## 3 Applying the Methodology to the Example of Dabar Power Tunnel
### Instabilities around the Contour Leading to Overbreaks
#### 3.2.2 Probabilistic Analysis  
The range of values of the input parameters for probabilistic analysis, including JRC, JCS, \(\phi_{r}\), persistence, azimuth, and dip angle (Table 1), were defined from the geological mapping and laboratory testing. As previously discussed, a normal distribution function was assumed for all variables. The value of the standard deviation of individual parameters was estimated to enable a realistic dispersion of the data around the expected (mean) value. The minimum and maximum values of the parameters, which define the limits of the set for the value \(\pm\) three standard deviations, cover 99.7% of the possible values of a considered parameter. The coefficients of variation of individual parameters indicate that the dispersion of data is relatively small and within the limits found in the literature [32]. The orientation of the discontinuity is defined in such a way that the azimuth is allowed to vary by \(\pm 9^{\circ}\) and the dip angle by \(\pm 3^{\circ}\) around the mean value of the corresponding discontinuity. This is a plausible assumption considering the (in)accuracy of measuring the angles while mapping the face of the tunnel excavation, as well as the spatial change of their orientation. Figure 6: Envelope of BB failure criterion at discontinuities at laboratory scale (green line) and field scale block of rock mass with side lengths of 3–5 m (red line). According to [PERSON] [33], coefficients of variation below 10% are considered low, between 15 and 30% are medium high, and above 30% are high. It can be concluded, according to [PERSON]'s criteria, that the values of coefficients of variation of the adopted parameters are low to medium high. This implies that the adopted range of each individual parameter is reasonable given their dispersion around a mean value. The normal distribution functions and characteristic values of each parameter are shown in Figure 8.  
Figure 7: Results of deterministic analysis at two selected sections: km 7 + 066.00 and km 8 + 514.50 (**a**,**c**) Measured orientation of wedges on contour diagram; (**b**,**d**) dimensions and positions of unstable wedges and overlap with observed excessive excavation (green line) for the two sections. As with the application of the deterministic method, the analyses were performed on dozens of arbitrarily selected cross-sections. The typical results are presented in Figure 9 for chainages km 7 + 066.00 and km 8 + 514.50, which are the same ones used in the deterministic analysis. The results of the probabilistic stability analysis shown in Figure 9 are also reproduced in Table 2.  
It can be seen that at chainage km 7 + 066.00, the stability criterion is not met around the entire contour of the underground excavation (note that the probability of failure is less than 7% in the lower portion of the right shoulder, and the safety factor criterion is not met). This points to the conclusion that the documented overbreak in this tunnel section is most likely the result of the fallout of smaller blocks of rock mass. At section km 8 + 514.50, the probability of failure is less than 7% in the left shoulder, and the safety factor value is higher than >1.0, which indicates that in this section, the left side of the tunnel excavation is expected to be stable. In both deterministic and probabilistic analyses of this tunnel section, it can be observed that there is almost no overbreak in the area of the left shoulder, which is in good agreement with the results of the geodetic survey. All of this indicates that the input data are well determined for both analyses.