## 4 Conclusions  
This paper has proposed a new method for formulating a monitoring index to address the problem of deviation in monitoring indexes caused by the neglect of material uncertainty in traditional safety monitoring methods, which makes it difficult to accurately and comprehensively determine the true operational status of reactor rock dams. The method adopts the correlated log-normal random field to simulate the uncertainty of the parameters, and it determines the water pressure component through the SFEM and then establishes the SFEMM model. Then, based on the probability density distribution of the dam displacement at different reservoir levels, the boundary value of the displacement confidence interval is calculated, and thus, the monitoring index of the dam displacement is determined. The significance of each physical factor in this method is clear, and the index determination process is efficient and reasonable. By actual engineering case analysis, there are some main conclusions, as follows:  
(1) The SFEMM model established in this paper, considering the uncertainty of the rockfill material, achieves smaller errors in the prediction of the dam displacement, higher prediction accuracy, and a more realistic distribution of the predicted values, compared with other monitoring models. In addition, the variation in the displacement prediction error for different measuring points is small, and the prediction stability is strong, showing the high accuracy and applicability of the model. (2) In establishing the SFEMM model, the minimum sample size for analyzing and calculating should be larger than 400 sets to ensure that the probability density distribution of the dam displacement has a high stability. When the predicted sample size is within 60-80 sets, the prediction accuracy of the model is at a high level. (3) The method proposed in this paper to determine the monitoring index links the structural deformation characteristics and utilizes SFEM to build the water pressure component to consider the material parameters uncertainty of the rockfill, reflecting the deformation mechanism of the dam body more realistically and accurately. The determined monitoring index achieves higher accuracy and adaptability compared to the traditional method, and the monitoring interval is more scientific and reasonable, reducing the waste of human resources caused by multiple warnings. It has a sufficient theoretical basis and a better application effect. (4) It is worth discussing that both the SFEMM model and its corresponding monitoring indexes are based on SFEM analysis results; therefore, the accuracy of the SFEM results has a significant impact on the former. When there are errors in the parameter values, unreasonable random field parameters, and insufficient simulation quantities, the accuracy of the established SFEMM model is inevitably reduced, and even the error is greater than that of traditional statistical models. When there is significant uncertainty in parameter  
Figure 14: Comparison of monitoring indexes. values, parameter inversion can be used to obtain relatively accurate parameter reference values. In addition, the specific impact of parameter values and random field parameters on the accuracy of SFEMM models still requires further exploration by the authors. Conceptualization, L.R. and M.L. ; data curation, L.R. and Y.S. ; formal analysis, L.R. and M.L. ; investigation, Y.S. and S.D. ; methodology, L.R. and M.L. ; software, L.R. and C.M. ; validation, S.D. and J.Y. ; writing--original draft, L.R. ; writing--review and editing, J.Y. and C.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 52279140) and the General Program of Natural Science Basic Research Program of Shaanxi (Youth) (No. 2023-JC-QN-0562). Not applicable. The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.