# Improved Mandel System for Prefabricated Vertical Drain Installation: A Macro to Micro Analysis
## 3 Methodology  
### Large-Scale Model Test  
#### 3.1.1 Model Testing  
The main apparatus of the large-scale consolidation test is illustrated in Figure 2, and functions and remarks are provided in Table 3. The chamber apparatus material was made of a thick glass cell with a 460 mm internal diameter and 700 mm height. Furthermore, the axial loading system was an air jack-compressor system with a maximum axial loading capacity of 1000 kPa. A vacuum pump that could generate up to 100 kPa suction pressure was employed at the top of PVD. Pore water pressure (PWP) was placed at the bottom of the chamber and connected directly to the data logger. The LVDT performed the settlement measurement of the axial displacement placed at the top of the acrylic plate. The water tank with a balance was used to measure the volume of water, and it was connected to the center of the PVD connector. In addition, the designed rectangular mandrel was made \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Prototype**} & \multicolumn{4}{c}{**Model in Laboratory**} \\ \cline{3-5}  & & **PVD Type A** & **PVD Type B** & **PVD Type C** \\ \hline Material & \multicolumn{4}{c}{Polyppropylene core} \\ Thickness (m) & 0.0050 & 0.0035 & 0.0040 & 0.0055 \\ Width (m) & 0.1 & & 0.09 & \\ Permeability, \(k_{0}\) (m/s) & 2.99 \(\times\) 10\({}^{-4}\) & 1 \(\times\) 10\({}^{-2}\) & 1 \(\times\) 10\({}^{-2}\) & 1 \(\times\) 10\({}^{-1}\) \\ Young’s modulus, \(E\) (kPa) & 68.6 & 2.5 & 2.5 & 4.8 \\ \hline \end{tabular}
\end{table} 
Table 2: The PVD properties. Figure 1: The illustration of PVD types: (**a**) shapes of PVD types A, B, and C; (**b**) PVD type C structure. from iron steel, with a length of 750 mm and a width of 90 mm; it was used to install the PVD in the ground. \begin{table}
\begin{tabular}{l l l} \hline \hline
**No** & **Component** & **Functions and Remarks** \\ \hline
1 & Vacuum pressure & The technique of applying a vacuum suction into an isolated soil mass to reduce the atmosphere pressure; measurement range: 100 kPa \\
2 & Pore water pressure & Measuring the pore water pressure; measurement range: 200 kPa/0.0391 kPa/ \(\mu\); accuracy: 0.9 kPa. \\
3 & LVDT & Measuring displacement; accuracy: 100 \(\times\) 10\({}^{-6}\)/mm \\
4 & Sample chamber & Contains the soil sample; diameter: 460 mm; height: 700 mm \\
5 & Acrylic mold & The cell container is made of transparent acrylic tube \\
6 & Sponge packing & Technique using sponge packing material for sealing to prevent air leaking \\
7 & Acrylic plate & Hanging from the top of chamber and following volume changes during the test \\
8 & Doughnut pressure chamber & Inner diameter: 190 mm; outer diameter: 450 mm; thickness: 12 mm \\
9 & Hanging loading system & Steel frame, moveable up and down during the test \\
10 & PVD & Ground improvement technique: three types of shape used in this study \\
11 & Placemat frame chamber & Steel frame to support the chamber \\
12 & Moveable placemat frame chamber & Horizontally moveable chamber for sample preparation \\
13 & Mandel actuator driving motor & Steel handle, which can move up and down during mandrel penetration \\
14 & Loading device & Screw jack (max load: 1000 kPa) \\
15 & Penetration supporting frame & Steel frame to support the steel handle for mandrel penetration \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The functions and remarks of schematic of large-scale consolidations. Figure 2: Schematic of large-scale consolidation test setup used in the experiment. The mandrel has an influence on the resulting smear zone for the equivalent drain radius of PVD, as proposed in the literature [22; 23; 24; 25]. Furthermore, Equations (4)-(6) were used to describe the drain radius of the smear zone's influence on PVD with mandrel in this study, shown in Figure 3.  
\[r_{w\text{ (Type A)}}=\frac{a+1.6\ x_{1}}{\pi} \tag{4}\]  
\[r_{w\text{ (Type B)}}=\frac{a+1.4\ x_{2}}{\pi} \tag{5}\]  
\[r_{w\text{ (Type C)}}=\frac{a+x_{3}}{\pi} \tag{6}\]  
The model in a general form is expressed in Equation (7).