## 2 Theoretical Background
While the trace length distribution of individual fracture sets usually can be acquired in the field by window and scanline mapping, a measurement of the length of the intact rock bridges is still a big challenge and nearly impossible. Furthermore, persistent fracture traces/planes are generally not aligned one by one along a plane but rather are randomly distributed within the rock mass [20]. An additional limitation of some DFN modelling software products is the requirement of at least one fully persistent fracture set or a spacing parameter that is valid for the Veneziano model only. Besides that, for many cases, the applied persistence factor [17] does not consider the relation to other fracture sets and is a simplification concerning its impact for IBSD considerations. In practice, the determined IBSD is only a rough estimate because all mentioned restrictions do not consider natural conditions and limitations. Consequently, a method of analyzing the IBSD of a rock mass composed of non-persistent fractures on the basis of geometrical parameters that can be easily acquired in the field is needed. Typically, only the orientation, spacing and trace lengths of fractures are acquired in the field concerning fracture geometries (e.g., by applying the widely accepted scanline mapping method [21]). Similar parameters of large datasets can be acquired by non-contact survey methods, such as photogrammetry and terrestrial laser scanning, e.g., [22; 23; 24; 25; 26; 27]. The application of the interconnectivity index, \(l_{ij}\), proposed by [12], as an alternative parameter to the persistence factor, is a possibility for such a parameter, which can be acquired based on the above-mentioned field parameters. The interconnectivity index is independent of the knowledge of the lengths of intact rock bridges and can be determined between two fracture sets within a rock mass. \[I_{ij}=\frac{l_{i}}{s_{j}}\cdot\sin\bigl{(}\gamma_{ij}\bigr{)} \tag{5}\]  
where \(l_{i}\) is the mean trace length of the fracture set \(i\) [m]; \(s_{j}\) is the mean normal set spacing of fracture set \(j\) [m]; \(\gamma_{ij}\) (\(\Omega\
eq\mathrm{j}\)) is the average angle in [\({}^{\circ}\)] between the two fracture sets \(i\) and \(j\). For a fractured rock mass containing several fracture sets, the total interconnectivity index (\(l_{i}\)) for each fracture set can be determined by summation of the interconnectivity indexes,  
\[I_{i}=\sum_{j=1}^{n}I_{ij}(i\
eq j) \tag{6}\]  
where \(n\) is the number of fracture sets. Although the index does not rely on a theoretical background, it provides a useful parameter to characterize interconnectivity based on fracture orientation, trace length and spacing. From a practical perspective, the index is easier to determine for a rock mass than the persistence factor proposed by [17]. Nevertheless, the resulting values for the interconnectivity index may show a much larger range than the persistence factor (i.e., \(0<p\leq 1\) while \(0<I_{i}<\infty\)). Consequently, \(p\) and \(I_{i}\) are not comparable, and thus \(l_{i}\) cannot be directly implemented in Equations (3) and (4). However, so far, no equations were established to implement the interconnectivity index for the determination of an IBSD. Generally, DFN modelling is the most appropriate approach to analyze IBSDs of rock masses. Currently, there are only a few software products, e.g., FracMan (Golder 2021), UDEC, 3 DEC (Itasca 2021), ELFEN (Rockfield 2021) [28; 29; 30], mostly commercial and proprietary codes, available that are able to calculate the block sizes by DFN modelling. Most of them have limitations in considering rock bridge failure. The adaptation of these proprietary codes to implement rock bridge failure is challenging. While there have been recent improvements in using DFN for open source code analyses, especially in the field of hydrogeology [31; 32], the simulation of the IBSD for various scenarios (e.g., including rock bridge failure) still needs further investigation.