# Non-Probabilistic Reliability Analysis of Slopes Based on a Multidimensional Parallelepiped Model
## 4 Example Analysis
### Calculation Results and Analysis
#### 4.2.1 Feasibility Validation of the Non-Probabilistic Reliability Analysis Method for the Slope
According to Figure 6, the non-probabilistic reliability indexes of the slope obtained based on the MP-1 model and those obtained based on the MP-2 model are very close and almost equal. Regardless of how the correlation coefficients of the geotechnical parameters change, the calculation results based on the MP-1 model and the MP-2 model are always smaller than those based on the ellipsoid model. None of the values are smaller than the non-probabilistic reliability indexes calculated based on the traditional interval model, which proves again that the non-probabilistic reliability method of the slope based on the multidimensional parallelepiped model not only can take into account the correlation of the uncertain parameters, but also can obtain more appropriate calculation results than the ellipsoid model. 2.3 Influence of Variability of Shear Strength Parameters on the Non-Probabilistic Reliability of the Slope  
The variability of shear strength parameters is also an important factor affecting slope stability. In order to study the influence of the variability of the cohesion \(c\) and internal friction angle \(\varphi\) on the non-probabilistic reliability indexes of the slope, the data of the internal friction angle presented in Table 1 were first kept unchanged, and the cohesion was taken to have five different coefficients of variation (in this study, the coefficient of variation was defined as the ratio of the deviation to the median of the interval of an uncertainty variable, which served to compute the marginal interval of the parameter. For example, when the coefficient of variation \(\delta_{c}\) of the cohesion was taken as 0.5, the marginal interval of the cohesion \(c\) was [7.51, 22.55]), which was taken on the basis of the mean values of the original data, such as 0.1, 0.3, 0.5, 0.7, and 0.9. After randomly generating 25 sets of sample data for each, the influence of the variability of the cohesion on the non-probabilistic reliability indexes of the slope with different correlation coefficients was determined using the method proposed in this paper, and the results are shown in Figure 7.  
Similarly, while keeping the data of the cohesion presented in Table 1 unchanged, the internal friction angle was taken to have five different coefficients of variation on the basis of the mean values of its original data, such as 0.1, 0.3, 0.5, 0.7, and 0.9. After randomly generating 25 sets of sample data for each, the influence of the variability of the internal friction angle on the non-probabilistic reliability indexes of the slope with different correlation coefficients was determined using the method proposed in this paper, and the results are shown in Figure 8.  
As shown in Figures 7 and 8, the non-probabilistic reliability indexes of the slope calculated based on the MP-1 model and the MP-2 model are very close. As the cohesion or the internal friction angle coefficient of variation increases, the non-probabilistic reliability index of the slope decreases. This is consistent with the evaluation obtained using the probabilistic reliability method. When using the probabilistic reliability method to calculate the failure probability of the slope, the stability reliability of the slope is lower when the variability of the cohesion \(c\) or the internal friction angle \(\varphi\) is larger. By comparing Figures 7 and 8, it can also be seen that the variability of the cohesion has a greater impact on the non  
Figure 8: The curve of variation coefficients of the internal friction angle and non-probabilistic reliability indexes under different correlation coefficients. Figure 7: The curve of variation coefficients of the cohesion and non-probabilistic reliability indexes under different correlation coefficients. probabilistic reliability index of the slope for the example slope, which indicates that the stability of the slope is more sensitive to the variability of the cohesion.