## 5 Conclusions  
A slope failure risk analysis method based on EFP was proposed. A UBM parallel calculation program is prepared in Python to obtain the distribution law of external overload coefficient, bulk overload coefficient and slope stability coefficient, which provided an efficient calculation method for slope failure risk. Through in-depth analysis of two examples of homogeneous slope and heterogeneous slope, the effectiveness of the proposed method is verified, and its main conclusions are as follows:  
1. The slope failure risk calculation method based on EFP provides engineers with practical reference significance for reinforcement design and risk assessment by counting the possibility of slope failure through \(k_{F}(t_{m})\), \(k_{\gamma}(t_{m})\) and \(k_{m}(t_{m})\) and the difference in the spatial distribution of the slope failure area through the information of element location. 2. Compared with traditional failure risk analysis methods, the proposed method based on EFP can not only effectively avoid the problem of the stability coefficient between multi-failure modes and the correlation between slide volume, but also accurately quantify the failure risk of slope multi-failure modes. In particular, when calculating the overall failure risk of slope with multi-failure modes, it can be obtained only according to the failure probability and the failure risk coefficient (the area of the area) of the element, avoiding the statistics of failure modes and the calculation of the failure risk coefficient (the area of each failure mode). This method has important theoretical value for slope failure risk assessment. 3. The traditional LEM has a high rate of error in the failure risk analysis of a heterogeneous slope. In this study, the failure of the slope element is judged by the double attributes of \(k_{F}(t_{m})\), \(k_{\gamma}(t_{m})\), \(k_{m}(t_{m})\) and the centroid velocity of the element. The failure of the slope is judged by \(k_{F}(t_{m})\), \(k_{\gamma}(t_{m})\) and \(k_{m}(t_{m})\) and the failure area of the slope is located via the centroid velocity of the element. This method can capture all potential slope failure modes simultaneously, thus obtaining more reasonable results than the LEM. 4. The failure risk of a slope is essential in order to calculate the influence caused by the slope failure. In this paper, only the area is used to measure the slope failure risk and other factors are ignored, such as the importance of the slope, the environmental impact assessment, the vulnerability of the bearing body, etc. Although a simplified failure consequence assessment method is adopted, it does not affect the applicability of the proposed method. If there is a more accurate element failure consequence, it should simply be replaced. 5. It should be noted that the UBM parallel computing program prepared in Python can make full use of the advantages of multi-threaded parallel computing on a small workstation. Theoretically, it could call 64 threads at the highest level for parallel computing of each sample, but only 42 threads are called due to other operational requirements. When GEO-studio software is called by MATLAB to calculate each sample, random fields need first to be generated through pre-processing, then the calculation of each sample is carried out on this basis. The 8-node FEM based on OptumG2 can only obtain the result of one sample each time and cannot carry out large-scale parallel calculation. Conceptualization, P.P., Z.L., X.Z., W.Z. and W.D. ; methodology, X.Z. ; software, P.P. and Z.L. ; validation, X.Z. ; formal analysis, P.P. ; investigation, P.P. and Z.L. ; resources, Z.L. and X.Z. ; data curation, W.D. ; writing--original draft preparation, P.P. and Z.L. ; writing--review and editing, P.P. and Z.L. ; visualization, X.Z. and W.Z. ; supervision, P.P., W.Z. and Z.L. ; project administration, X.Z. and W.D. ; funding acquisition, Z.L. and X.Z. All authors have read and agreed to the published version of the manuscript.