## 3 Methods
### Established Dataset  
To eliminate the influence of the scale effect, the data used in this study were obtained from centrifuge experiments [23] conducted at the University of Western Australia (UWA) with an acceleration of 20\(\times\)\(g\). In these centrifuge experiments, fine, dry silica sand [46; 47] was used and prepared by air pluviation to control the relative density of soil in the range of \(\sim\)85-96% at single gravity. The model anchors used in the centrifuge experiments, as shown in Figure 5a, consisted of a shaft, which can be divided into several sections with different lengths, plates, and anchor caps; all the anchors were manufactured from aluminum. Model anchors were placed with a \"wished-in-place\" approach at relevant embedment depths to avoid the installation effect. This was achieved by pausing pluviation when the soil reached the targeted height for the lowermost helix or plate. At this point, the plate or helix with the first shaft extension segment was located carefully on the sample surface, and pluviation commenced until the sample height reached the targeted location for the next helix. The information about the dimension of helical anchors and the UWA sand used in these centrifuge experiments are shown in Table 1. The details about the setup are shown in Figure 5b. During the experimental process, the model anchors were pulled by applying a force on the anchor cap through a hook; the force was then captured by a load cell attached to the hook. The relevant parameters and results of 33 experiments are listed in Table 2. In the predictive models, the relative density of soil, \(Dr\), embedment ratio, \(H/D\), helix spacing ratio, \(S/D\), and the number of helices, \(n\), were treated as input parameters; the anchor mobilization distance, \(u_{\text{p}}\), and the ultimate monotonic uplift resistance, \(Q_{\text{u}}\), were treated as output parameters. Table 3 contains a summary of the statistical description of the model's inputs and outputs. The authors note that variations in \(Dr\) in the current study were relatively small as we are focusing primarily on dense sand. In addition, the difficulty  
Figure 4: General process of GBDT–PSO model construction and evaluation. involved in data collection for loose and medium-dense sand makes the above selection reasonable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Efficient Anchor** & \multicolumn{3}{c}{**Soil**} \\ \hline
**Dimensions** & **Value** & **Properties** & **Value** \\ \hline Helix diameter, \(D\) (mm) & 20 & Specific gravity, \(G_{\text{s}}\) & 2.65 \\ Helix pitch, \(p\) (mm) & 5 & Median grain size, \(d_{\text{50}}\) (mm) & 0.25 \\ Helix thickness, \(t\) (mm) & 2 & Coefficient of uniformity, \(C_{\text{u}}\) & 1.87 \\ Shaft diameter, \(d\) (mm) & 4.7 & Coefficient of curvature, \(C_{\text{c}}\) & 0.938 \\ Number of helix, \(n\) & 0, 1, 2, 3, 4 & Maximum void ratio, \(\epsilon_{\text{max}}\) & 0.703 \\ Helix spacing, \(S\) & 1.5, 2, 3, 4.5, 6 \(D\) & Minimum void ratio, \(\epsilon_{\text{min}}\) & 0.516 \\  & & Critical state friction angle, & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The information about the helical anchor and soil [18].