## 4 Results  
### Calculation of Ejecting Force Pk and Angles \(\alpha_{1},\alpha_{2}\)  
The analysis was performed based on 625 unique input datasets composed of values of four basic parameters: \(p_{x}\), \(p_{z}\), \(B\), and \(\varphi\). Each parameter had been represented by a set of five different values. The results of calculations have been visualized as diagrams which allow immediately evaluating the values of angles \(\alpha_{1}\) and \(\alpha_{2}\) and values of unbalanced forces as well (Figure 7). In order to assess the sensitivity to the variations of base parameters, a sensitivity analysis has been carried out. As a basic model for such an analysis, the solution with the model characterized by the following parameters was adopted: \(B\) = 6 m, \(p_{x}\) = 5 MPa, \(p_{z}\) = 20 Mpa, \(\Phi\) = 45 deg., \(H\) = 4 m, and \(c\) = 4 MPa. This solution is treated as a reference and its result values are \(P_{k}\) = 4.64 MN, \(\alpha_{1}\) = 64.1 deg., and \(\alpha_{2}\) = 86.1 deg. The obtained changes describing the basic model sensitivity are shown in Table 1.  
As one may notice, the value of the force expelling the detached wedge is positively correlated with the value of the excavation height. For small values of cohesion, it is almost a linear relationship. For large values of cohesion, this correlation will become negative until the \(P_{k}\) value reaches zero. Moreover, in the LGCB region, the values of the base parameters remain approximately in the range \(B\) = 6 \(\div\) 10 m, \(p_{x}\) = 5 \(\div\) 35 MPa, \(p_{z}\) = 15 \(\div\) 30 MPa, and \(\phi\) = 31.5 \(\div\) 62.7 deg. Therefore, using the data presented in Table 1, the results are as follows: 0 \(\leq P_{k}\leq\) 16.7 MN, 50.4 \(\leq\alpha_{1}\leq\) 90 deg. and 80.5 \(\leq\alpha_{2}\leq\) 90 deg.  
Figure 7: Values of unbalanced forces \(P_{k}\) which should be compensated by the appropriate ground support system **(top)**, angle \(\alpha_{2}\)**(middle)**, and angle \(\alpha_{1}\)**(bottom)**, assessed for a specific case of excavation geometry, load, and strength characteristics of surrounding rocks.  
The presented procedure for assessing the stability of mining excavations turned out to be effective because the determined shape of an ejected wedge matches the real case studies observed in Polish copper mines. The information provided by the proposed approach in terms of ejecting forces as a function of geological and mining conditions is extremely valuable in terms of the possibility of assessing the rockburst risk. Moreover, knowing the dynamic forces of wedge ejection, an attempt at rockburst risk mitigation may be utilized by the rock mass reinforcement; for example, by using a ductile rock bolt support system.  
In the top of Figure 6, a selected set of diagrams corresponding to the unique combination of parameters \(p_{x}\), \(p_{x}\), \(B\), and \(\varphi\), are presented. The first diagram shows values of the unbalanced by friction and cohesion, forces \(P_{k}\) which may be ejected from the rock wedges ABCD and ACD. The next two diagrams deal with the values of the angles describing the possible geometry of the ejected rock wedge (Figure 7--center and Figure 7--bottom). Analyzing Figure 7, it can be seen that the value of the stability index increases with increasing cohesion and decreases with increasing the excavation height. For a fixed cohesion value, the stability index reaches a value equal to 1.0 when the angles \(\alpha_{1}\) and \(\alpha_{2}\) reach the same value, which means that the area where a limit state could have developed disappears (see Figure 7, curve c = 8 MPa, H = 3.44 m, \(\alpha_{1}=\alpha_{2}=76.8\) deg)