# Improved Mandel System for Prefabricated Vertical Drain Installation: A Macro to Micro Analysis
## 4 Results and Discussion
### Microstructure Analysis
#### 4.2.1 PVD Structure
If this occurs, the consolidation process may be slowed down or ineffective, leading to potential long-term stability issues. Therefore, it is crucial to understand the interaction between the PVD filter and the pores caused by vacuum preloading to optimize the design and properties of the system accordingly. Thus, the effectiveness of the PVD system during installation using a mandrel was ensured in this study. Figure 14 shows the structure of the PVD filter and pore changes caused by vacuum preloading with reference to deformation modes [18]. After vacuum preloading, SEM images of both the soil-facing and drain channel-facing sides were captured. Additionally, the opening in the filter was filled with fine soil particles on both sides, with notable differences existing. On the side contacting the soil, more fine particles filled the filter interspacing. The filter structure changed due to the effect of vacuum preloading. In this study, the approach used was based on the shape of the deformation effect of the PVD. The PVD filter could present one of three different  
Figure 13: Pores and filter area of PVD structure-based SEM images. structures after consolidation, namely, uniform, local, and sinusoidal bending, referring to the deformation modes in a previous study [42]. For more detail, Figure 15a shows the quantitative analysis results in terms of area and percentage to understand the effectiveness of PVD depth. The results show that, in the bottom area of PVDs, the particle area was 4.3 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) and pore area was 8.9 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) for type A, 4.9 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) and 8.4 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) for type B, and 4.7 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) and 8.6 \(\times\) 10\({}^{4}\)\(\upmu\)m\({}^{2}\) for type C. These results show that the bottom area of all PVD types in this study had a higher particle area due to vacuum preloading, and that using the PVD filter decreased the pore size. These results indicate that the fine particles moved to fill the areas with large pores during vacuum preloading. This can be considered a clogging effect [38], as also proven by \(D_{\rm 85}\) being larger than 50% of \(n^{\prime}\) in Figure 15b. Figure 14: SEM images of PVD, pores, and particles in the three zones: (**a**) PVD type A, top area; (**b**) PVD type A, middle area; (**c**) PVD type A, bottom area; (**d**) PVD type B, top area, (**e**) PVD type B, middle area; (**f**) PVD type B, bottom area; (**g**) PVD type C, top area; (**h**) PVD type C, middle area; (**i**) PVD type C, bottom area. The general form of the PVD filter, pore, and particle areas was analyzed using ImageJ and expressed as follows:  
\[n=n^{\prime}=\alpha.\mathcal{O}^{\prime}+{n^{\prime}}_{0} \tag{16}\]  
where \(n\) is the pore area, \(n^{\prime}\) is the PVD and pore area, \(\alpha\) is the slope of the pore area, \(\mathcal{O}^{\prime}\) is the particle area, and \({n^{\prime}}_{0}\) is the initial PVD and pore area before the test. In summary, the clogging effect on PVD filters caused by vacuum preloading was influenced by the filter's geometry, stiffness, and surrounding soil properties. The design and properties of the PVD filter should be optimized to ensure that it can withstand external loads and maintain its stability during installation and use.