# 2D Numerical Analysis of Prefabricated Vertical Drains Using Different Matching Methods
## 2 Objectives and Scope  
During the consolidation of subsoil-improved-PVDs, the water flows both radially and vertically, requiring three-dimension (3D) numerical analysis to model the effects of PVDs [29]. However, 3D modelling necessitates a significant amount of time and an efficient computer. In reality, hundreds of drains are installed under an embankment in a large project. FEA of PVDs frequently encounters problems with their size in relation to the overall dimensions of the issue [30]. PVDs typically have a square section of 100 mm \(\times\) 4 mm, which is significantly less than the width of a normal road embankment, so they are commonly constructed at a spacing of 1-2 m. Furthermore, through a 3D analysis, the exact shape of the drain section has to be depicted in multiple soil layers [30]. Therefore, finite element meshes must be extremely fine in order to correctly represent the geometry of the PVDs, which results in significant model preparation and computational costs and mesh error as well.  
Therefore, in order to reduce the computation time, most available finite element analyses on embankment stabilized with PVDs are conducted for 2D plane-strain conditions [24; 31; 32]. [PERSON] [33] and [PERSON] [8] were introduced the initial consolidation concept of fine-grained soils using single drain wells. Nevertheless, certain negative aspects are found regarding this research, such as how the influence of depth on the well was not taken into consideration, as well as the distinction in elasticity between soil surrounding and elements in the sand well [34]. Following that, various approaches were developed to match the equivalent value of the axisymmetric analysis with the plane-strain conditions [27; 35]. [PERSON] et al. [36], [PERSON] et al. [37], [PERSON] et al. [38], [PERSON] et al. [39], [PERSON] al. [40], [PERSON] et al. [41], [PERSON] et al. [15], [PERSON] et al. [42], and [PERSON] [43] proposed different approaches for analyzing the soft soil stabilized with PVD in plane-strain conditions. These approaches were basically applied to unit cell concept using a single PVD, and FEA converts from axial symmetry to plane-strain conditions by altering the distance between vertical drains and/or the permeability of the ground around the vertical drain.  
The main objective of this research is to analyze the accuracy and feasibility of these matching methods in FEA by considering the smear zone, which is the soil disturbance due to the placement of PVDs.  
All matching methods were developed based on the unit cell concept with single vertical drain. For this purpose, large-scale consolidometer experimental research was carried out by [PERSON] [44] and [PERSON] et al. [45] in the laboratory. For this reason, in this paper, the experimental of laboratory consolidometer was examined with FEA to analyze the accuracy of these matching methods. In this section, the laboratory consolidometer experiment in the literature ([PERSON] et al. [45]) is first modeled as axisymmetric, and the parameters used in the analyzes are validated. Then, the experimental setup is converted to plane-strain conditions using matching methods, and the numerical analyses are compared with the experimental measurements.  
In the second part of this study, a real embankment with PVD-improved multilayered ground and under numerous vertical drains was converted into plane-strain conditions to examine the effectiveness of these matching methods. Following that, FEA results were obtained by comparing the settlement and EPP distributions to field measurements.