## 5 Analysis
### Relationship between Plugging Condition and the Pile Diameter, Length, and L/D Ratio  
[PERSON] et al. [8] concluded that beyond a certain penetration depth to diameter ratio (L/D) most piles plug. [PERSON] and [PERSON] [50] also determined that as the pile diameter increases, open-ended piles tend to become unplugged; however, these studies did not examine a large number of piles. Thus, the relationship between the plugging condition and piles' geometric properties namely diameter (D), length (L), and L/D ratio was explored in Figure 4, where piles are tagged by their voted overall plugging condition. It should be noted that important information needed to investigate plugging, such as the Plug Length Ratio (PLR), and the Incremental Filling Ratio (IFR) was not available in the databases. Hence, the discussion herein is limited to observed \(Q_{c}\)/\(Q_{m}\) values and their respective pile properties.  
The L/D ratio was plotted against the pile diameter in Figure 4a. Multiple observations were made. It was observed that piles larger than or equal \(\sim\)0.9 m (36 in) in diameter are likely to be unplugged (31 out of 39 cases), irrespective of L/D ratio, while piles with diameters less than 0.5 m (20 in) are likely to be plugged (12 out of 15 cases), which is expected since small diameter piles have a higher likelihood of being plugged and vice versa. This observation has critical implications for the design of large diameter open-ended piles (LDOEPs), since these are typically defined as piles larger than 36 in (\(\sim\)0.9 m) in diameter. It was also noted that the piles in between vary in terms of plugging conditions,  
Figure 4: Relationship between: (**a**) L/D ratio and pile diameter, (**b**) L/D ratio and pile length, and (c) pile length and diameter, for the average \(Q_{c}\)/\(Q_{m}\) ratio, by the best plugging condition for each pile.  
which suggests that this could be a transition zone between the plugged and unplugged conditions. This is shown in the figure where the shading represents the transition from a zone of plugged high likelihood, to a transition and uncertain zone, and finally a high likelihood unplugged zone. The authors also attempted to separate unplugged from internal plug, as well as internal plug from plugged; however, this was difficult due to the small number of load tests (8 cases) coded as internal plug. Using these two major zones, nearly 80% of the cases in these zones were identified correctly, which is encouraging.  
The relationship between L/D and length for all piles under consideration coded by the voted plugging conditions is presented in Figure 4b. Similarly, the relationship between length and diameter is presented in Figure 4c. It was observed that the majority of the plugged piles are small diameter piles with low L/D ratios (L/D <- 50). No further pattern of plugging is discernable, as the data scatter makes it hard to make conclusive observations regarding pile plugging. In particular, the available data do not support the popular notion that most piles plug beyond a certain L/D ratio. Notably, [PERSON] et al. [8] suggest that piles with L/D smaller than 75 are unlikely to plug, but it is difficult for us to agree considering the data presented in Figure 4. In addition, prior studies suggest that when a pile plugs, load is transferred by arching to the inner pile surface within the first two pile diameters [51]; thus, it was concluded that soil, driving, and load testing conditions have significant effects on plugging of piles, and recommendations based solely on length or L/D are difficult to formulate based on the available data.