## 7 Conclusions  
Based on the conducted study, the following conclusions can be inferred:  
(1) Polish National and Industrial Standards introduced the deformational pressure model for calculating loads acting on the support systems of underground excavations located at significant depths. These Standards distinguish between the softening elasto-plastic and elasto-plasto-fractured models. The choice of the appropriate rock mass model is contingent upon the value of the critical longitudinal strain of the rock mass, which marks the point at which the rock mass transitions from a plastic to a fractured medium. Since Equation (4), provided by the National Standards to calculate the value of the critical longitudinal strain of the rock mass, is not supported by any empirical studies, further investigation on this topic may be necessary. (2) The three-phase rock mass model outlined in the Polish National and Industrial Standards is based on the assumption that under certain conditions, a rock mass may act as an elasto-plasto-fractured medium. In this scenario, two coaxial inelastic zones form around the excavation: a fracture zone, where the rock mass lacks cohesion and therefore is devoid of its compressive strength, and a plastic zone, where the rock mass can retain its residual compressive strength. For an elasto-plasto-fractured model of the rock mass, the support pressure value increases after reaching a certain ground displacement threshold, which appears to align with engineering practice. (3) The convergence-confinement method (CCM) is a widely recognized, straightforward analytical tool for predicting the ground action and support design of underground roadways, chambers, and tunnels. Compared to the method outlined in Polish National Standards, it can more accurately capture the three-dimensional nature of underground excavations. Furthermore, it facilitates the design of a rigid support system, unlike the  
Figure 13: SCC curve coupled with the GRC curve for the ventilation roadway in the “Knuröw” coal mine. method prescribed by Polish Standards, which requires the support system to be able to transfer the entirety of the predicted rock mass displacement. (4) In Section 4 of this paper, a method for the establishment of the ground reaction curve for an elasto-plasto-fractured rock mass model was presented; this detailed equations for determining the value of ground displacement and the radii of the plastic and fracture zones, which are dependent on the value of fictitious pressure. These formulations provide a basis for establishing the ground reaction curve and can be applied in practical engineering calculations. (5) In Section 5 of this paper, a series of analyses were conducted on a typical circular roadway to verify the algorithm proposed in Section 4. Three rock mass classes with different mechanical properties were considered. Ground reaction curves for each rock mass class were calculated based on the elasto-plasto-fractured model. These curves were compared with the GRC curves obtained for the typical elasto-plastic model. The elasto-plasto-fractured model showed distinct action compared to the elasto-plastic model--most importantly in terms of displacement increments. (6) In the second part of the analyses conducted for the various rock mass classes, exemplar calculations of a support system were performed. Yielding steel arches were considered as the primary support system due to the expected large deformations. Support characteristics curves were determined for different rock mass classes, taking into account the action of the yielding steel sets. Based on ground-support equilibrium points, the factors of safety for the designed support system and the surrounding rock mass were calculated, indicating the correct choice of support parameters. Additionally, a real engineering case of a ventilation roadway in the \"Knurow\" coal mine was introduced.