## 4 Results and Discussion
### Relationship between \(n\) and Depth  
The analysis results of the flow dimension \(n\) were used not only to explain the fracture network density around a borehole, but also to understand the variation of the fracture network density with depth in the mountainous area of Taiwan as a practical study. This result provides essential reference information for the development and design of rock engineering in mountainous areas. For example, in view of the problem of the development depth of mountainous groundwater resources that have more economic development \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interval of** & **Average of** & **Average Flow** & \\
**log(K\({}_{\text{f}}/\text{K}_{\text{m}}\))** & **log(K\({}_{\text{f}}/\text{K}_{\text{m}}\))** & **Dimension \(n\)** & **Quantity** \\ \hline
0\(\sim\)1 & 0.4 & 1.96 & 3 \\
1\(\sim\)2 & 1.72 & 2.06 & 5 \\
2\(\sim\)3 & 2.47 & 2.12 & 8 \\
3\(\sim\)4 & 3.51 & 2.27 & 20 \\
4\(\sim\)5 & 4.47 & 2.41 & 18 \\
5\(\sim\)6 & 5.48 & 2.54 & 15 \\
6\(\sim\)7 & 6.53 & 2.56 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for grouping \(\text{K}_{\text{f}}/\text{K}_{\text{m}}\) data. Figure 9: Relationship between \(n\) and \(\text{K}_{\text{f}}/\text{K}_{\text{m}}\). benefits, the depth range of the fracture network with higher density in the drilling can be used to provide a reference for the development depth position. Regarding the relationship between the depth factor and the density of fractured rock masses at the sites in Taiwan's mountainous areas, this study analyzed 262 sets of double-packer hydraulic test data and obtained the flow dimension \(n\) value for each test data by [PERSON]'s general radial flow model [23]. Subsequently, the test depth for each double-packet test section and its corresponding \(n\) value were arranged in order according to the depth from the ground to 100 m or the drilling depth of each borehole. The arranged samples were grouped into fixed depth intervals. The average depth of all samples in each interval was calculated, and the average \(n\) value of the samples in each interval was obtained as shown in Table 7. Finally, the correlation analysis between average depth and \(n\) value was conducted. Figure 10 shows that the average depth for each grouped interval is between 7.96 and 93.459 m, and its corresponding n\({}_{\text{ave}}\) is between 2.27 and 2.58. The average \(n\) value decreases with the increase of depth, showing an exponential relationship. The average \(n\) value of the first depth interval (0-10 m) nearest to the surface is 2.58, which is the highest \(n\) value and belongs to the medium-high level of fracture network density; the average \(n\) value of the deepest interval (80-100 m) is 2.27, which is the lowest \(n\) value and belongs to the medium level of fracture network density. From the perspective of the entire depth profile, the fracture network density in the shallow area is higher and more developed than that in the deep area. There is an apparent trend of decreasing from the top to bottom of a borehole, which the geostress may cause. Because of this effect, the porosity and amount of fractures may decrease with depth, and, thus, the density of the rock fracture network may decrease. Especially for open fractures, such as exfoliation joins and microcracks, presented commonly in all rock types, they decrease their fracture aperture and density with depth [55; 56; 57]. Thus, the hydraulic conductivity may be reduced due to the structural change of deeper strata, which is detrimental to groundwater resources development in the mountainous areas of Central and Southern Taiwan.