## 4 Results
### Impact of Rock Bridge Failure on Block Areas  
For each geometrical fracture network scenario (i.e., variation of fracture orientation, trace length and frequency), a total of six DFNs were generated by setting the maximum threshold length of potential rock bridge failures to (a) 0 m (i.e., no rock bridge failure), (b) 0.05 m, (c) 0.1 m, (d) 0.2 m, (e) 0.3 m, and (f) 0.4 m, respectively. For each rock bridge failure length, surface areas were calculated and analyzed. Depending on the geometrical parameters of the DFN, i.e., trace length, fracture frequency, and fracture orientation, consideration of rock bridge failure can have a minor or major impact on the resulting block areas (Figure 6). All simulations of the selected example shown in Figure 6 are characterized by the same fracture network, but varied regarding the threshold lengths for rock bridge failure from (a) 0 m, (b) 0.05 m, (c) 0.1 m, (d) 0.2 m, (e) 0.3 m, and (f) 0.4 m. The illustrated fracture networks were generated by implementing two fracture sets. Fracture set #1 has a mean dip angle of 1.16\({}^{\circ}\), with a standard deviation of std = 5, a mean trace length of 5.65 m, and a mean 1D frequency of 0.74 m\({}^{-1}\). Fracture set #2 is based on a mean dip angle of 94.72\({}^{\circ}\) (std = 5), a mean trace length of 2.33 m, and a mean 1D frequency of 1.20 m\({}^{-1}\). In comparison to scenarios without rock bridge failure, the scenarios with rock bridge failure lead to cumulative distribution curves shifting towards smaller block areas. However, the shape of the cumulative distribution curves (Figure 7) between these scenarios remains almost similar. Thus, rock bridge failure affects block areas of all sizes, and there is no linear decrease in block areas with increasing maximum length of rock bridge failure. However, the shift along the \(x\)-axis of the cumulative block area distribution curves in the graph of Figure 7 for the individual threshold values is approximately in the same order of magnitude. Implementation of rock bridge failure decreases the number of blocks with unrealistic complex shapes, which is dominating for larger block areas. As a result of implementing rock bridge failure in the simulations, blocks are representing more natural shapes and less bounding surfaces. In addition, it was observed that rock bridge failure has a stronger impact on the resulting block area for DFNs with smaller interconnectivity factors than those with larger interconnectivity factors. Comparing similar DFNs, the resulting mean block areas of simulations without rock bridge failure are approximately five times larger than those obtained for simulations considering rock bridge failure and implementing a maximum rock bridge failure length of 0.4 m.  
For DFNs with rock bridge failure thresholds larger than 0 m, no correlation between the geometric mean interconnectivity factor and the ratio between the mean block area (\(A_{0}\)) assuming persistent fractures and the mean block area (\(A_{b}\)) considering non-persistent fractures (in contrast to simulations in Figure 5) is observed. Instead, the impact of the threshold length on the resulting mean block area, \(A_{\text{br}}\), is a function of both the geometric mean interconnectivity factor and the mean block area with a threshold level of 0 m (\(A_{nb}\), Figure 8). For large \(I_{g}\) values (approximately \(>\) 10), the ratio between the mean block area without rock bridge failure, \(A_{nb}\), and the mean block area with rock bridge failure, \(A_{br}\), is nearly constant and varies only between 1.0 and 1.5, depending on the maximum length of rock bridge failure. This suggests that the block areas do not decrease with the implementation of rock bridge failure if \(I_{g}\) is larger than approximately 10. The power law of Equation (15) fits the data set and shows a clear correlation trend (Figure 8). \[\frac{A_{nb}}{A_{br}}=a\cdot I_{g}^{\ b}+c \tag{15}\]Figure 6: 2D discrete fracture networks showing 30 \(\times\) 30 m detail views, extracted out of the 50 \(\times\) 50 m total models.