# Probabilistic Analysis of Infinite Slope Stability Considering Variation in Soil Depth
## 4 Conclusions  
Soil depth is a crucial parameter in landslide assessments and is known to exhibit high spatial variation compared with other soil properties. In this study, the variability of soil depth was identified, and its influence on the probabilistic analysis of slope stability was assessed. Based on the study results, the following conclusions were drawn:  
1. To identify the variability of soil depth on natural slopes, a method utilizing seismic wave surveys was introduced. Seismic refraction survey data were collected from 70 slopes located in South Korea. Each slope was segmented into 5 m horizontal intervals, and soil depth was estimated based on a P-wave velocity of 700 m/s;
2. The average soil depth across 70 slopes was 2.5 m, with an average COV of 29%, indicating high variability. The average skewness and kurtosis of soil depth were 0.19 and 2.32, respectively. These findings indicate that the distribution of soil depth was relatively symmetrical, and the data were concentrated around the center, supporting the assumption that the data follows a normal distribution;
3. The average soil depth and its COV were found to have a negative correlation, with a p-value of 0.0016. Accordingly, lower soil depth could be associated with higher variability in the soil depth within a slope;
4. The probabilistic analysis results showed that Pf could vary significantly depending on whether the variability of soil depth was considered, as well as the saturation depth. When the saturation depth was relatively low, Case 1 (with the variability of soil depth not considered) exhibited the lowest Pf. However, as the saturation depth approached the maximum soil depth, Pf in Case 1 increased rapidly, resulting in the highest Pf;Global sensitivity analysis results show that soil depth had a negative correlation with Pf, and its overall effect on Pf was greater compared with that of the shear strength of the soil. Therefore, Pf showed significant differences depending on whether soil depth variability was considered, indicating the need to consider this factor in the probabilistic analysis of slope stability;
6. In this study, a P-wave velocity of 700 m/s was applied as the criterion for estimating soil depth. However, this value may vary depending on the geological conditions. To accurately estimate and determine the distribution of soil depth, it is necessary to verify this through investigations at specific points. These findings underscore the importance of accounting for soil depth variability in slope stability assessments, providing critical insights for future studies and practical applications in landslide risk assessment.  
Conceptualization, T.K. and T.B.; data curation, T.B. and D.K.; methodology, T.K. and T.B.; validation, T.B. and D.K.; writing--original draft preparation, T.K. and T.B.; writing--review and editing, D.K.; visualization, D.K.; funding acquisition, T.B. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2022R1A2C4002583).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.