## 4 Results and Discussion
### FA  
Before establishing a correlation between FA and n, it is necessary to select relevant data from the existing data based on the theory of flow dimension \(n\). According to this theory, the value of \(n\) is mainly controlled by water-conducting fractures. However, not all the data collected meet this condition. To reduce the influence of the verification caused by non-conductible fractures, this study excluded data samples with the following two conditions: (1) the lithology of test sections without fracture characteristics (e.g., semi-consolidated rock formation); (2) the geological structure that hinders the flow of groundwater (e.g., high-angle fractures, fractures containing fractured shear mud, and shear fracture zones) of test sections. After filtering out the unqualified data, a total of 129 test data that met the conditions were included for correlation analysis. Subsequently, the accumulated FA value for each double-packer test section with a fixed packer length of 1.5 m was calculated, and then the accumulated FA value and its corresponding \(n\) value were arranged in order according to the width from small to large. The arranged samples were grouped into fixed-width intervals. The average width (FAave) of all samples in each interval was calculated, and the average \(n\) value (nave) of the samples in each interval was obtained (Table 3). Finally, the correlation analysis between FAave and nave value was conducted. Figure 5 shows that FAave for each grouped interval is between 0.6 and 10.9 cm and its corresponding nave is between 2.05 and 2.72. nave increases with the increase of FAave, showing a positive correlation. This correlation result indicated that the fracture width influences the magnitude of flow dimension \(n\). This hydrogeologic index FA verified the feasibility for interpreting potential fracture network density based on the result of flow dimension \(n\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**FA**} & \multicolumn{3}{c}{**FD**} \\ \hline
**Interval of** **Aperture (cm)** & **Average** **Aperture (cm)** & **Average Flow Dimension \(n\)** & **Quantity of** **Samples** & **Quantity of** **Fractures per** & **Average Flow Dimension \(n\)** & **Quantity of** **Samples** \\ \hline
0\(\sim\)1 & 0.63 & 2.05 & 19 & 1 & 2.24 & 7 \\
1\(\sim\)2 & 1.33 & 2.2 & 23  
Before establishing a correlation between FD and n, raw data selection also plays a vital role in obtaining a good correlation. The selection of the data was divided into two stages. The first stage was to apply the same screening method as FA. Each data sample with the existence of water-conducting fractures in each test section was selected. A total of 129 data points were chosen at this stage. However, these data need to be further filtered, due to the fracture width's effect on groundwater flow characteristics. For example, six fractures are presented in both double-packer test sections, as illustrated in Figure 6. Nevertheless, the width of the fractures may be quite different. Due to this discrepancy, the groundwater flow characteristics of the two test sections may be different. This hypothesis was confirmed from different flow dimension \(n\) values at both sides of Figure 6. The \(n\) value at the left-hand side of Figure 6 is 2.33; the other one is 1.59. Therefore, 129 data points of the first stage need to be rechecked, to avoid the influence of fracture width. Figure 5: Relationship between n and FA. Figure 6: Schematics of different fracture width patterns in a fixed test interval. Among 129 samples, this study looked for samples in which the width of each fracture in each test section was less than 1 cm. Finally, 67 samples were selected for analysis. The samples were grouped into seven fracture density values from one to eight, excluding the value of seven. The corresponding average \(n\) value for each FD value was computed as shown in Table 3. The average \(n\) value for the seven groups ranged from 2.1 to 2.51.