## 4 Results and Discussion
### FA
The correlation analysis between FD and n was performed as shown in Figure 7. The outcome indicated a positive relationship between the average \(n\) value and FD. Among them, the average \(n\) value of eight fractures was 2.51. The result shows that when the \(n\) value in a test section presents to be higher, a higher FD value appears in the test section. This finding implies that the fracture network density tends to be denser. (D) Hydraulic conductivity (K)  
The density of the fracture network may be correlated with the magnitude of the hydraulic conductivity. This study attempts to use it as one of the hydrogeological indicators to verify the concept of flow dimension \(n\). To understand that the density of the fracture network is consistent with the groundwater transmit capacity or groundwater potential, this study performed a correlation analysis between the \(n\) value and the hydraulic conductivity. Based on 80 sets of single-packer hydraulic test data with the theory in Section 2.1, n and K values of the stratum to which the 80 drilling sites belong were obtained. Subsequently, the n and K data were grouped according to their respective numerical values. The flow dimension \(n\) value is divided into five different levels of fracture network density: high (3.00 < n < 2.75), medium-high (2.75 < n < 2.25), medium (2.25 < n < 1.75), medium-low (1.75 < n < 1.25), and low (1.25 < n < 1.00). The hydraulic conductivity coefficient is further divided into four levels (H, M, L, and P) with reference to [PERSON]'s [54] water supply potential table (Table 4). Finally, this study integrated the classification results of n and K and counted the number of fracture network density levels in each level of hydraulic conductivity, as shown in Table 5.  
Figure 7: Relationship between n and FD. According to the statistical results in the proportion of various hydraulic conductivity levels at the same fracture network density level, a high proportion appears in low hydraulic conductivity, as the fracture network density tends to be lower and vice versa. Thus, the flow dimension \(n\) in interpreting fracture network density can also be confirmed by the indicator of K. In addition, Table 5 shows that the main fracture network density of the study area is medium, accounting for about 50%, followed by medium and high density. This finding also indicated the characteristics of geological fragmentation in Taiwan's mountainous areas. (E) \(\rm K_{f}/K_{m}\) ratio  
This study attempts to integrate the analysis results of flow dimension \(n\) and \(\rm K_{f}/K_{m}\) ratio to understand whether the higher the \(n\) value (fracture network density is high), the higher the \(\rm K_{f}/K_{m}\) ratio (fractures dominate the groundwater flow behavior), so as to establish a relationship between them. A two-stage data-selection process was applied based on the target and purpose of obtaining a well correlation. The first stage was to exclude data samples of geological structures that do not have the characteristics of fractures and obstruct the flow of groundwater in each double-packer test section. Through this screening mechanism, a total of 88 data samples were chosen at this stage. The second stage was to exclude data samples for which a high \(\rm K_{f}/K_{m}\) ratio did not accompany a value with high n. According to the concept of flow dimension \(n\), the high \(n\) value is expected to have a higher fracture density network, resulting in the appearance of a high \(\rm K_{f}/K_{m}\) ratio (fractures dominate the groundwater system). However, among 88 data points, few data samples were found to be a reverse trend. For example, a high \(n\) value was accompanied by a low \(\rm K_{f}/K_{m}\) ratio. Figure 8 shows a schematic diagram of two rock mass structures with high fracture network density (high \(n\) value). Figure 8a illustrates the rock mass structure with high fracture network density that is consistent with the hypothesis of the flow dimension