## 4 Results and Discussion
### Relationship between \(n\) and Lithology  
In total, 253 out of 262 flow dimension data for the lithologies of consolidated rock formations were selected to understand a relationship between flow dimension \(n\) and lithology in the mountainous areas of Central and Southern Taiwan. Based on the results, the geometries of groundwater flow in different lithological formations were disclosed to describe their fracture network density. Such information can be used to provide a reference for the subsequent selection of hydrogeological analysis models.  
Table 8 is the summary of the flow dimension \(n\) values for a variety of lithologies, mainly showing the range of flow dimension \(n\) values and the pattern of groundwater flow that may appear in each type of lithologies. This table also summarizes the difference in the flow dimension \(n\) values between the two main types of lithologies, including sedimentary rocks and metamorphic rocks, as well as the difference in the \(n\) values between the sub-lithology of each main rock type.  
The sub-lithology of the sedimentary rock at the test sites of this study includes sandstone, sandstone interbedded with shale, shale, argillaceous sandstone, sandy shale, and mudstone. The average \(n\) values range from 1.53 to 3. The flow patterns include linear-cylindrical combined flow, cylindrical flow, cylindrical-spherical combined flow, and spherical flow. The sandstone is the lithology with the largest number of samples among the sedimentary rock types, but the \(n\) values of the samples vary widely from 1.13 to 3. Although the lithologies are both classified as sandstone, the fracture condition of rock masses is different, which may affect the groundwater flow pattern and cause the \(n\) value to vary significantly. The flow pattern of the overall sandstone test sections is a combination of cylindrical-spherical flow, and the fracture degree of the fractured rock mass is medium to high.  
Figure 10: Relationship between \(n\) and depth factor.  
Regarding the results of metamorphic rock types, the analyzed sub-lithology includes schist, slate, gneiss, quartzite, argillite, and marble, which are mainly distributed in the east and west flanks of the Central Mountain Range and between the Coastal Mountains. The average flow dimension \(n\) values range from 2.14 to 2.83, and the flow patterns include cylindrical flow, cylindrical-spherical combined flow, and spherical flow. Among them, slate, quartzite, argillite, and schist are the lithologies analyzed more in the metamorphic category in this study area, and the results are representative. According to the statistics, most of the groundwater flow patterns in most test sections are mainly cylindrical flow and cylindrical-spherical combined flow. The fracture degree of the fractured rock mass is a medium and medium-high degree of fragmentation.  
The results of all statistical analyses from various lithologies show that significant differences in the degree of fracture and geometry of the fractured rock masses have been found. The main reason comes from the geological complexity of Taiwan, coupled with the active orogenic movement. Thus, samples with the same lithology often have a large difference in the \(n\) value of flow dimension due to the effect on the rock structure.