A slope stability multi-sensitive field clustering partition statistical analysis and early warning method

Abstract

The present application relates to a kind of slope stability multi-sensitive field clustering partition statistical analysis and early warning method, it has wide data adaptability, can accept from slope monitoring, indoor test and finite element numerical calculation etc. Multiple data as input data set.By finite element etc. Numerical simulation technique obtains the information of multiple field quantity of slope under static / dynamic condition;And filter out the most sensitive key index and carry out normalization and clustering analysis, divide the clustering partition of slope into different stability state;Based on clustering partition generation mask, reverse extraction the probability distribution and statistical characteristics of key field quantity in each partition, to determine the critical threshold of slope instability;Finally, the rationality of critical threshold and stability evaluation result is verified by strength reduction method and limit equilibrium method.The present application overcomes the limitation of traditional single safety factor evaluation, can accurately identify potential slip surface of slope, quantifies instability precursor information, realizes the fusion of single safety factor strong standard and multi-index weak standard, provides quantitative, multi-index fusion critical criterion for slope stability accurate evaluation and disaster early warning forecast.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering, specifically relating to a method and system for statistical analysis and early warning of multi-sensitive field clustering of slope stability. Background Technology

[0002] Landslides, debris flows, and other severe geological disasters often cause immense harm and damage to people's lives and property, as well as the natural environment. Only by accurately assessing slope stability can we effectively predict the probability of such disasters and take appropriate preventative measures to ensure the safety of the surrounding area. Therefore, slope stability assessment is a core issue in geotechnical engineering. Traditional methods mainly rely on the limit equilibrium method and the strength reduction method, evaluating slope stability by calculating an overall stability coefficient and comparing it with a safety factor standard. However, this method cannot reveal the detailed distribution of stress, strain, and displacement within the slope, makes it difficult to accurately locate potential slip surfaces, and fails to quantify the precursory characteristics of instability and failure. Furthermore, it does not conform to the multi-indicator, multi-variable, and regional evolution characteristics of actual slope failure.

[0003] Currently, the mainstream methods in the field of quantitative slope stability assessment mainly fall into two categories. The first is the strong standard method, which involves theoretical calculations and mechanical analysis of anti-sliding strength under various loads, using the stability coefficient as the core and calculating the safety threshold through soil and rock strength parameters. The parameters of this type of method (such as the limit equilibrium method) rely on empirical assumptions and are difficult to reflect the nonlinear response of materials under actual stress paths. The results of stability evaluation include the slope stability coefficient, the most unfavorable sliding surface, and the residual sliding force at different slider locations.

[0004] Another type is the weak standard, which mainly focuses on the development trend and amount of deformation, but cannot take into account abrupt changes and uncontrollable deformation. It also lacks a direct correlation with strength parameters and a universally applicable critical threshold, relying mostly on regional empirical values, leading to a high degree of subjectivity in the evaluation results. Therefore, it is urgently necessary to develop a comprehensive slope stability analysis method and index system that considers multiple fields, multiple variables, multiple indicators, and failure zones.

[0005] With the development of computer technology, numerical simulation methods such as finite element method and finite difference method have been widely used. They can provide rich information on real field quantities, such as stress, strain, and displacement. However, current research focuses on using a single field quantity (such as plastic zone penetration or displacement abrupt change) to determine stability, lacking collaborative analysis and comprehensive utilization of information from multiple field quantities. How to automatically and intelligently extract key information that can characterize the critical features of slope stability from massive numerical simulation results and transform it into quantitative thresholds that can be used for engineering early warning remains a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method and system for statistical analysis and early warning of slope stability based on clustering and partitioning of multiple sensitive fields. This method uses sensitive data from the slope deformation and failure process, such as stress, strain, and displacement fields output by each node of a finite element method, as the dataset. First, the data is cleaned and truncated to remove missing values ​​and prevent outliers from dominating the calculation of cluster center distances. Then, normalization is used to eliminate dimensional differences between different features. Based on this, features are extracted, and clustering is performed using the k-means function. Next, statistical data and visualized partitioning results are analyzed to achieve a quantitative fusion of strong and weak standards. Finally, the results are comprehensively evaluated using the strength reduction method and the limit equilibrium method, ultimately establishing a slope stability evaluation method and index system based on clustering partitioning and multi-index statistical analysis of different zones. Specifically, this invention relates to a method for statistical analysis and early warning of slope stability based on clustering and partitioning of multiple sensitive fields, including the following steps: S1: Numerical simulation calculation of multivariable field data of slope: Establish a refined numerical model of the slope to be evaluated, and simulate the mechanical response of the slope under static or dynamic conditions through the finite element method, finite difference method or discrete element method; calculate and derive the real global multiple physical and mechanical field quantities of the slope. S2: Multi-index sensitivity analysis and key index screening: Statistical analysis of the physical and mechanical fields of all variables obtained in S1 is performed to calculate the global maximum, minimum and average values ​​of each variable. Sensitivity analysis is used to calculate the sensitivity of each variable to the slope stability state. Based on the sensitivity ranking results, the top N most sensitive indicators are selected as key evaluation indicators. S3: Key Indicator Normalization and Clustering Partitioning: The field quantity data of the selected N key evaluation indicators are normalized to unify their value range to the [0,1] interval. The normalized N-dimensional data is used as the input feature of each unit, and unsupervised learning is performed by clustering algorithm to form partitions. S4: Mask-based critical threshold extraction: The clustering partitioning results obtained in S3 are used as a spatial mask. This mask is then applied to the unnormalized original key index fields. For each clustering partition, the numerical sets of total displacement, maximum shear strain, and point safety factor within it are statistically analyzed. A probability distribution histogram of each index within each partition is plotted, and its statistical characteristic values, including mean, standard deviation, median, mode, and 85th percentile, are calculated. By comparing the statistical characteristic values ​​of adjacent stable state partitions, a boundary value between adjacent partitions is determined. S5: Threshold Rationality Verification: The original slope model is calculated using the strength reduction method and the limit equilibrium method to obtain the slope's shear strength reduction coefficient and overall stability coefficient. Simultaneously, the deformation and failure process and failure mode revealed by the slope's plastic strain zone or shear strain zone during the strength reduction process are observed. Using the overall stability coefficient and most unfavorable sliding surface determined by the limit equilibrium method, the deformation and failure process, sliding surface, stability coefficient, and slope stability data (statistical characteristics of point safety factor, horizontal displacement, vertical displacement, and shear strain, generally including: maximum value, minimum value, average value, and standard deviation; the four zones are ranked according to stability and safety level as follows: green stable zone (generally the area below the sliding bed with basically no deformation), blue basically stable zone (generally the area below the sliding bed with slight deformation), yellow understability zone (generally the core shear deformation zone of the sliding zone), and red zone (generally the area of ​​the sliding body with major overall displacement) are compared and verified. If the verification passes, the extracted critical threshold and partitioning results are reasonable and reliable, and proceed to the next step S6; If the verification fails, return to step S3). S6: Stability Assessment and Early Warning: The critical thresholds of each key indicator determined in step S4 are used as early warning indicators for slope stability monitoring, and the real-time monitoring data are compared with the corresponding critical thresholds. When the monitoring data continues to approach the critical threshold of the blue to yellow zone, a yellow warning is issued, indicating that the slope has entered the accelerated deformation stage and monitoring needs to be strengthened. When the monitoring data reaches or exceeds the critical threshold of the yellow to red zone, a red alarm is issued, indicating that the slope is in a critical instability state and emergency measures must be taken immediately.

[0007] Furthermore, the multiple physical and mechanical fields include horizontal displacement field, vertical displacement field, total displacement field, shear strain field, horizontal stress field, vertical stress field, maximum principal stress field, minimum principal stress field or shear stress field, and the point safety factor field of each unit is calculated based on the stress field.

[0008] Furthermore, the sensitivity analysis method employs any one or more of the following methods: 1) Analysis of variance: Calculate the variance of each variable's data. The larger the variance, the greater the difference of the variable in different areas of the slope, the stronger the ability to distinguish the stable state, and the higher the sensitivity; 2) Correlation coefficient method: Calculate the correlation coefficient between each variable and a reference index. The higher the correlation coefficient, the higher the sensitivity. The reference index includes the reciprocal of the overall safety factor or the average value of the stress field.

[0009] Furthermore, the static or dynamic operating conditions include self-weight, earthquake, or rainfall.

[0010] Furthermore, where N is 2 or 3, the key evaluation indicators include total displacement, maximum shear strain, or point safety factor.

[0011] Furthermore, the method for determining an adjacent partition boundary value includes a boundary value that maximizes the difference in probability distribution between the two partitions on the evaluation index, wherein the boundary value is the critical threshold for the evaluation index to evaluate slope stability.

[0012] Furthermore, the verification conditions include: a. Does the location of the slip surface calculated by the strength reduction method and the limit equilibrium method basically match the boundary of the "potential slip zone" obtained by cluster analysis in S3? b. Can cluster analysis results identify potential failure modes before the strength reduction method completely fails? c. Whether the minimum point safety factor is greater than the shear strength reduction factor and the overall stability factor.

[0013] 8. The method according to claim 1, wherein the clustering algorithm comprises the following steps: S3.1 Determine the optimal number of clusters K using the elbow rule or the profile coefficient method. S3.2 uses the K-means or DBSCAN clustering algorithm to divide all units of the slope into K categories, each category representing a clustering partition with similar stable state characteristics, where K is a positive integer.

[0014] Furthermore, the number of clusters K is 4.

[0015] Furthermore, the normalization formula is as follows: Xnorm= Where X represents the original data, Xmin and Xmax represent the minimum and maximum values ​​of the field, respectively, and Xnorm represents the normalized data.

[0016] Compared with the prior art, this application has the following advantages: (1) Multi-source information fusion for more comprehensive evaluation: It breaks through the limitations of traditional single safety factor or single quantitative criterion, integrates multi-dimensional information such as displacement, strain and stress, and realizes the fusion of strong standard of safety factor and weak standard of multiple indicators, so as to describe the slope stability state more finely and comprehensively. Data-driven, objective and accurate: It adopts data mining technology such as sensitivity ranking and cluster analysis, and automatically selects key indicators and identifies critical features from the data itself, avoiding the subjectivity of human experience, and the results are more scientific and objective.

[0017] (2) Quantification of critical thresholds and strong foresight in early warning: This invention proposes for the first time to extract the statistical critical value of field quantity in reverse by means of "clustering partitioning-mask statistics", capture the local change characteristics of slope, and transform the abstract "precursor of destruction" into specific and quantifiable thresholds, which greatly improves the accuracy and foresight of early warning.

[0018] (3) Strong universality and wide range of applications: This method does not depend on specific numerical simulation software or constitutive models and can be applied to various types of slopes such as soil slopes and rock slopes, as well as stability evaluation under various working conditions such as static, dynamic and seepage.

[0019] (4) Good integration with existing technologies: The results are verified by strength reduction method and limit balance method, which ensures the reliability of the new method. At the same time, it is also linked with traditional evaluation methods, making it easy to be accepted and adopted by the engineering community. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] The structures, proportions, sizes, etc., shown in the accompanying drawings are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the implementation conditions of this application. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size should still fall within the scope of the technical content disclosed in this application, provided that they do not affect the effects and purposes that this application can produce.

[0022] Figure 1 This is a flowchart of the evaluation method of the present invention.

[0023] Figure 2 This is a model diagram of the road cut slope for the evaluation method of the present invention.

[0024] Figure 3 This is a mesh diagram of the model for the evaluation method of the present invention.

[0025] Figure 4a , 4b The evaluation method of this invention includes clustering partitioning, four-color partitioning, and probability distribution and statistical characteristic values ​​of data in different partitions.

[0026] Figures 5a-5d The evaluation method of this invention includes the maximum shear strain field, total displacement field, point safety factor field, and plastic zone of the model.

[0027] Figure 6 The result is the calculation result of the automatic search for slip surface using the limit equilibrium method of this invention.

[0028] Figure 7 The results are calculated using the simplified boundary input limit balance method for the red-red clusters of this invention. Detailed Implementation

[0029] The embodiments of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0030] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the following description is provided in conjunction with the appendix. Figure 1 The present application will be further described in detail with reference to specific embodiments.

[0031] The purpose of this invention is to provide a slope stability evaluation method that can overcome the above-mentioned defects. This method can accurately and quantitatively determine the critical threshold of slope instability through multi-index critical characteristic analysis, providing a scientific basis for intelligent early warning.

[0032] To achieve the above objectives, this invention relates to a slope stability evaluation method based on multi-index critical characteristic analysis, see [link to relevant documentation]. Figure 1 First, a model is established using the finite element method, data parameters are calculated, and the data is preprocessed. Feature extraction and cluster analysis are then performed on the preprocessed data to generate cluster analysis results. These results are compared with those from the strength reduction method and the limit equilibrium method, and the quality of this analysis method is comprehensively evaluated based on actual sampling data, establishing a comprehensive feedback system. The method specifically includes the following steps: S1: Numerical Simulation Calculation of Multiple Fields in Slope A refined numerical model of the slope to be evaluated is established, and the mechanical response of the slope under static or dynamic conditions such as self-weight, earthquake, and rainfall is simulated using the finite element method, finite difference method, or discrete element method. Multiple physical and mechanical fields across the entire slope are calculated and derived, including but not limited to: horizontal displacement field, vertical displacement field, total displacement field, shear strain field, horizontal stress field, vertical stress field, maximum principal stress field, minimum principal stress field, and shear stress field. Based on the stress field, the point safety factor field for each element is calculated.

[0033] S2: Multi-indicator sensitivity analysis and key indicator screening Perform statistical analysis on all field variables obtained in S1, calculating the global maximum, minimum, and average values ​​for each variable. Use sensitivity analysis to calculate the sensitivity of each variable to the slope stability. Specifically, one or more of the following methods can be used: Analysis of variance (ANOVA): Calculate the variance of each variable. The larger the variance, the greater the difference of the variable in different areas of the slope, the stronger the ability to distinguish the steady state, and the higher the sensitivity.

[0034] Correlation coefficient method: Calculate the correlation coefficient between each variable and a reference indicator (such as the reciprocal of the overall safety factor). The higher the correlation coefficient, the higher the sensitivity.

[0035] Based on the sensitivity ranking results, the top N most sensitive indicators are selected as key evaluation indicators, where N is usually 2-3, preferably total displacement, maximum shear strain and point safety factor.

[0036] S3: Key Indicator Normalization and Clustering Partitioning The selected N key indicator data are normalized to unify their value range to the [0, 1] interval. The formula is as follows: Xnorm=

[0037] Where X represents the original data, Xmin and Xmax represent the minimum and maximum values ​​of the field, respectively, and Xnorm represents the normalized data.

[0038] Normalized N-dimensional data is used as the input feature for each unit, and unsupervised learning is performed using clustering algorithms. First, the optimal number of clusters K is determined using the elbow rule or silhouette coefficient method. Then, clustering algorithms such as K-means and DBSCAN are used to divide all units of the slope into K categories, each category representing a "clustering partition" with similar stable state characteristics, thus obtaining the clustering analysis results.

[0039] S4: Mask-based critical threshold extraction The clustering partitioning results obtained in S3 are used as a spatial mask. This mask is then applied to the unnormalized original key index fields. For each cluster partition, the numerical sets of total displacement, maximum shear strain, and point safety factor within it are statistically analyzed. Histograms of the probability distributions of each index within each partition are plotted, and their statistical characteristics, including mean, standard deviation, median, mode, and 85th percentile, are calculated.

[0040] By comparing the statistical characteristic values ​​of adjacent stable zones (such as stable zones and potential slip zones), a zone boundary value is determined. This boundary value maximizes the difference in probability distribution between the two zones for this indicator. This boundary value is the critical threshold for this key indicator to evaluate slope stability.

[0041] S5: Threshold Reasonableness Verification Threshold rationality verification: The original slope model is calculated using the strength reduction method and the limit equilibrium method to obtain the slope's shear strength reduction coefficient and overall stability coefficient. Simultaneously, the deformation and failure process revealed by the plastic strain zone or shear strain band of the slope during the strength reduction process is observed. The stability coefficient and the most unfavorable sliding surface calculated by the limit equilibrium method are compared and verified with the slope stability evaluation results obtained by the above traditional methods and the slope stability evaluation results output by the patent. The verification content of the deformation and failure process revealed by the plastic strain zone or shear strain band includes: Does the location of the slip surface calculated by the strength reduction method and the limit equilibrium method basically match the boundary of the "potential slip zone" obtained by cluster analysis in S3?

[0042] Whether cluster analysis results can identify potential failure modes before the strength reduction method completely fails, and whether the minimum point safety factor is greater than the shear strength reduction factor and the overall stability factor.

[0043] If the verification is successful, it proves that the critical threshold and partitioning results extracted by the method of the present invention are reasonable and reliable.

[0044] S6: Stability Evaluation and Early Warning The critical thresholds of each key indicator identified in S4 are used as early warning indicators for slope stability monitoring. In actual engineering, sensors are deployed to monitor data such as total slope displacement, surface cracks, and deep deformation. Real-time monitoring data are compared with the corresponding critical thresholds. When the monitoring data continues to approach the critical threshold of the blue to yellow zone, a yellow warning is issued, indicating that the slope has entered a stage of accelerated deformation and monitoring needs to be strengthened.

[0045] When the monitoring data reaches or exceeds the critical threshold of the yellow to red zone, a red alarm is issued, indicating that the slope is in a critical instability state and emergency measures must be taken immediately.

[0046] The above method will be further explained below with reference to the embodiments.

[0047] The slope failure mode and shear strength reduction coefficient calculated using the strength reduction method, and the sliding surface location, morphology, and slope stability coefficient calculated using the limit equilibrium method, are compared with the output results of this method to conduct a multi-dimensional comprehensive evaluation, thereby verifying the effectiveness of the method. This evaluation method includes the following steps: 1) Edge data simulation and field quantity calculation. For example... Figure 2As shown, a finite element model was first established to obtain finite element data. This model represents the seismic condition of the K12 road cut slope of the Yongchang Expressway after slope cutting treatment. Retaining walls and anti-slide piles have been added, and a seismic load of 0.06375 is applied from right to left.

[0048] The material parameters are shown in Table 1 below: Table 1 Material Parameter Table

[0049] 2) Multi-index sensitivity analysis and key index screening. Statistical analysis is performed on all field variables obtained in step 1), calculating the global maximum, minimum, and average values ​​for each variable. Sensitivity analysis is then used to calculate the sensitivity of each variable to the slope stability state. Specifically, one or more of the following methods can be used: Analysis of variance (ANOVA): Calculate the variance of each variable. The larger the variance, the greater the difference of the variable in different areas of the slope, the stronger the ability to distinguish the steady state, and the higher the sensitivity.

[0050] Correlation coefficient method: Calculate the correlation coefficient between each variable and a reference indicator (such as the reciprocal of the overall safety factor). The higher the correlation coefficient, the higher the sensitivity.

[0051] Based on the sensitivity ranking results, the top N most sensitive indicators are selected as key evaluation indicators, where N is usually 2-3, preferably total displacement, maximum shear strain and point safety factor.

[0052] Specifically, such as Figure 3 As shown, the model is meshed: the model is divided into multiple three-node triangular elements, with a default number of 300 nodes for the outer contour. Data from 2885 nodes is output and integrated into a table of 2885 rows and 4 columns, with the four columns representing the x-coordinate, y-coordinate, point safety factor, total displacement, and maximum shear strain.

[0053] 3) Normalization and clustering of key indicators.

[0054] 3.1 Data Processing: In MATLAB, the data was cleaned to remove invalid values, reducing the number of valid rows to 2332. A threshold of 14.6 was set for the data in the column using statistical eigenvalues ​​and confidence interval limits. The `min(B(:,3),14.6)` function was used to truncate the third column to avoid the influence of abnormally large values ​​from retaining walls and corner points dominating the Euclidean distance calculation. Next, min-max normalization was used to linearly map the data to the [0,1] interval, eliminating the influence of dimensions and avoiding gradient descent direction shifts caused by differences in feature scales. Finally, the K-means function was used to cluster the data, completing the data processing. The interpretability and operability were strongest when the number of clusters k=4. The clustering results are shown below. Figure 4a The probability density plot and histogram are shown below. Figure 4b The data characteristics of each cluster are shown in Table 2.

[0055] Table 2. Clustering Results Statistics

[0056] 3.2 Clustering Results Analysis. This step is the core of slope stability assessment. Based on the visualization and statistical characteristics of the clustering results in step 3.1, this section focuses on an in-depth analysis of the four clusters (red, yellow, blue, and green), explaining their engineering significance from the perspective of multi-indicator fusion. The clustering results distinguish the risk levels of slope areas through color, providing a quantitative basis for subsequent engineering decisions.

[0057] (1) The red clusters have the lowest safety factor, the largest total displacement, and the largest maximum shear strain, which means that the soil and rock mass or the overall structure in this area has weak resistance to instability, significant cumulative deformation effect, and concentrated internal shear stress. It is a "high-risk breeding area" for disasters such as landslides and collapses, and it is necessary to prioritize the deployment of detection equipment and take reinforcement measures.

[0058] (2) The yellow clusters have a low safety factor, a large total displacement, and the largest maximum shear strain, which reflects that although the soil or rock mass or structure in this area has not reached the critical state of instability, the deformation has accumulated significantly. The shear deformation is concentrated in the potentially weak parts and is prone to evolve into the high-risk state of the red clusters. It belongs to the "risk transition zone" and requires proactive preventive reinforcement measures to block the development of the disaster chain.

[0059] (3) The blue clusters have the highest safety factor, the smallest total displacement, and the smallest maximum shear strain, reflecting their strong resistance to instability. The deformation is always within the elastic controllable range, and the shear deformation is strictly suppressed, indicating that the soil and rock structure in this area has good integrity. This area can be used as a reference for determining the safety reserve factor and support type in engineering design; (4) The green clusters have a high safety factor, the smallest total displacement and the smallest maximum shear strain, which means that the area has ultra-high stability and disaster resistance redundancy. Even under extreme loads, the structure can maintain its integrity, with weak deformation response and no obvious internal shear damage. It can serve as a natural safety barrier and reduce the maintenance requirements throughout the entire life cycle of the project.

[0060] 4) Mask-based critical threshold extraction. The clustering partitioning results obtained in step 3) are used as a spatial mask. This mask is then applied to the unnormalized original key index fields. For each cluster partition, the numerical sets of total displacement, maximum shear strain, and point safety factor within it are statistically analyzed. Histograms of the probability distributions of each index within each partition are plotted, and their statistical characteristic values ​​are calculated, including mean, standard deviation, median, mode, and 85th percentile.

[0061] By comparing the statistical characteristic values ​​of adjacent stable zones (such as stable zones and potential slip zones), a zone boundary value is determined. This boundary value maximizes the difference in probability distribution between the two zones for this indicator. This boundary value is the critical threshold for this key indicator to evaluate slope stability.

[0062] 5) Threshold rationality verification and optimization. By comparing the results with the clustering results using the strength reduction method and the limit equilibrium method, the aim is to verify whether the risk partitions identified by the clustering are consistent with the actual mechanical response. The reliability of the method is comprehensively evaluated from both quantitative and qualitative perspectives, providing a basis for engineering decision-making.

[0063] (1) Strength reduction method The original slope model was calculated using the strength reduction method to obtain the shear strength reduction factor (SRF) of the slope. Simultaneously, the deformation and failure process revealed by the plastic strain zone or shear strain band of the slope during the strength reduction process was observed. Verification included: Does the slip surface location calculated using the strength reduction method basically match the boundary of the "potential slip zone" obtained from the cluster analysis in S3? The maximum shear strain, total displacement, safety factor, and plastic yield region of the model are analyzed using the finite element method, such as... Figures 5a-5d As shown. Specifically, the shear strength reduction factor (SRF) of the slope, obtained using the strength reduction method, is 1.45, while the minimum average point safety factor for the red clusters in the clustering results is 1.70. SRF reflects the overall stability of the slope (a higher value indicates greater safety), while the point safety factor describes the local stress state. The average point safety factor (1.70) of the clustering results is higher than the SRF (1.45), indicating that the slope has sufficient safety reserves after slope cutting and is not prone to overall instability, which is consistent with the actual engineering situation.

[0064] Furthermore, the red clusters are highly similar to the maximum shear strain and total displacement maps, and largely overlap with the plastic yielding region. This indicates that the clustering method accurately captures the high-risk areas of the slope, namely the plastic strain concentration zone in the limit equilibrium method, confirming the sensitivity of clustering to the localization of failure characteristics. The blue clusters on the slope surface correspond one-to-one with the maximum shear strain, safety factor cloud map, and plastic yielding region, identifying stable areas within the dangerous area.

[0065] The results validate the ability of clustering to identify the "dynamic failure front," providing precise location information for monitoring deployment. The clustering results and the limit equilibrium method show excellent consistency in failure modes and safety thresholds, demonstrating the effectiveness of the clustering fusion method in quantifying the critical state of slopes and effectively supporting slope analysis and engineering control.

[0066] (2) Limit Equilibrium Method The limit equilibrium method, a traditional and robust standard method, is based on static equilibrium theory. It determines the overall stability threshold of a slope by calculating the ratio of the resisting force to the sliding force on the slip surface, i.e., the slope stability coefficient. This method assumes the sliding mass is rigid, ignores the deformation process, and directly focuses on the critical failure state, neglecting deformation details.

[0067] Import the model into the slide, and it will automatically search for slip surfaces and identify the most dangerous ones. Figure 6 As shown, the limit equilibrium method automatically searches for slip surface calculation results with a safety factor of 1.492. However, when the simplified red cluster boundaries obtained from cluster analysis are input into the limit equilibrium method, as shown... Figure 7 As shown, the calculation results of the red cluster simplified boundary input limit balance method yield a safety factor of 1.752.

[0068] This result shows that the red cluster area highly matches the spatial distribution of the most dangerous slip surface in the limit equilibrium method, confirming the clustering's accurate identification capability of the failure front. Furthermore, its higher slope stability coefficient value compared to the global search results indicates that the clustering method can more sensitively capture local risk characteristics, revealing that even with sufficient strength parameter reserves, this area still possesses a progressive failure risk due to deformation accumulation. The comparison demonstrates that the clustering fusion method effectively compensates for the limitation equilibrium method's neglect of dynamic deformation processes, achieving a quantitative fusion of strong criteria (safety factor) and weak criteria (displacement, shear strain), providing a scientific basis for slope zoning control that considers both overall stability and focuses on the evolution of local risks. Based on the clustering analysis results, it can be determined whether potential failure modes can be identified before the strength reduction method completely fails.

[0069] If the verification is successful, it proves that the critical threshold and partitioning results extracted by the method of the present invention are reasonable and reliable.

[0070] If the verification fails, return to step 3) for optimization.

[0071] 6) Stability Assessment and Early Warning Application. The critical thresholds of each key indicator determined in step 4) are used as early warning indicators for slope stability monitoring. In actual engineering, sensors are deployed to monitor data such as total slope displacement, surface cracks, and deep deformation. Real-time monitoring data are compared with the corresponding critical thresholds: When the monitoring data continues to approach the critical threshold of the blue to yellow zone, a yellow warning is issued, indicating that the slope has entered a stage of accelerated deformation and monitoring needs to be strengthened.

[0072] When the monitoring data reaches or exceeds the critical threshold of the yellow to red zone, a red alarm is issued, indicating that the slope is in a critical instability state and emergency measures must be taken immediately.

[0073] This method has two main advantages: First, it has the ability to integrate multiple indicators. By simultaneously integrating strength parameters and deformation dynamics, it breaks through the limitations of traditional methods that rely solely on a single strength standard, and more accurately captures the characteristics of localized progressive slope failure. Second, it has the advantage of spatial visualization. The clustering and partitioning results present the risk distribution intuitively with color gradients. The gradient maps of red high-risk areas, yellow transition areas, blue stable areas, and green ultra-high stability areas provide clear targeting basis for engineering prevention and control.

[0074] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0075] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

[0076] The various embodiments in this specification are described in a progressive, parallel, or combined manner. Each embodiment focuses on its differences from other embodiments, and similar or identical parts between embodiments can be referred to interchangeably. For the apparatuses disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0077] It should also be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes the aforementioned element.

[0078] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for clustering and zoning statistical analysis and early warning of slope stability across multiple sensitive fields, characterized in that: Includes the following steps: S1: Numerical simulation calculation of multivariable field data of slope: Establish a refined numerical model of the slope to be evaluated, and simulate the mechanical response of the slope under static or dynamic conditions through the finite element method, finite difference method or discrete element method; calculate and derive the real global multiple physical and mechanical field quantities of the slope. S2: Multi-index sensitivity analysis and key index screening: Statistical analysis of the physical and mechanical fields of all variables obtained in S1 is performed to calculate the global maximum, minimum and average values ​​of each variable. Sensitivity analysis is used to calculate the sensitivity of each variable to the slope stability state. Based on the sensitivity ranking results, the top N most sensitive indicators are selected as key evaluation indicators. S3: Key Indicator Normalization and Clustering Partitioning: The field quantity data of the selected N key evaluation indicators are normalized to unify their value range to the [0,1] interval. The normalized N-dimensional data is used as the input feature of each unit, and unsupervised learning is performed by clustering algorithm to form partitions. S4: Mask-based critical threshold extraction: The clustering partitioning results obtained in S3 are used as a spatial mask. This mask is then applied to the unnormalized original key index fields. For each clustering partition, the numerical sets of total displacement, maximum shear strain, and point safety factor within it are statistically analyzed. A probability distribution histogram of each index within each partition is plotted, and its statistical characteristic values, including mean, standard deviation, median, mode, and 85th percentile, are calculated. By comparing the statistical characteristic values ​​of adjacent stable state partitions, a boundary value between adjacent partitions is determined. S5: Threshold rationality verification: The original slope model is calculated using the strength reduction method and the limit equilibrium method to obtain the slope shear strength reduction coefficient and the overall stability coefficient. At the same time, the deformation and failure process and failure mode revealed by the plastic strain zone or shear strain zone of the slope during the strength reduction process are observed. The overall stability coefficient and the most unfavorable sliding surface of the slope determined by the limit equilibrium method are compared and verified with the deformation and failure process, sliding surface, stability coefficient and the stability data of the four stable and safe zones of red, yellow, blue and green output by the model. The statistical characteristics of the point safety factor, horizontal displacement, vertical displacement, and shear strain include: maximum value, minimum value, average value, and standard deviation; the four stable safety zones are, in order of stability and safety level, green stable zone, blue basically stable zone, yellow understability zone, and red displacement zone; if the verification is successful, the extracted critical threshold and partitioning results are reasonable and reliable, and proceed to the next step S6; If the verification fails, return to step S3). S6: Stability Assessment and Early Warning: The critical thresholds of each key indicator determined in step S4 are used as early warning indicators for slope stability monitoring, and the real-time monitoring data are compared with the corresponding critical thresholds. When the monitoring data continues to approach the critical threshold of the blue to yellow zone, a yellow warning is issued, indicating that the slope has entered the accelerated deformation stage and monitoring needs to be strengthened. When the monitoring data reaches or exceeds the critical threshold of the yellow to red zone, a red alarm is issued, indicating that the slope is in a critical instability state and emergency measures must be taken immediately.

2. The method according to claim 1, wherein the plurality of physical and mechanical field quantities include a horizontal displacement field, a vertical displacement field, a total displacement field, a shear strain field, a horizontal stress field, a vertical stress field, a maximum principal stress field, a minimum principal stress field, or a shear stress field, and the point safety factor field of each unit is calculated based on the stress field.

3. The method according to claim 1, wherein the sensitivity analysis method adopts any one or more of the following methods: 1) Analysis of variance: calculate the variance of each variable data. The larger the variance, the greater the difference of the variable in different areas of the slope, the stronger the ability to distinguish the stable state, and the higher the sensitivity; 2) Correlation coefficient method: calculate the correlation coefficient between each variable and a reference index. The higher the correlation coefficient, the higher the sensitivity. The reference index includes the reciprocal of the overall safety factor or the average value of the stress field.

4. The method according to claim 1, wherein the static or dynamic operating conditions include self-weight, earthquake, or rainfall.

5. The method according to claim 1, wherein N is 2 or 3, and the key evaluation indicators include total displacement, maximum shear strain or point safety factor.

6. The method according to claim 5, wherein the method for determining an adjacent partition boundary value includes the boundary value maximizing the difference in probability distribution between the two partitions on the evaluation index, wherein the boundary value is the critical threshold of the evaluation index for evaluating slope stability.

7. The method according to claim 1, wherein the verification conditions include: a. Does the location of the slip surface calculated by the strength reduction method and the limit equilibrium method basically match the boundary of the "potential slip zone" obtained by cluster analysis in S3? b. Can cluster analysis results identify potential failure modes before the strength reduction method completely fails? c. Whether the minimum point safety factor is greater than the shear strength reduction factor and the overall stability factor.

8. The method according to claim 1, wherein the clustering algorithm comprises the following steps: S3.1 Determine the optimal number of clusters K using the elbow rule or the profile coefficient method; S3.2 uses the K-means or DBSCAN clustering algorithm to divide all units of the slope into K categories, each category representing a clustering partition with similar stable state characteristics, where K is a positive integer.

9. The method according to claim 8, wherein the number of clusters K is 4.

10. The method according to claim 1, wherein the normalization formula is as follows: Xnorm= in, X represents the original data, Xmin and Xmax represent the minimum and maximum values ​​of the field, respectively, and Xnorm represents the normalized data.

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