# 2D Numerical Analysis of Prefabricated Vertical Drains Using Different Matching Methods
## 4 Results and Discussion
### FEA of Full Test Embankment in Eastern China  
In this section, as previously described, 2D FEA of a real embankment built on numerous vertical drains is analyzed because multiple drain behavior is neglected in unit cell analysis. To evaluate the behavior of PVDs, a full-trial embankment in eastern China was analyzed using three different matching methods, as previously discussed. The equivalent permeability in plane-strain conditions for all matching approaches, and in situ taken from Ba-Phu [43], are summarized in Table 8. During consolidation, bottom boundary displacements are not permitted in both directions \(\left(u_{x}=u_{y}=0\right)\). Horizontal displacements are not allowed on the right and left boundaries \(\left(u_{x}=0\right)\), and they are closed to the consolidation boundary. Finite element mesh for three matching methods in plane-strain conditions are shown in Figure 8.  
As seen from these results in Figure 9, although the matching methods are based on unit cell with single vertical drain, they are successfully capable to predict the settlement and the EPP in full-scale embankment. Moreover, despite the real behavior of consolidation of soft soil deposit stabilized with PVDs is in 3D, 2D plan strain conditions using matching methods are capable to predict the vertical settlement and EPP in FEA. Furthermore, even though these three approaches are completely different, their FEA results were close together and are very comparable with the field measurements. As seen in Figure 9a, the time-dependent settlement for all matching methods were attained about 200 cm after 900 days. However, there is a minor variation among the predicted outcomes and field measurement within the early stage (from 0 to around 120 days). According to [PERSON] et al. [57], the settlements are small due to the subsoil clay being overconsolidated throughout the early phase of execution, which behaves in a quasielastic manner and has a high stiffness. Figure 8: Finite Element Mesh for three matching methods in plane-strain conditions. (**a**) Method A; (**b**) Method B; and (**c**) Method C.  
Figure 9: _Cont._  
Based on Method A, the predicted vertical settlement most accurate agreement compared with other methods with the field measurement. However, the application of this approach requires complex works because the smear zone around each vertical drain must be defined in the numerical analysis, and the values of horizontal permeabilities in the smear zone and undisturbed soil must be input separately for each layer. According to Method B, FEA produced a somewhat slower consolidation rate. However, this method is a much simpler concept, and does not require modeling of vertical drains. This approach is more convenient and simpler to employ in real-world engineering practice due to its simplicity. Method C yielded a somewhat faster vertical settlement rate. However, differences between the two other methods are quite small. This approach has a slight advantage over Method A, since the smear zone surrounding each vertical drain is not modelled in the simulation. Moreover, as shown in Figure 9b, the simulated EPP are also compared with the field measurements. Generally, the accurate prediction of EPP is more challenging than the prediction of settlement [2]. It can be seen that the predicted EPP were in good agreement from the initial stage up to 280 days or so, and afterwards they underestimated the field measurement. It is possible that the large discrepancies between the numerical analysis and measurements are due to potential errors in piezometric measurement [2]. Piezometers are commonly used to measure pore water pressure in deep soil. As a result, these piezometers can get clogged when dirt particles pass into the filter's pores. Thus, a certain quantity of excess pore pressure is trapped in the piezometers [15; 58].