## 4 Conclusions  
This research investigated the patterns of soil plug formation during pile driving and the effects of pile diameter on the plugging effect by employing DEM simulation of physical model pile tests conducted in previous research. It enabled the direct capture and visualization of the stress state within the soil plug along with the particle displacement field, which is highly challenging in physical experiments. The simulation was carried out by controlling the displacement of the pile from the physical test against the simulation time and was verified in terms of soil-soil and soil-wall interactions. Subsequent simulations of piles with outer diameters of 90, 100, 110, and 130 mm were performed to further investigate the influence of pile diameter on the soil plug formation and its internal state. Based on the aforementioned results, the following conclusions can be drawn:  
* Successful simulation of soil plug formation through the DEM was conducted and verified by calibrating both biaxial compression test results and plug length indices from the simulation to the physical test results. * Plug length indices (e.g., _PLR_ and _IFR_) started at approximately 1 at the beginning of the penetration and generally decreased with the progression of pile installation. The _PLR_ exhibited a gradual decrease without any fluctuation, ending at 0.5, whereas the _IFR_ showed significant fluctuation, including a sudden increase from 0.006 to 0.5 and a drastic drop from 0.8 to 0.1. Hardening and release in the horizontal stress within the soil plug were accompanied by a sudden drop and increase in the _IFR_, respectively. It is considered that the _IFR_ better indicates the internal state of the soil plug than the _PLR_. * Due to the high degree of spatial variance in the internal horizontal stress during penetration, dividing the soil plug into three equal parts based on length results in each section showing distinctive variations in mechanical behavior. While the top  
Figure 15: Variation in the horizontal stress inside the soil plug at the bottom section for each model. section did not exhibit any stress variation due to penetration, the middle and bottom sections experienced substantial changes in the horizontal stress, surging from the overburden stress to a maximum stress of 349 kPa, corresponding to a coefficient of lateral earth pressure (\(K\)) of 3.4. The _IFR_ of 0.1 at this stage also indicated a high degree of plugging state. A phenomenon was also observed where the excessive horizontal stress developed at the bottom section in the former penetration stage was pushed upward to the middle section with a slight alleviation in magnitude during subsequent impact driving. * The active length, where excessive horizontal stress developed within the soil plug, was measured as 2 \(D_{in}\) from the pile tip at specific penetration phases in which the degree of plugging was highly developed. The location of the maximum horizontal stress within the active length was 1 \(D_{in}\) from the pile tip. * The plug length increased with pile diameter, as indicated by larger _PLR_ and _IFR_ values. However, the longer formation of the soil plug did not indicate a trend of the internal stress state since the maximum horizontal stress per each impact driving was not significantly affected by the pile diameter. * In the results from all parametric models, the earliest plugging effect was observed at a penetration progress of 60-65% of the total penetration, where the maximum horizontal stress developed regardless of the pile diameter. * The beta index obtained from the known _PLR_ and \(\beta\) relationship (\(\beta_{PLR}\)) was determined to be 0.6, while the one obtained from the direct stress state within the soil plug (\(\beta_{stress}\)) was 1.7. It showed that for a given plugging state, there was a possibility of underestimating the inner skin friction of an open-ended pile if it was designed in terms of plug length indices.