# Evaluation of Methods Based on CPTu Testing for Prediction of the Bearing Capacity of CFA Piles
## 3 Results
### Analysis of Predicted Pile Bearing Capacity
Unfortunately, this issue cannot be confirmed by the pile load tests but several studies show lower influence of pile tip on the bearing capacity of bored piles (replacement piles) [41, 64]. Comparison of the overall predicted pile bearing capacity based on prediction methods \(Q_{p}\) and measured bearing capacity \(Q_{m}\) is plotted in Figure 8.  
Evaluation of ability to predict the pile bearing capacity based on CPT output was initially performed through \(Q_{m}/Q_{p}\) plot analysis. Ideally, \(Q_{m}/Q_{p}\) pair represented by the data point should create the best fit line, which intersects the beginning of the x- and y-axes, with the slope of 1 (or 45\({}^{\circ}\)) within the set of \(Q_{m}/Q_{p}\) couples. However, the slope of the line differs from the ideal slope for real data. Coefficient of determination \(R^{2}\) indicates the proportionate amount of variation in the response of variable \(Q_{p}\) explained by the independent variable \(Q_{m}\) in the linear regression model. The larger the \(R^{2}\) is, the more the variability is explained by the linear regression model. We can judge the ability of particular method to predict the pile bearing capacity using this coefficient. Because the best fit line should intersect the beginning of axes and should be in 45\({}^{\circ}\) slope, we cannot directly apply \begin{table} \end{table} 
Table 3: Bearing capacity components and overall pile bearing capacity. linear regression. Such a regression line may not be in 45\({}^{\circ}\) slope and calculated coefficient of determination is not reliable. The coefficient was calculated for a 45\({}^{\circ}\) line which intersects the beginning of the x- and y-axes (red line in Figure 9). We can utilize the regression line formula \(Q_{\#t}\) to evaluate the over- or underestimation of pile bearing capacity. The least square method was applied to construct the regression line for the particular prediction method (black line in Figure 9). The UniCone method overestimates the pile bearing capacity by 8%, while the other two methods underestimate the bearing capacity by 5 or 4%, respectively (Table 4). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Best Fit Calculation**} & \multicolumn{3}{c}{**Statistic**} & \multicolumn{3}{c}{**Complexative**} & \multicolumn{3}{c}{**Log-Normal**} & \multicolumn{3}{c}{**Overall Rank**} \\  & \multicolumn{3}{c}{**and Regression**} & \multicolumn{3}{c}{\(Q_{\#}\)/\(Q_{m}\) Ratio**} & \multicolumn{3}{c}{**Probability**} & \multicolumn{3}{c}{**Distribution**} & \multicolumn{3}{c}{**Overall Rank**} \\ \hline Method & \(Q_{\#t}\)/\(Q_{m}\) & \(R^{2}\) & R1 & \(\mu\) & \(\sigma\) & R2 & \(P_{50}\) & \(P_{90}\) & R3 & RL (\%) & R4 & RI & R \\ \hline UniCone & 1.08 & 0.78 & 2 & 1.07 & 0.20 & 1 & 1.09 & 1.34 & 1 & 66.65 & 1 & 5 & 1 \\ \hline LCPC & 0.95 & 0.89 & 1 & 1.08 & 0.30 & 2 & 1.05 & 1.60 & 2 & 53.20 & 2 & 7 & 2 \\ \hline EC 7—2 & 0.94 & 0.65 & 3 & 1.09 & 0.53 & 3 & 0.90 & 2.08 & 3 & 33.70 & 3 & 12 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of efficiency of prediction methods. Figure 8: Pile bearing capacity based on prediction methods and measurements. Figure 9: Regression and 45\({}^{\circ}\) lines and coefficients of determination \(R^{2}\) for measured and predicted pile bearing capacity data pairs. (**a**) UniCone method; (**b**) LCPC method; (**c**) EC 7—2 method. The probability density function and cumulative probability chart for ranking of prediction methods are plotted in Figure 10.  
Overall efficiency of methods to predict the pile bearing capacity was evaluated by the rank index (RI) as a sum of ranks of method in particular criteria R1 to R4 (Table 4). Lower rank index (RI) means higher efficiency of method for bearing capacity prediction [24; 50; 63]. Coefficient of determination \(R^{2}\) was considered in R1 criterion. Higher value means stronger relation between measured and predicted bearing capacity and higher reliability in bearing capacity prediction.