## 3 Test Results and Analyses
### \(d_{m}\)/\(D_{h}\) and \(D_{s}\)/\(D_{h}\) Analyses of Test Results for \(N_{c}\)  
As shown in Figure 8, the curves representing the uplift bearing capacity coefficient \(N_{c}\) versus the shaft-to-plate diameter ratio for the four different diameter ratios indicate that \(N_{c}\) decreases as the shaft-to-plate diameter ratio increases. This occurs because, when the diameter of the anchor helix remains constant, increasing the pitch (i.e., increasing the shaft-to-plate diameter ratio) leads to greater spacing between the helical threads of the anchor. This increase in spacing reduces the bearing area of the helical anchor and decreases the friction between the anchor and the soil. Therefore, as the shaft-to-plate diameter ratio increases, \(N_{c}\) decreases. In Figure 8, the variation in \(N_{c}\) with a decreasing diameter ratio is shown as follows: (1) For a diameter ratio of 0.43, as the shaft-to-plate diameter ratio increases from 0.0375 to 0.3375, \(N_{c}\) decreases by 13.9%. (2) For a diameter ratio of 0.33, as the shaft-to-plate diameter ratio increases from 0.0375 to 0.3375, \(N_{c}\) decreases by 12.6%. (3) For a diameter ratio of 0.26, as the shaft-to-plate diameter ratio increases from 0.0375 to 0.3375, \(N_{c}\) decreases by 9.5%. (4) For a diameter ratio of 0.22, \(N_{c}\) decreases by 9.5% as the shaft-to-plate diameter ratio increases from 0.0375 to 0.3375. These results indicate that \(N_{c}\) decreases as the shaft-to-plate diameter ratio increases. Furthermore, as the diameter ratio decreases, the rate of the decrease in \(N_{c}\) gradually slows and tends to stabilize. In Figure 9, the relationship between the pullout load-bearing capacity coefficient \(N_{c}\) and the depth ratio for four different diameter ratios can be observed. Initially, as the depth ratio increases, \(N_{c}\) typically shows a gradual upward trend. However, as the depth ratio continues to increase, this growth trend gradually slows until a critical depth ratio is reached, at which point \(N_{c}\) stabilizes and does not increase further with additional increases in the depth ratio. This behavior occurs because increasing the embedment depth increases the effective length of the anchor within the soil, enhancing the friction and bond between the anchor and the soil, leading to a gradual increase in \(N_{c}\). However, as the embedment depth increases further, the lateral constraint of the soil also increases, making the stress field around the helical anchor more compact. This compaction reduces the relative displacement and deformation of the helical anchor, resulting in a gradual decrease in the growth rate of \(N_{c}\). Figure 8: Curve of the relationship between the coefficient of uplift bearing capacity and the ratio of the helical diameter. In Figure 9, it is assumed that the \(N_{c}\) values for the four diameter ratios increase with the depth-to-diameter ratio (\(H\)/\(D_{H}\)) in the interval \(0.5\leq H\)/\(D_{H}\leq 4\); this is referred to as the change interval. The \(N_{c}\) values that stabilize in the interval \(H\)/\(D_{H}\geq 4\) are referred to as the stable interval. As seen in Figure 9, within the change interval, \(N_{c}\) gradually decreases hierarchically as the diameter ratio increases. Thus, the behavior of the four diameter ratios in the change interval can be approximated by a linear equation with the same slope. In the stable interval, all diameter ratios converge to the same fixed \(N_{c}\) value. However, in the change interval, the initial \(N_{c}\) value decreases as the diameter ratio increases. Based on the data presented in Figure 8, we calculated the bearing capacity coefficients, \(N_{c}\), of the pullout-resistant system for four different diameter ratios and presented their average values in Figure 10, where \(N_{c,max}\) = 9.4. As the shaft-to-plate diameter ratio (\(d_{m}\)/\(D_{H}\)) increases, the ratio of the average value of each point to the maximum value of \(N_{c}\) is 1, 0.98, 0.95, 0.91, and 0.89.