## 3 Methodology  
### Discrete Fracture Network Generation  
A total of about 1500 models with random fracture networks (DFN) were generated to analyze their 2D block areas. These models comprise non-persistent fractures and are generated by using MATLAB (R2015b, Mathworks) [33]. Fractures are represented by their traces, i.e., lines (see Figures 1b and 2). Stochastic analyses were performed on the basis of all simulations by varying values for each input parameter of the simulations, comprising of fracture orientation, the number of sets, linear frequency along the normal to the \(i^{\text{th}}\) fracture set, and trace length. For all simulations, a discrete fracture network with two fracture sets was generated for a 50 m \(\times\) 50 m study region. In this study, the four outer boundaries of the region were defined as fully persistent fractures in contrast to other approaches (e.g., [34]).  
The number of fractures, \(n_{\gamma}[-]\), which are generated in each of the 50 m \(\times\) 50 m study regions, is based on the linear fracture frequency, \(\lambda_{i}[\text{m}^{-1}]\), according to the following equation:  
\[n_{f}=\lambda_{i}\cdot L_{y}\cdot\frac{L_{x}}{t_{l}} \tag{7}\]  
where \(L_{x}\) and \(L_{y}\) are the lengths of the analyzed region in the \(x\)- and \(y\)-direction [m], respectively, and \(t_{l}\) is the mean fracture trace length [m]. The linear fracture frequency is usually measured by the application of scanlines and is similar to P10 proposed by [35], which is perpendicular to the mean fracture set orientation. According to [36], the linear fracture frequency is the reciprocal of the normal set spacing of a fracture set. The central locations of all fractures within the analyzed study region were determined randomly by a 2D Poisson process, which causes a negative exponential distribution of normal set spacing values. This type of probability distribution was chosen because it is able to represent many naturally occurring fracture spacing patterns (e.g., [14; 37; 38; 39]). Other common distributions would be, e.g., the logarithmic normal (e.g., [40; 41; 42]) or fractal (e.g., [43; 44; 45]) distributions, which can be generated by a Kolmogorov process or a scale-invariant process, respectively [46].  
The following geometric restrictions were implemented in the random fracture generation for the two fracture sets of the approx. 1500 models: (a) mean values for the fracture trace length (0.5-12 m), (b) linear fracture frequency (0.15-3 m\({}^{-1}\)), and (c) fracture orien  
Figure 2: Determination of the intersection of two intersecting fractures.  
tation (0-90\({}^{\circ}\)). As an additional limitation, a minimum difference of the angle between the two sets was defined as 15\({}^{\circ}\). Based on the mean orientation of the fracture set and a standard deviation of Std = 5, the fracture orientation of each fracture of a set was simulated randomly on the basis of a normal probability distribution (e.g., [47]). In addition, the individual fracture trace lengths were generated with the randomly defined mean trace length and a negative exponential probability density distribution (e.g., [12; 36; 48]). Fractures simulated and located partly outside of the 50 \(\times\) 50 m study region (central locations of fractures were set to be located always within the boundaries of the study region though) were deleted and not considered for further analyses, i.e., the trace map was cropped along the outer boundary of the analyzed region.