# Semiautomated Statistical Discontinuity Analyses from Scanline Data of Fractured Rock Masses
## 5 Discussion  
The basic statistical discontinuity parameters that can be determined by the workflow and the scripts presented herein, comprising (i) normal set spacing for each set, (ii) linear frequency for each set, (iii) semi-trace length distribution and mean trace length of each set based on several approaches, and (iv) termination index of each set, are used for a wide variety of practical applications. These parameters serve as input for discontinuity characterization in the field of rock mechanics, groundwater flow, reservoir engineering, and geothermal energy extraction in fractured rocks. For applications in rock mechanics, these parameters are essential to characterize the degree of fracturing and fragmentation of a rock mass. The volumetric joint count (\(J_{v}\), [40]), a key value to describe the degree of jointing of a rock mass, represents the number of discontinuities intersecting a volume of 1 m\({}^{3}\) and is calculated by summation of the inverse of the mean normal set spacing of each set. The mean block volume, (\(V_{b}\)), of a rock mass that is fractured by three sets is determined from the discontinuity set orientation and mean normal set spacing [1; 40]. The in situ block size distribution (ISBD) can be determined by empirical or numerical approaches based on statistical discontinuity data (e.g., [10; 41; 42]). Finally, the theoretical rock quality designation (RQD) value of the rock mass in any arbitrary direction is calculated from the linear frequency of the sets [14]. For the assessment and characterization of the rock mass properties in underground construction and slope stability, empirical methods based on rock mass failure criterions [43; 44] and rock mass classification systems were developed [45]. All of these methods require data on the discontinuity network. Due to the increasing computing power of PCs and workstations, the discrete fracture network (DFN) approach offers new possibilities to simulate the geomechanical and hydro-geological behavior of a rock mass with reasonable effort [5]. Applications related to slope stability, open pit mining, tunneling, dam foundations, groundwater flow in fractured rocks, radioactive waste disposals, and geothermal energy extraction are common and state of the art. Beside others, stochastically generated fracture networks are by far the most widely used DFNs for numerical modeling studies. Statistical discontinuity data from surface and subsurface scanline sampling and borehole imaging serve as the input for these models. However, it should be noted that a statistical analysis of discontinuity data is also based on assumptions and limitations [14]. A key assumption is that the discontinuities are plane surfaces in 3D models and straight lines (traces) in 2D models. Accurate measurements of trace lengths are challenging due to the outcrop situation and accessibility. The real shape of discontinuity surfaces can hardly be determined at the outcrop and certainly not statistically recorded. Planar disks or polygons are therefore used as idealized shapes for the analyses and modeling. According to [PERSON] [14], the normal set spacing is measured along a line oriented parallel to the mean normal to the set. Therefore, in the workflow presented here, it is assumed that the discontinuities of a set are aligned in parallel for the spacing calculation (i.e., \(\cos\left(\delta\right)\) remains constant for a set and a selected scanline), leading to over- and underestimations of the distance. However, in comparison to RQD or total spacing, the normal set spacing value of each set of a rock mass is direction-independent. Statistical discontinuity analyses and their implementation into DFN models consider the geometrical parameters as independent random variables belonging to certain probability density distributions, such as negative exponential, normal, lognormal, gamma, or power law distributions [5].