## 3 Research Method
### Quantitative Screening of Evaluation Indicators  
The quantitative screening stage is based on the improved grey correlation-Delphi model, aiming at mining the core influencing factors from the qualitatively screened indicators through the combination of mathematical modeling and expert empowerment. The specific process is as follows:  
Improved Grey Correlation-Delphi Model  
Grey correlation analysis is a research method in grey system theory, which assesses the strength of correlation by quantifying the similarity of the dynamically changing characteristics of data series [29]. The core step is to divide the target indicator into reference and comparison sequences and analyze the degree of coincidence between the two change trends; the higher the correlation, the greater the contribution of the indicator to the system's behavioral pattern. With the core function of identifying the main controlling factors of the system, this method has been widely used in engineering practice, ecological research, economic analysis, and other fields [30; 31; 32]. However, in the traditional grey correlation model, the value of the discrimination coefficient \(\lambda\) has a strong subjective dependence due to the lack of objective criteria. In slope stability assessment, the same index may beclassified as a core or secondary factor due to the different values of \(\lambda\), which leads to bias in the development of engineering solutions [33]. Moreover, a slight adjustment of the \(\lambda\) value can trigger a large fluctuation of the correlation coefficient, resulting in a significant shift in the weighting of indicators and a non-stationary fluctuation of decision-making results. Aiming at this limitation of the traditional model, this study constructed an improved grey correlation analysis framework [34], and its improvement process is described as follows:  
1. The Delphi method, also known as the expert survey method, is a process for making decisions that involves anonymous rounds of expert consultation. It involves screening and optimizing the evaluation index system using principal component analysis, hierarchical analysis, and other techniques [35; 36; 37]. The implementation process includes designing a structured questionnaire, inviting experts to independently rate or suggest, and adjusting opinions after multiple rounds of data statistics and anonymous feedback until the expert group reaches a consensus. The method reduces subjective bias through anonymous interaction and guarantees objective and reliable conclusions. In the application, m experts can anonymously rate the weights of n indicators and construct the decision matrix D characterizing the weights of the indicators. This is shown in Equation (1): \[D=\begin{bmatrix}d_{11}&d_{12}&\cdots&d_{1m}\\ d_{21}&d_{22}&\cdots&d_{2m}\\ \vdots&\vdots&\ddots&\vdots\\ d_{n1}&d_{n2}&\cdots&d_{nm}\end{bmatrix}\] (1) where \(D\) is the matrix of indicator weights and \(d_{nm}\) is the value of the mth expert's assessment of the weight of the nth indicator to be screened.
2. Construct the reference vector \(D_{0}\) by extracting the maximum value of each column of the matrix \(D\), as shown in Equation (2): \[D_{0}=\begin{pmatrix}d_{01}&d_{02}&\cdots&d_{0m}\end{pmatrix}\] (2)
3. According to Equation (3), the spatial difference value between each evaluation index and the reference series can be calculated, which intuitively characterizes the degree of dynamic shift of the index, and provides a quantitative basis for weight allocation and correlation analysis. \[D_{0i}=\sum_{k=1}^{m}(d_{0k}-d_{ik})^{2}\] (3) where \(d_{ik}\) is the weight that the Kth expert awarded to the ith indicator, and \(D_{0i}\) is the distance between the ith indicator and the reference indicator.
4. As shown in Equations (4) and (5), we calculate the weight coefficients of each assessment index using the standardized processed data matrix. \[w_{i}=\frac{1}{1+D_{0i}}\] (4) \[\overline{w}_{i}=\frac{w_{i}}{\sum_{l=1}^{n}w_{l}}\] (5)