# Prediction of Pile Axial Bearing Capacity Using Artificial Neural Network and Random Forest
## 5 Results and Discussion
### Comparison with Empirical Equations and Multi-Variable Regression  
In this section, comparisons of the RF model on the prediction of bearing capacity of driven piles are conducted with traditional formulas. These formulas used SPT value to estimate the bearing capacity of driven pile, as in the works of [PERSON] (1976) [4], [PERSON] (1982) [7], [PERSON] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Part** & **Method** & **Avr. R\({}^{2}\)** & **StD. R\({}^{2}\)** \\ \hline \multirow{2}{*}{Testing} & ANN & 0.811 & 0.318 \\  & RF & 0.861 & 0.277 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of the Monte Carlo simulations  
Figure 8: Scatter plot of R\({}^{2}\) values for 1.000 simulations for (**a**) RF, (**c**) ANN and the corresponding histograms of R\({}^{2}\) values, (**b**) RF, (**d**) ANN. (1995) [10], [PERSON] et al. (2008) [8], and AIJ (2004) [11]. The values for unit base (Q\({}_{\text{b}}\)) and unit shaft (Q\({}_{\text{s}}\)) resistance are summarized in Table 7.  
The value of the bearing capacity could be then estimated in function of Q\({}_{\text{b}}\) and Q\({}_{\text{s}}\), following the well-known formula  
\[\text{P}_{\text{u}}=\text{D}^{2}\text{Q}_{\text{b}}+\sum_{i=1}^{n}4\text{DL}_{ \text{i}}\text{Q}_{\text{s}(i)} \tag{5}\]  
where \(n\) refers to the number of soil layers, \(\text{L}_{\text{i}}\) denotes the thickness and Q\({}_{\text{s}(\text{i})}\) indicates the value for unit shaft resistance of the i\({}^{\text{th}}\) soil layer which piles penetrated through. In addition, the use of classical MVR to predict the bearing capacity of pile was also applied. Multi-variable regression technique is commonly used in several studies, such as [PERSON] et al. [70] and [PERSON] et al. [71] to predict the properties and chemical composition of soil. The regression coefficient results are shown in Table 8.  
Figure 9 and Table 9 show several results and detail information of measured pile bearing capacity of the testing part, along with the bearing capacity predicted by RF model and MVR, [PERSON] (1976), Shioi and Fukui (1982), [PERSON] (1995), [PERSON] (2008), and AIJ (2004). The RF was found the best model in predicting the experimental pile bearing capacity. Indeed, RF significantly outperformed traditional approaches with respect to R\({}^{2}\), RMSE, MAE (i.e., R\({}^{2}\) = 0.866, 0.702, 0.467, 0.485, 0.334, 0.391, 0.611; MAE = 2.924, 94.267, 77.830, 280.727, 312.297, 340.668, 205.72; RMSE = 98.161, 183.046, 224.5, 340.606, 483.335, 400.470, 265.53 using RF and [PERSON] (1976), [PERSON] and Fukui (1982), [PERSON] (1995), [PERSON] (2008), and AIJ (2004), respectively). The results also showed that the MVR was less accurate than the RF model, but both models gave better accuracy than traditional formulas. It is worth noticing that these formulas were developed for granular soil. However, the effect of soil type in estimating the bearing capacity of piles was neglected in this study, knowing that such bearing capacity depends on soil types. The main purpose of this section was to demonstrate the higher prediction capacity of ML approach compared with empirical equations even without information related to soil types.