of the analysis, in order to determine the optimal moment for the installation of the support, longitudinal deformation profiles (LDP) were established for different rock mass classes. The determination of the LDP curve followed the algorithm outlined in [8]. Considering that for the rock mass model based on an elasto-plasto-fractured medium, the plastic zone radius and the value of the ground displacement consistently tended towards infinity, a maximum value of these parameters could not be unambiguously determined. Therefore, a plastic zone radius and the value of the ground displacement at the equilibrium point between the static and deformational pressures were adopted for the calculations. Although this assumption was simplified, further exploration into the solution of LDP for elasto-plasto-fractured media seems to be necessary. An exemplary LDP curve based on the solution given by [8] is illustrated in Figure 7.  
The extent of the plastic and fracture zones, as well as the magnitude of rock mass displacement, can be mitigated by the application of an appropriate support system. In Polish underground coal mines, the most prevalent support system for long-lasting roadways and chambers consists of yielding steel arches, sometimes combined with a thin layer of shotcrete. Since a large amount of support deformation is to be expected, it was assumed that the roadway support system should consist of yielding steel sets fitted with sliding joints. These sets are installed immediately behind the roadway face, ensuring safety for personnel working at the face. Figure 7: Exemplary LDP curve for a fair rock mass (class II). Support characteristics curves (SCC) for yielding steel sets, determined using the algorithm outlined in [39], consist of four parts:  
1. First part involves elastic deformation, where steel arches act as rigid elements. 2. Second part involves yielding, where overlapped segments of the steel sets start to slide and the arch section diminishes. 3. Third part once again involves elastic deformation, wherein the maximum yielding capacity of the steel arch is reached, and therefore, it acts again as a rigid element. 4. Fourth part involves plastic deformation, wherein the bearing capacity of the rigid steel support is reached, and therefore, a certain amount of plastic deformation occurs. The input parameters and calculation results for SCC curves are shown in Table 3. The resulting SCC curves, in conjunction with GRC curves, obtained for different mass classes are  
The graphical interpretation of the SCC and GRC curves along with the ground-support equilibrium point included in Figures 8-10 allows for the estimation of the deformational pressure applied to the roadway support (\(p_{asp}\)).