Research on Screening Method of Loess Slope Stability Evaluation Indexes Based on Validity and Reliability Coefficient
Abstract
:1. Introduction
2. Regional Geological Setting
2.1. Topography and Geomorphology
2.2. Lithological Characteristics
2.3. Tectonic Features
2.4. Meteorology and Hydrology
2.5. Human Activities
3. Research Method
3.1. Preliminary Selection and Qualitative Screening of Evaluation Indicators
3.2. Quantitative Screening of Evaluation Indicators
Improved Grey Correlation-Delphi Model
- 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):
- Construct the reference vector by extracting the maximum value of each column of the matrix D, as shown in Equation (2):
- 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.
3.3. Validity and Reliability Verification
3.3.1. Validity Test of Evaluation Indicator System
- Data collection and standardization: Let the evaluation index system be containing a total of n indicators. Invite M experts to participate in independent scoring. According to the relative importance of the indicators, the experts need to assign scores to the indicators within the standardization interval, forming the scoring matrix , where indicates the scoring value of the jth expert for the indicator .
- Calculation of the validity coefficient of the single indicator: Define the validity coefficient for indicator as:
- Global validity coefficient synthesis: Integrate the validity coefficients of each index through the arithmetic average method to get the overall validity coefficient of the evaluation system:
- Validity determination criteria: The validity coefficient is often used as a core parameter to measure the scientificity of the evaluation system, and when the value is lower than the empirical threshold (routinely set at 0.15), the consensus of the expert group on the evaluation dimensions is significantly enhanced, and the validity of the indicator system in reflecting the objective reality is also enhanced.
3.3.2. Reliability Test of Evaluation Index System
- Calculation of the mean value of a single indicator: For expert rating data processing of the jth indicator in the evaluation system, its arithmetic mean can be determined using Equation (9). This calculation process integrates the results of the multidimensional assessment of the members of the expert group for a particular indicator.
- Calculation of the global mean for the data set: Equation (10) illustrates how the baseline scoring standards of the expert panel for each indicator are first established to create the comprehensive evaluation model. represents the expert scoring dataset corresponding to an evaluation system with n indicators. Based on this, the comprehensive mean score of this dataset must be determined using Equation (11), a formula system that integrates expert assessment data from multiple dimensions to achieve the quantitative characterization of the overall level of the evaluation system.
- Calculating the single-indicator reliability coefficient . can be done using Equation (12):Among these, when , it means that has a positive correlation with the whole evaluation and that the score is consistent; the more closely approaches one, the more reliable the indicator is and the more powerful it is at explaining the total results.
- The synthetic total reliability coefficient can be calculated using Equation (13). This value synthetically reflects the stability and internal consistency of the whole indicator system. When is high, it indicates that the indicators within the indicator system are highly correlated and the degree of consensus of expert scores is high; when is low, it means that the logic between the indicators is loose or there is redundancy, and the structure needs to be optimized.
- Reliability level determination: Generally speaking, when , it indicates that the reliability of the evaluation index system is high, when , its reliability is at a general level, and when , its reliability is relatively low.
4. Engineering Application
5. Conclusions
- Multi-dimensional indicator screening framework: A qualitative analysis framework was constructed based on engineering geology, hydrogeology, and anthropogenic factors, and the preliminary selection of 60 indicators was quantitatively screened by combining it with the improved grey correlation model, and 10 core indicators were finally identified, including rock structure, slope height, groundwater body, internal friction angle, cohesion, maximum monthly rainfall, and geological structure. The framework achieves the precision and efficiency of the indicator system through a hierarchical screening mechanism, providing a scientific basis for the evaluation process.
- Evaluation system validity and reliability test: By calculating the validity coefficient () and reliability coefficient (), the logical rationality and data consistency of the screening indicator set were verified. The results show that the method takes into account expert experience and objective data analysis, significantly reduces human bias, and can provide a highly credible indicator basis for slope stability evaluation.
- Engineering practice value: The research results provide a standardized analysis tool for loess slope stability assessment, which can systematically identify potential risk factors, guide the deployment of the monitoring network, optimize the reinforcement scheme, and help improve the refinement of mine safety management. The method also has cross-regional adaptability and can be extended to the evaluation of loess slopes with different geological backgrounds.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Indicator Number | Indicator Name | Indicator Number | Indicator Name |
---|---|---|---|
Indicator 1 | Rock Mass Structure | Indicator 12 | Permeability Coefficient of Loess |
Indicator 2 | Thickness of Loess Stratum | Indicator 13 | Moisture Sensitivity of Loess |
Indicator 3 | Geological Formation | Indicator 14 | Degree of vertical fracture development |
Indicator 4 | Slope Height | Indicator 15 | Vertical fracture connectivity |
Indicator 5 | Irrigation-Induced Seepage Intensity | Indicator 16 | Surface Runoff Intensity |
Indicator 6 | Underground Water Body | Indicator 17 | Seismic Intensity |
Indicator 7 | Surface Water Infiltration Capacity | Indicator 18 | Cyclic Freeze–Thaw Degradation Effects |
Indicator 8 | Internal Friction Angle | Indicators 19 | Gully Erosion Depth |
Indicator 9 | Cohesion | Indicators 20 | Hydrological Conditions |
Indicator 10 | Maximum Monthly Rainfall | Indicator 21 | Rainfall-Induced Erosion |
Indicator 11 | Slope Gradient | Indicator 22 | Anthropogenic Engineering Activities |
Marker | Value | Symbol | Value | Symbol | Value |
---|---|---|---|---|---|
0.1324 | 0.8831 | 0.0456 | |||
0.1973 | 0.8352 | 0.0431 | |||
0.2255 | 0.8160 | 0.0421 | |||
0.0691 | 0.9354 | 0.0483 | |||
0.2051 | 0.8298 | 0.0429 | |||
0.1076 | 0.9029 | 0.0466 | |||
0.2004 | 0.8331 | 0.0430 | |||
0.0432 | 0.9586 | 0.0495 | |||
0.0567 | 0.9463 | 0.0489 | |||
0.0045 | 0.9955 | 0.0514 | |||
0.0774 | 0.9282 | 0.0479 | |||
0.2272 | 0.8149 | 0.0421 | |||
0.2186 | 0.8206 | 0.0424 | |||
0.2185 | 0.8207 | 0.0424 | |||
0.1855 | 0.8445 | 0.0436 | |||
0.2130 | 0.8244 | 0.0426 | |||
0.0710 | 0.9337 | 0.0482 | |||
0.2006 | 0.8330 | 0.0430 | |||
0.2020 | 0.8319 | 0.0430 | |||
0.0432 | 0.9586 | 0.0495 | |||
0.2184 | 0.8208 | 0.0424 | |||
0.0054 | 0.9946 | 0.0514 |
Indicator Number | Indicator Name | Indicator Number | Indicator Name |
---|---|---|---|
Indicator 1 | Rock Mass Structure | Indicator 10 | Maximum Monthly Rainfall |
Indicator 4 | Slope Height | Indicator 11 | Slope Gradient |
Indicator 6 | Underground Water Body | Indicator 17 | Seismic Intensity |
Indicator 8 | Internal Friction Angle | Indicator 20 | Hydrological Conditions |
Indicator 9 | Cohesion | Indicator 22 | Anthropogenic Engineering Activities |
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Liao, J.; Sun, H.; An, J. Research on Screening Method of Loess Slope Stability Evaluation Indexes Based on Validity and Reliability Coefficient. Appl. Sci. 2025, 15, 6216. https://doi.org/10.3390/app15116216
Liao J, Sun H, An J. Research on Screening Method of Loess Slope Stability Evaluation Indexes Based on Validity and Reliability Coefficient. Applied Sciences. 2025; 15(11):6216. https://doi.org/10.3390/app15116216
Chicago/Turabian StyleLiao, Jianlong, Hongjun Sun, and Jianchao An. 2025. "Research on Screening Method of Loess Slope Stability Evaluation Indexes Based on Validity and Reliability Coefficient" Applied Sciences 15, no. 11: 6216. https://doi.org/10.3390/app15116216
APA StyleLiao, J., Sun, H., & An, J. (2025). Research on Screening Method of Loess Slope Stability Evaluation Indexes Based on Validity and Reliability Coefficient. Applied Sciences, 15(11), 6216. https://doi.org/10.3390/app15116216