# 2D Numerical Analysis of Prefabricated Vertical Drains Using Different Matching Methods
## 1 Introduction  
In recent years, construction projects around the world tend to focus more on low-lying areas, such as peat and organic soil, as a result of rapid population growth. However, these soil layers have a significant impact on vital infrastructures consisting of roads, buildings, and railways due to their relatively low load-bearing capacity [1, 2]. Thus, it is extremely important to consolidate the soil clay layers before starting any construction projects to prevent large settlement. The ground can be consolidated by applying loads to stabilize superstructure work. However, the low vertical permeability requires a considerable amount of time to achieve the target settlement compared to the available construction period [3, 4]. In this case, various vertical drainage systems, such as sand compacting piles and prefabricated vertical drains, have become extensively employed to enhance the soft ground. This idea was initially presented in the 1920s and published in 1926 by an American engineer, [PERSON]. According to [PERSON] [5], [PERSON] proposed using sand drains for the first time to stabilize the mud soil below the highway approach to the San Francisco Oakland Bay Bridge. However, [PERSON] [6] explained that vertical sand drain behavior was not well-known, since the foundation-bearing capacity was assumed to be adequate for a full load right away following installation, resulting in common foundation collapse. Consequently, [PERSON] [7] introduced ground improvement techniques using PVDs, utilizing cardboard wick drains. The technique of installing prefabricated vertical drains (PVDs) under embankment is among one of the most widely employed ways for shortening the consolidation process time which, to dissipate excess pore pressure rapidly, also provide horizontal drainage in addition to vertical, [3]. By using PVDs, the drainage line is reduced from the soil layer's thickness to the drain's effect zone's radius, whichspeeds up consolidation [8]. The durability and performance of PVD are dependent on the specific polymers employed to create the drain and soil properties at the place of installation, which is determined by its discharge capacity [9; 10]. The discharge capacity of PVD is affected by a variety of parameters, such as the type and form of the core, the cross-sectional area of the drain, and the effect of lateral pressure [9; 11; 12]. Some researchers evaluated various types of band-shaped drains in the laboratory to assess the performance of a bent PVD [9; 13; 14; 15; 16; 17]. [PERSON] et al. [15] discovered that the discharge capacity of PVD decreased by up to 10% approximately 200 days of installation. [PERSON] [9] stated that, to ensure that PVD perform properly, the flow capacity must meet a minimum discharge capacity requirement, considering the effects of lateral pressure, drain deformation, and creep. [PERSON] et al. [13] found that discharge capacity should be at least 10-15 m/year under 300-500 kPa lateral stress and for drains up to 20 m in length. However, the average laboratory test values of discharge capacity evaluated by [PERSON] et al. [13] were inadequate, and the amount of acceptable discharge capacity was subsequently increased to 100-150 m\({}^{3}\)/year in soft clay [14]. Several researchers have highlighted the benefits of PVDs, which include an improvement in soil strength [18], reduce the amount of surcharge material needed to attain the specified precompression, and show a reduction in total settlement time as well [19]. Moreover, this method is also capable of improving the rate of road construction while simultaneously having a favorable influence on the environment [20]. However, despite improvements in comprehending the behavior of embankment on soft soil in last decade [21; 22; 23; 24], it remains a problem, and it is difficult in geotechnical engineering to estimate the settlement and excess pore pressure (EPP) of improved subsoils with PVDs. Furthermore, field testing is frequently both a time-consuming and expensive process [25].