# 2D Numerical Analysis of Prefabricated Vertical Drains Using Different Matching Methods
## 4 Results and Discussion  
### FEA of Large-Scale Consolidometer Experiment  
In the model, boundary conditions and lower boundary displacements are not allowed in both directions \(\big{(}u_{x}=u_{y}=0\big{)}\). The right and left edges do not allow for horizontal displacements \(\big{(}u_{x}=0\big{)}\) (Figure 4a). The right and bottom edges are closed to drainage, and the groundwater level is defined at the lower boundary (Figure 4c). Figure 5a shows the predicted vertical settlement of axisymmetric unit cell in the FEA analysis and laboratory measurements. It can be seen that, in FEA, the time-dependent settlement value was obtained around 119 mm after 47 days, while the experimental measurement result was determined to be approximately 120 mm. It is clear that FEA results and experimental data match extremely well. Moreover, EPP versus time of the large-scale consolidometer in FEA result and the laboratory measurement are also presented in Figure 5b. Although the simulations slightly overestimated the EPP values, numerical analysis generally matches up fairly well with the measurements. As can be seen, the numerical analysis and the experimental measurement are in very good agreement. Afterwards, they differed slightly beyond 20 days. According to [PERSON] [44], it is not surprising to see a discrepancy of EPP between the numerical analysis and the laboratory measurement. This is because the EPP experimental is installed near the PVD, which means that the maximum EPP closer to the PVD under cyclic load was considerably lower compared to that near the cell border, and EPP at the vicinity of the drain reduced dramatically as a result of the permeable barrier established using PVD [44]. From these results, it was seen that the consolidation behavior of PVD on soft clay was successfully modeled in the FEA program with the SSM model. As mentioned previously, in the next part of the numerical analysis of consolidometer, the experiment which was carried out with axisymmetric is analyzed into two-dimensional plane-strain conditions using three different matching methods, and the results are compared to axisymmetric and laboratory measurements. Table 7 shows the experimental permeability of soft soil and equivalent permeability in plane-strain conditions. In view of these results presented in Figure 6a,b, although the real behavior of the consolidation of soft soil deposit stabilized with PVD is in 3D, 2D plane-strain conditions using matching methods are able to predict the settlement and the EPP in FEA. Generally, it can be seen that, even though a relatively differences, all predicted vertical settlements of matching methods are extremely good agreement with the axisymmetric result and the experimental measurement as well. The discrepancy between Method A and the axisymmetric method was 6% at the beginning of the consolidation. However, it was decreased to 1.5% at the end of 47 th day, as shown in Figure 7. According to Method B, the gap was roughly 4.15% at the end of 47 th day of consolidation, whereas Method C showed a 4% difference at the end of 47 th day. Based on Method B, [PERSON] et al. [35] demonstrated that the difference is due to the fundamental approximation approach, which incorporates the effect of both vertical and radial drain  
Figure 4: Finite Element Modeling of the large-scale consolidometer experiment. (**a**) Geometric model; (**b**) axisymmetric mesh; (**c**) initial conditions. Moreover, these results show that the matching EPP analysis agree well with both the axisymmetric and laboratory measurements. However, a quite discrepancy can be seen between EPP in axisymmetric and plane-strain analysis results. As indicated by [PERSON] et al. [55], the error in EPP calculation was probably due to a decrease in global permeability. Furthermore, [PERSON] [56] demonstrated that, although perfect matching is achieved, EPP at a similar location in the axisymmetric and plane-strain unit cells might differ, which is caused by an underestimating of geometry and global permeability.