## 3 Calibration and Application
### Case 1: A Homogeneous Slope
#### 3.1.2 Result of Homogeneous Slope
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Method**} & \multicolumn{2}{c}{\(\mathbf{R^{\text{M}-IFF}}\)**by Equation (14)**} & \multicolumn{2}{c}{\(\mathbf{R^{\text{M}-EFF}}\)**by Equation (20)**} \\ \hline \multirow{3}{*}{UBM} & \(M=k_{F}\) & 297.49 & 297.49 \\  & \(M=k_{\gamma}\) & 303.78 & 303.78 \\  & \(M=k_{m}\) & 308.13 & 308.13 \\ \hline \multicolumn{2}{c}{LEM} & 503.47 & / \\ \hline \multicolumn{2}{c}{FEM} & 453.04 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of homogeneous slope failure risk. Figure 6: Homogeneous slope failure modes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Failure Mode** & **Failure Area** & **Failure Times** & **Failure Probability (\%)** & **Failure Risk (m\({}^{2}\))** \\ \hline \multirow{3}{*}{\(R_{k}^{k_{r}(t_{m})-\text{IFP}}\)} & Mode 1 & 42.86–43.30 & 2 & 0.2 & 86.15 \\  & Mode 2 & 48.85–50.14 & 3 & 0.3 & 148.31 \\  & Mode 3 & 63.03 & 1 & 0.1 & 63.03 \\ \hline \multirow{3}{*}{\(R_{k}^{k_{r}(t_{m})-\text{IFP}}\)} & Mode 1 & 42.86–45.19 & 2 & 0.2 & 88.04 \\  & Mode 2 & 50.37–53.93 & 3 & 0.3 & 154.83 \\  & Mode 3 & 60.91 & 1 & 0.1 & 60.91 \\ \hline \multirow{3}{*}{\(R_{k}^{k_{m}(t_{m})-\text{IFP}}\)} & Mode 1 & 44.20–45.19 & 2 & 0.2 & 89.62 \\  & Mode 2 & 52.50–54.05 & 3 & 0.3 & 159.91 \\ \cline{1-1}  & Mode 3 & 58.59 & 1 & 0.1 & 58.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of homogeneous slope failure modes. Figure 7: Histogram of homogeneous slope failure area. analyzing slope stability. Unfortunately, the constitutive relation of soil mass is complex and there is no unified constitutive model to characterize it at present. In addition, the FEM contains more human factors when judging slope failure modes. 2. Three slope failure modes are obtained based on \(k_{F}(t_{m})\), \(k_{\gamma}(t_{m})\) and \(k_{m}(t_{m})\) by the UBM. The failure probability of each failure mode is equal, but there are slight differences in the failure risk of each failure mode and overall failure risk. Theoretically, there is only one slope limit state under the action of each random field, which corresponds to a unique external overload coefficient, bulk overload coefficient and slope stability coefficient. However, due to the influence of calculation errors, rounding errors and calculation accuracy, the accumulation of subtle differences is caused. 3. Table 4 compares the calculation results of the UBM, LEM and FEM. It can be observed that the failure risk obtained by Equations (14) and (20) based on the UBM are the same. However, it should be noted that Equation (14) is the slope failure risk calculation based on IFP. Therefore, it is necessary to first count all slope failure modes, including the failure risk coefficient and failure probability of each failure mode; Equation (20) is the slope failure risk calculation based on EFP by the failure probability and failure risk coefficient of each discrete element, which can be easily obtained via the element failure function Equations (15)-(17) and the element failure probability Equation (18) proposed in this paper.