## 5 Summary and Conclusions  
The purpose of this paper was to investigate the effects of ACFs on the reliability analysis of layered soil slopes, where soil properties of different soil layers are considered by different ACFs. Five commonly used classical ACFs and a non-classical model (W-M model) in the literature constituting different cases were investigated. A two-layered cohesive slope and a cohesive-frictional slope with a weak seam were studied to illustrate the influence of ACFs and SOFs on the reliability analysis. The results showed that the autocorrelation structures generally have an influence on the reliability analysis of layered slopes. The ACF types have little influence on the slope reliability, whereas the SOFs can significantly affect the reliability assessment. When different ACFs are used for different soil layers, the reliability results are not sensitive to the change of ACFs either in the lower or upper soil stratum. However, it was found that when the SEF and CEF are used, the reliability results can be quite different from those estimated from other ACFs or from the conventional analysis. The reliability results from SEF tend to be underestimated, whereas those from the CEF can be overestimated. Furthermore, for layered slopes, there might be different SOFs for different soil layers, suggesting that the conventional reliability analysis with the same SOFs for different soil layers could be biased. It is also noted from the two examples that when two ACFs used for two soil layers are exchanged, the reliability results can be significantly varied. In the W-M model, the reliability of the slope would be affected by the smoothness parameter, where the probability of failure increases with the increase of the smoothness parameter to some extent.  
To conclude, owing to the nature of soil spatial variability, the autocorrelation structure plays an important role in slope reliability analysis and should be carefully considered in practical reliability analysis. To accurately assess the reliability of slopes, geodata from the field and/or laboratory tests should preferably be used to estimate the autocorrelation structure. For practical situations where geotechnical data is limited, sensitivity studies are necessary in order to obtain a desirable safety assessment. The current study, therefore, can serve as a useful reference for such situations. It is also worthwhile to point out that only lognormal distributions were considered for describing the stochastic nature of soil properties in the current study. This can be a potential limit of this study because lognormal is always skewed to the right and the degree of skewness increases as the standard deviation increases for a fixed mean value. Furthermore, it is also worthwhile to study the effect of slope geometry uncertainty in the future study.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Case** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Clay 1 & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) & 0.1 & 0.2 & 0.5 & 1.5 \\ Clay 2 & \(\infty\) & 0.1 & 0.2 & 0.5 & 1.5 & \(\infty\) & \(\infty\) & \(\infty\) & \(\infty\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Different cases for the study of the effects of the smoothness parameter \(\
u\).  
Figure 13: Probability of failure for various cases with the W–M model.  
**Author Contributions:** Conceptualization, L.L.; Data curation, Y.L. and J.L.; Investigation, Y.L. and J.L.; Project administration, S.Z. and L.L.; Software, J.L.; Supervision, S.Z.; Writing--original draft, J.L. and Y.L.; Writing--review & editing, S.Z. and L.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by grants from the Natural Science Foundation of China (Project Nos. 41902291 and 41872186).  
**Conflicts of Interest:** The authors declare no conflict of interest.