# A Novel Approach Proposal for Estimation of Ultimate Being Capacity Based on Pile Loading Test Data
## 3 Results and Discussion
### Evaluation Methods of Pile Loading Test Based on Mathematical Models
As a result of the evaluations, although the proposed method gave results close to the Alku method among the pile loading test evaluation methods, since the load-settlement values of the linear section after failure were not used in piles that collapsed, excessive iteration was prevented [24]. Accordingly, the proposed method, as the graphical method, offers a more reasonable value of failure load, which is close to the truth in the parabola part during failure. The descriptive statistical values of the ultimate bearing capacity values calculated for the 8 methods and the proposed method in the study were calculated for each method and shown in Figure 10:0 When Table 4 is examined, it is seen that the highest average ultimate bearing capacity values were calculated by the [PERSON] method with 990.6 tons and the Chin-Kondner method with 976 tons, respectively [21; 23]. It is seen that the lowest average ultimate bearing capacity values were calculated by the proposed method with 623.4 tons and the [PERSON] and Jackson methods with 628.8 tons, respectively [10]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Number of Data**} & **Value** & **Minimum** & **Maximum** & **Avarage** & **Standard** & **Standard** & **Variance** \\  & & **Range** & **Value** & **Value** & **(tons)** & **Error** & **Deviation** & **(ton2)** \\ \hline Chin-Kondner [21] & 8 & 1913.0 & 235.0 & 2148.0 & 976.0 & 230.3 & 651.5 & 424,442.0 \\ [PERSON] (1999) [23] & 8 & 2445.0 & 230.0 & 2675.0 & 990.6 & 277.2 & 784.0 & 614,710.3 \\ [PERSON] [24] & 8 & 1482.0 & 209.0 & 1691.0 & 729.0 & 169.2 & 478.6 & 229,052.6 \\ Recommended Method & 8 & 1059.0 & 206.0 & 1265.0 & 623.4 & 134.4 & 380.1 & 144,465.7 \\ [PERSON] (1995) [5] & 8 & 1398.0 & 277.0 & 1675.0 & 783.0 & 178.5 & 504.8 & 254,861.7 \\ [PERSON] and [PERSON] [4] & 6 & 1338.0 & 246.0 & 1584.0 & 770.7 & 207.5 & 508.4 & 258,442.3 \\ [PERSON] and [PERSON] [9] & 6 & 1377.0 & 211.0 & 1588.0 & 764.2 & 209.3 & 512.7 & 262,867.0 \\ [PERSON] and [PERSON] [10] & 6 & 1164.0 & 204.0 & 1368.0 & 628.8 & 171.7 & 420.6 & 176,893.8 \\ Plaxis 2D [55] & 8 & 1152.0 & 284.0 & 1436.0 & 739.0 & 156.2 & 441.7 & 195,062.6 \\ \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistical values for the bearing capacity calculation methods and the proposed method. When the correlation table (Table 5) was examined, it was seen that there were very high and positive correlations between the methods. The highest correlation coefficient (0.998) was between [PERSON] and Kurkur and O'Neil and Reese methods at a high level, while the lowest correlation coefficient was between [PERSON] and finite element method (Plaxis 2D) methods with 0.837, which indicated a high level of coefficient [4; 9; 24; 55]. On the other hand, it was understood that the highest correlation coefficient between the proposed approach and the other approaches was between the Chin-Kondner method with 0.984 and the finite element method (Plaxis 2D) with 0.911 [21; 55]. An ANOVA test was applied to the ultimate bearing capacity averages, and there are two hypotheses regarding this test:  
H\({}_{0}\): There is no difference among group means (\(p>0.05\));  
H\({}_{1}\): There are significant differences among group means (\(p\leq 0.05\)). It was investigated whether there was a difference between the ultimate bearing capacity values obtained for the eight methods calculated according to the data obtained as a result of the studies and the bearing capacity values obtained for the proposed method by performing multiple comparison tests at the 95% confidence interval (Table 6). Accordingly, it was seen that there was no difference in the 95% confidence interval between the proposed method and the other methods, and the significance (\(p\)) value for all methods was much greater than 0.05. In the study conducted by [PERSON] and [PERSON], different methods were compared in the results obtained from the pile loading test studies conducted in different regions of the city of Nasiriyah [35].