## 3 Results
### Reliability Methods Suitability Assessment  
Reliability method suitability assessments were performed using the criterion defined in Section 2.4. The results were shown in Tables 8-11. Table 8 shows the results of suitability assessment of the ULS of shallow foundation from this study. Neither of the FOSM methods, except FOSM analytical-LN, satisfy the proposed criterion. More sophisticated methods, such as the Monte Carlo, FORM and Simplified FORM, meet the criterion. Despite the complex formulation of the reliability integral, their error values are negligible. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Sliding on Sand**} & \multicolumn{3}{c}{**Sliding in Clay**} \\ \cline{2-7}
**Method** & \begin{tabular}{c} **Error** \\ **(Absolute Value)** \\ \end{tabular} & \begin{tabular}{c} **Acceptable** \\ **Error** \\ \end{tabular} & \begin{tabular}{c} **Meet the** \\ **Criteria** \\ \end{tabular} & \begin{tabular}{c} **Error** \\ **(Absolute Value)** \\ \end{tabular} & \
\begin{tabular}{c} **Acceptable** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Meet the** \\ **Criteria** \\ \end{tabular} \\ \hline Simplified FORM & 0.00 & & Yes & 0.02 & & Yes \\ Taylor Series-N & 0.38 & & No & 0.07 & & Yes \\ PEM-N & 0.28 & & No & 0.34 & & No \\ PEM-LN & 0.04 & & Yes & 0.16 & & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Reliability methods suitability assessment in the case of retaining wall [2] according to the proposed criteria. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Mean Error [Absolute Value]** & **Mean Error [\%]** \\ \hline FOSM analytical-LN & 0.16 & 6.1 \\ PEM -LN & 0.30 & 11.3 \\ Taylor Series-LN & 0.43 & 16.1 \\ PEM-N & 1.57 & 59.2 \\ FOSM analytical-N & 1.24 & 46.7 \\ Taylor Series-N & 1.30 & 48.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Errors of FOSM analytical, Taylor Series and PEM methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Error (Absolute Value)** & **Acceptable Error** & **Meet the Criteria** \\ \hline Monte Carlo & \(3\times 10^{-3}\) & & Yes \\ FORM & \(8\times 10^{-3}\) & & Yes \\ Simplified FORM & 0.05 & & Yes \\ FOSM analytical-LN & 0.16 & & Yes \\ PEM-N & 0.29 & 0.25 & No \\ Taylor Series-LN & 0.42 & & No \\ PEM-N & 1.08 & & No \\ FOSM analytical-N & 1.24 & & No \\ Taylor Series-N & 1.35 & & No \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Reliability methods suitability assessment for the case of ULS of shallow foundation according to the proposed criteria. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**CASE 1 **} & \multicolumn{3}{c}{**CASE 2 **} \\ \cline{2-5}
**Method** & \begin{tabular}{c} **Error** \\ **(Absolute Value)** \\ \end{tabular} & \begin{tabular}{c} **Acceptable** \\ **Error** \\ \end{tabular} & \begin{tabular}{c} **Meet the** \\ **Criteria** \\ \end{tabular} & \begin{tabular}{c} **Error** \\ **(Absolute Value)** \\ \end{tabular} & \
\begin{tabular}{c} **Acceptable** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Meet the** \\ **Criteria** \\ \end{tabular} \\ \hline Taylor Series-LN & 0.84 & & No & 0.78 & & No \\ Taylor Series-N & 0.48 & No & 1.00 & & No \\ PEM-N & 0.27 & No & 1.19 & 0.5 & No \\ Simplified FORM & 0.13 & & Yes & 0.03 & & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Reliability methods suitability assessment in the case of stability of embankments [1] according to the proposed criteria. Similar results were obtained for the reliability methods suitability assessment in the case of the stability of embankments from [1]. The analysis used data from Table 1, and the assessment results were shown in Table 9. As in the case studied by this paper, the control method of choice is the Direct Integration method. The Taylor Series method and the PEM do not meet the criterion, while Simplified FORM does, as in the previous example.