A method and system for determining recommended slope ratio of rock slope of a hydroelectric project

Abstract

The present application relates to the technical field of machine learning, and provides a method and system for determining recommended slope ratio of rock slope of hydropower engineering, the present application combines rock fracture angle theory inversion and machine learning data driven correction, the whole process follows the special specification of hydropower engineering, through constructing the closed loop method of test inversion, specification formulation, machine learning correction, multi-working condition checking, special geological reinforcement, both the historical engineering data is used to improve the slope ratio design precision and engineering adaptability, and the safety control requirements under the complex geological conditions and various working conditions are strictly met, the long-term safety of the slope can be ensured while the engineering economy is optimized, the method is standardized, easy to operate and widely applicable, and can effectively adapt to the excavation design requirements of high and steep and complex geological slope of hydropower engineering.

Description

Technical Field

[0001] This invention relates to the field of machine learning technology, and in particular to a method and system for determining the recommended slope ratio for rock slopes in hydropower projects. Background Technology

[0002] Determining the appropriate slope ratio for rock slopes is a crucial aspect of hydropower engineering design, directly impacting construction safety, cost control, and long-term operational stability. Currently, determining the slope ratio for rock slopes in hydropower projects primarily relies on traditional rock fracture angle calculation methods. Widely used methods include those specified in the "Technical Specification for Building Slope Support" and the critical angle calculation method recorded in the "Engineering Geology Handbook." However, both methods have significant limitations.

[0003] Traditional fracture angle calculations only consider a few core parameters such as the internal friction angle of the rock mass and the slope dip angle, failing to fully take into account the comprehensive influence of multiple geological and engineering conditions, including lithology, rock mass integrity, weathering degree, and slope height. This leads to discrepancies between the calculated slope ratio and the actual engineering conditions. Furthermore, traditional methods struggle to quantify the nonlinear mapping relationship between various factors and the optimal slope ratio under complex geological conditions, often requiring designers to rely on experience for corrections. This inherent subjectivity can result in overly conservative slope ratio designs (increasing excavation volume and cost) or overly aggressive designs (posing safety hazards).

[0004] With the expanding application of machine learning technology in geotechnical engineering, using historical engineering data to train regression models to predict slope ratios has become a new research direction. However, existing machine learning-based slope ratio prediction methods have the following shortcomings in their training process and design applications: First, during the model training phase, stratified sampling is not used to ensure the consistent distribution of different lithologies and weathering degrees between the training and test sets, leading to unstable model evaluation indicators. Second, existing methods rely solely on historical data to output a single prediction result, failing to effectively integrate with standard design methods and lacking guidance and constraints from physical and mechanical theories. Third, the prediction results are directly used as the design basis without undergoing limit equilibrium verification of slope stability under numerous working conditions, lacking systematic verification of the safety of the predicted slope ratio under extreme conditions such as natural conditions, sudden drops in water level, and earthquakes, making it difficult to meet the safety requirements of engineering design.

[0005] Therefore, it is necessary to propose a method and system for determining the recommended slope ratio for rock slopes in hydropower projects to solve or at least alleviate the above-mentioned defects. Summary of the Invention

[0006] The main objective of this invention is to provide a method and system for determining the recommended slope ratio for rock slopes in hydropower projects, in order to solve the technical problems of low parameter dimensionality and insufficient nonlinear fitting ability in traditional methods, as well as the lack of standardized constraints and safety verification in existing machine learning methods.

[0007] To achieve the above objectives, the present invention provides a method for determining the recommended slope ratio for rock slopes in hydropower projects, comprising the following steps: S1, obtain the rock mass fracture angle, internal friction angle and cohesion of the target slope after standard reduction, as well as basic geological parameters including lithology, rock mass integrity coefficient, weathering degree and slope height, and potential sliding surface dip angle and sliding surface length; S2. Based on the friction angle, cohesion and basic geological parameters of the rock mass, and in accordance with the slope design specifications, determine the initial slope ratio. S3, the rock mass fracture angle, the rock mass internal friction angle, the cohesion and the basic geological parameters are used as input features and input into a pre-trained machine learning model to obtain the predicted slope ratio; S4. Based on the risk level of the target slope, determine the weights of the initial slope ratio and the predicted slope ratio, and perform weighted fusion of the initial slope ratio and the predicted slope ratio to obtain the coupled slope ratio. S5, using the slope angle corresponding to the coupled slope ratio and the potential sliding surface inclination angle and sliding surface length information as input, perform slope stability limit equilibrium verification under at least one preset working condition to obtain a safety factor; wherein, each preset working condition corresponds to a preset safety factor threshold. S6. When at least one of the safety factors is less than the preset safety factor threshold for the corresponding working condition, the coupling slope ratio is increased, and the slope angle is updated based on the increased coupling slope ratio. The slope stability limit balance is recalculated until the safety factors for all working conditions are greater than or equal to the corresponding preset safety factor threshold. The coupling slope ratio that finally meets the conditions is then output as the recommended slope ratio.

[0008] Preferably, the friction angle and cohesion of the rock mass after standard reduction in step S1 include the following steps: Obtain the rock fracture angle of the target slope. and the uniaxial compressive strength σ of the rock mass n ; Based on the Mohr-Coulomb failure criterion, the friction angle φ within the rock mass is calculated using the formula φ=2×(β-45°). According to the formula c=σ n The cohesive force c is calculated using (1-sinφ) / (2·cosφ). The basic reduction coefficient is determined based on the weathering degree level. The basic reduction coefficient is then adjusted based on the rock mass integrity coefficient to obtain a comprehensive reduction coefficient. The comprehensive reduction coefficient is multiplied by the internal friction angle φ and cohesion c of the rock mass to obtain the internal friction angle φ' and cohesion c' of the rock mass after standard reduction.

[0009] Preferably, step S2 includes the following steps: Using the reduced internal friction angle φ', cohesion c', rock mass integrity coefficient, weathering degree, and slope height as query conditions, the initial slope ratio value is obtained by querying the preset recommended slope ratio table.

[0010] Preferably, the machine learning model in step S3 is obtained through the following steps: S31, obtain historical data of rock slopes of existing hydropower projects. Each historical data includes rock fracture angle, uniaxial compressive strength of rock mass, lithology, rock mass integrity coefficient, weathering degree, slope height, and the corresponding actual excavation slope ratio. S32, perform preprocessing on the historical data, including outlier removal and missing value completion; S33 uses lithology and weathering degree as the stratification basis to perform stratified sampling on the preprocessed historical data, dividing it into training set and test set; S34, For the historical data in the training set, the internal friction angle and cohesion of the rock mass after standard reduction are calculated from the rock mass fracture angle and the uniaxial compressive strength of the rock mass. The internal friction angle, cohesion, rock mass fracture angle, lithology code, rock mass integrity coefficient, weathering degree, and slope height after standard reduction are used as input features, and the actual excavation slope ratio is used as the target variable to train the XGBoost regression model to obtain the initial machine learning model. S35, the initial machine learning model is evaluated using the test set, and when the evaluation metric meets the preset accuracy requirement, the initial machine learning model is used as the machine learning model.

[0011] Preferably, step S4 includes the following steps: S41, Determine the risk level of the target slope based on the weathering degree and slope height; S42, determine the weight ω1 of the initial slope ratio and the weight ω2 of the predicted slope ratio based on the risk level, where ω1+ω2=1, and the higher the geological risk indicated by the risk level, the larger the weight ω1; S43, according to formula Calculate the coupling slope ratio ,in The initial slope ratio value is... The predicted slope ratio is denoted as .

[0012] Preferably, step S5 includes the following steps: S51, according to the formula α=arctan(1 / Calculate the slope angle α; S52, under natural working conditions, sudden drop in water level working conditions and earthquake working conditions, respectively, the safety factor for each working condition is calculated based on the values ​​of pore water pressure, water weight and horizontal seismic force corresponding to each working condition; The preset safety factor threshold for the natural working condition is 1.30, the preset safety factor threshold for the sudden drop in water level working condition is 1.25, and the preset safety factor threshold for the earthquake working condition is 1.25.

[0013] Preferably, step S6 includes the following steps: S61, determine whether the safety factors calculated under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions are all greater than or equal to their respective preset safety factor thresholds; if not, increase the coupling slope ratio value by a preset fixed step size. S62, Update the slope angle based on the increased coupling slope ratio; S63, with the updated slope angle, the slope stability limit balance verification under the natural working condition, the sudden drop in water level working condition and the earthquake working condition is performed again to obtain the updated safety factor. S64. Repeat steps S61 to S63 until the safety factor under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions is greater than or equal to the corresponding preset safety factor threshold, and the coupled slope ratio value that meets the conditions at this time is used as the recommended slope ratio output.

[0014] Preferably, before outputting the recommended slope, the following steps are also included: Determine whether the target slope has an outward-dipping weak structural surface; wherein, the outward-dipping weak structural surface is a structural surface that dips outward, has a dip angle smaller than the slope angle corresponding to the recommended slope ratio, and has a mechanical strength lower than the surrounding rock mass; if so, obtain the dip angle of the control surface of the outward-dipping weak structural surface; Determine whether the slope angle corresponding to the recommended slope ratio is greater than the control surface inclination angle; if so, increase the recommended slope ratio, update the slope angle based on the increased recommended slope ratio, and return to step S5 to recalculate the slope stability limit balance until the updated slope angle is not greater than the control surface inclination angle and the safety factor of all working conditions is greater than or equal to the corresponding preset safety factor threshold.

[0015] Preferably, before outputting the recommended slope, the following steps are also included: When the slope height of the target slope is greater than 50 meters, or the recommended slope ratio is greater than 1.0, the target slope shall be set up with graded slope, with each platform width not less than 2 meters and the number of grades not less than 3.

[0016] The present invention also provides a system for determining the recommended slope ratio of rock slopes in hydropower projects, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for determining the recommended slope ratio of rock slopes in hydropower projects as described above.

[0017] Compared with the prior art, the present invention has the following beneficial effects: This invention constructs a dual-driven design framework of physical inversion and data-driven approaches by simultaneously using the reduced strength parameters and basic geological parameters as inputs for both specification formulation and machine learning prediction. This addresses the technical problems of low parameter dimensionality and insufficient nonlinear fitting ability in traditional methods, as well as the lack of physical guidance in machine learning methods, enabling design results to possess both specification interpretability and data accuracy. By weighting and fusing the initial and predicted slope ratios based on risk levels, an adaptive balance between safety and economy under different geological conditions is achieved, solving the problem that existing methods with fixed design strategies cannot adapt to different risk scenarios. By performing multi-condition limit balance verification on the coupled slope ratio and automatically increasing the slope ratio when the safety factor is not met and iteratively correcting it until all condition thresholds are met, this invention solves the problems of existing machine learning methods lacking safety verification in their prediction results and traditional methods relying on manual experience for adjustments when verification fails.

[0018] This invention combines theoretical inversion of rock fracture angle with data-driven correction using machine learning. The entire process follows the special specifications for hydropower engineering. By constructing a closed-loop method that includes experimental inversion, specification formulation, machine learning correction, multi-condition verification, and reinforcement for special geological conditions, it not only utilizes historical engineering data to improve the accuracy of slope ratio design and engineering adaptability, but also strictly meets the safety control requirements under complex geological conditions and diverse working conditions. It can optimize the economic efficiency of the project while ensuring the long-term safety of the slope. The method is standardized, easy to operate, and widely applicable, and can effectively adapt to the excavation design needs of steep and complex geological slopes in hydropower projects. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0020] Figure 1 This is a schematic flowchart of one embodiment of the present invention.

[0021] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0022] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0024] Furthermore, the technical solutions of the various embodiments can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0025] Please refer to Figure 1 The present invention provides a method for determining the recommended slope ratio for rock slopes in hydropower projects, comprising the following steps: S1 obtains the rock fracture angle, internal friction angle and cohesion of the target slope after standard reduction, as well as basic geological parameters including lithology, rock mass integrity coefficient, weathering grade, and slope height, and the dip angle and length of the potential sliding surface. Lithology can be determined through on-site geological exploration and core drilling, reflecting the basic rock type, such as granite, limestone, and sandstone. The rock mass integrity coefficient Kv can be obtained through on-site acoustic wave testing, defined as the square of the ratio of the on-site rock mass wave velocity to the indoor core wave velocity. The smaller the Kv value, the more developed the joints and fractures in the rock mass, and the worse the integrity. The weathering grade is determined comprehensively through on-site outcrop observation and wave velocity testing, and is classified into fully weathered, strongly weathered, moderately weathered, and slightly weathered levels according to standards. The weathering grade reflects the degree of deterioration of the rock mass due to weathering; the more intense the weathering, the lower the rock mass strength, and the greater the impact on slope design. The slope height H is obtained through topographic mapping or on-site layout, reflecting the potential energy scale of the slope and the severity of the instability consequences. The potential sliding surface can be determined through on-site geological mapping and exploration, and is a geological interface in the slope rock mass that may constitute the sliding base, such as bedding planes, joint surfaces, or fault fracture zones. The dip angle of the sliding surface is the angle between the interface and the horizontal plane, and the length of the sliding surface is the oblique length of the interface extending from the toe of the slope to the tensile crack at the rear edge of the slope crest.

[0026] S2. Based on the friction angle, cohesion and basic geological parameters of the rock mass, and in accordance with the slope design specifications, determine the initial slope ratio. S3, the rock mass fracture angle, the rock mass internal friction angle, the cohesion and the basic geological parameters are used as input features and input into a pre-trained machine learning model to obtain the predicted slope ratio; S4. Based on the risk level of the target slope, determine the weights of the initial slope ratio and the predicted slope ratio, and perform weighted fusion of the initial slope ratio and the predicted slope ratio to obtain the coupled slope ratio. S5, using the slope angle corresponding to the coupled slope ratio and the potential sliding surface inclination angle and sliding surface length information as input, perform slope stability limit equilibrium verification under at least one preset working condition to obtain a safety factor; wherein, each preset working condition corresponds to a preset safety factor threshold. S6. When at least one of the safety factors is less than the preset safety factor threshold for the corresponding working condition, the coupling slope ratio is increased, and the slope angle is updated based on the increased coupling slope ratio. The slope stability limit balance is recalculated until the safety factors for all working conditions are greater than or equal to the corresponding preset safety factor threshold. The coupling slope ratio that finally meets the conditions is then output as the recommended slope ratio.

[0027] This invention constructs a dual-driven design framework of physical inversion and data-driven approaches by simultaneously using the reduced strength parameters and basic geological parameters as inputs for both specification formulation and machine learning prediction. This addresses the technical problems of low parameter dimensionality and insufficient nonlinear fitting ability in traditional methods, as well as the lack of physical guidance in machine learning methods, enabling design results to possess both specification interpretability and data accuracy. By weighting and fusing the initial and predicted slope ratios based on risk levels, an adaptive balance between safety and economy under different geological conditions is achieved, solving the problem that existing methods with fixed design strategies cannot adapt to different risk scenarios. By performing multi-condition limit balance verification on the coupled slope ratio and automatically increasing the slope ratio when the safety factor is not met and iteratively correcting it until all condition thresholds are met, this invention solves the problems of existing machine learning methods lacking safety verification in their prediction results and traditional methods relying on manual experience for adjustments when verification fails.

[0028] This invention combines theoretical inversion of rock fracture angle with data-driven correction using machine learning. The entire process follows the special specifications for hydropower engineering. By constructing a closed-loop method that includes experimental inversion, specification formulation, machine learning correction, multi-condition verification, and reinforcement for special geological conditions, it not only utilizes historical engineering data to improve the accuracy of slope ratio design and engineering adaptability, but also strictly meets the safety control requirements under complex geological conditions and diverse working conditions. It can optimize the economic efficiency of the project while ensuring the long-term safety of the slope. The method is standardized, easy to operate, and widely applicable, and can effectively adapt to the excavation design needs of steep and complex geological slopes in hydropower projects.

[0029] In a preferred embodiment, the reduced friction angle and cohesion within the rock mass in step S1 include the following steps: Obtain the rock fracture angle of the target slope. and the uniaxial compressive strength σ of the rock mass n Wherein, the rock mass fracture angle The uniaxial compressive strength σ of the rock mass can be measured through indoor rock fracture tests or through on-site slope failure trace measurements. n These two parameters can be obtained by selecting representative rock mass samples and conducting indoor uniaxial compressive strength tests according to specifications. They are the original measured values ​​that reflect the basic mechanical properties of the rock mass.

[0030] Based on the Mohr-Coulomb failure criterion, the internal friction angle φ of the rock mass is calculated using the formula φ=2×(β-45°); the fracture angle of the rock mass is then obtained. and the uniaxial compressive strength σ of the rock mass n Subsequently, strength parameters were inverted based on the Mohr-Coulomb failure criterion. The Mohr-Coulomb criterion indicates that when the rock reaches its ultimate equilibrium state, the angle between the fracture surface and the direction of the maximum principal stress is 45° + φ / 2. In this scheme, the direction of the maximum principal stress is vertical, and the rock mass fracture angle... The angle between the fracture surface and the vertical direction is φ, which satisfies the relationship φ = 2 × (β - 45°).

[0031] According to the formula c=σ n The cohesive force c is calculated using (1-sinφ) / (2·cosφ); based on the geometric relationship of the Mohr-Coulomb strength envelope, the cohesive force c can be derived from the uniaxial compressive strength σ. n The friction angle φ within the rock mass is derived from this. Under uniaxial compression conditions, the Mohr stress circle is tangent to the strength envelope. Based on this, an equation is established and solved to obtain the formula for calculating cohesion: c = σ n The cohesion c of the rock mass can be calculated from (1-sinφ) / (2·cosφ).

[0032] The basic reduction coefficient is determined based on the weathering degree level. The basic reduction coefficient is then adjusted based on the rock mass integrity coefficient to obtain a comprehensive reduction coefficient. The comprehensive reduction coefficient is multiplied by the internal friction angle φ and cohesion c of the rock mass to obtain the internal friction angle φ' and cohesion c' of the rock mass after standard reduction.

[0033] The internal friction angle φ and cohesion c of the rock mass mentioned above are theoretical values ​​obtained by inversion from the laboratory test of intact rock. However, due to the presence of joints, fissures and weathering, the actual strength of the rock mass in the field is significantly lower than the laboratory test values. If the internal friction angle φ and cohesion c of the rock mass are used directly for slope design, the bearing capacity of the rock mass will be overestimated, resulting in a design that is too dangerous.

[0034] Therefore, this step introduces a standardized reduction mechanism. Specifically, firstly, the foundation reduction coefficient is determined based on the weathering degree. The weathering degree reflects the extent of deterioration of the rock mass due to weathering; the more intense the weathering, the smaller the foundation reduction coefficient. Secondly, the foundation reduction coefficient is adjusted based on the rock mass integrity coefficient. The rock mass integrity coefficient is obtained through on-site acoustic wave testing and is the square of the ratio of the on-site rock mass wave velocity to the indoor rock core wave velocity. The smaller the value, the more fragmented the rock mass. The lower the rock mass integrity coefficient, the greater the adjustment range of the foundation reduction coefficient. The product of the foundation reduction coefficient and the adjustment coefficient is the comprehensive reduction coefficient. The comprehensive reduction coefficient is multiplied by the internal friction angle φ and cohesion c of the rock mass to obtain the internal friction angle φ' and cohesion c' of the rock mass after standardized reduction. The rules for determining the foundation reduction coefficient and the adjustment coefficient are pre-established based on the recommendations in Appendix D of the "Code for Geological Investigation of Hydropower Engineering" GB 50287-2016. This code is based on a large amount of practical experience in water conservancy and hydropower projects and is a recognized technical basis in the industry.

[0035] Preferably, step S2 includes the following steps: Using the reduced internal friction angle φ', cohesion c', rock mass integrity coefficient, weathering degree, and slope height as query conditions, the initial slope ratio value is obtained by querying the preset recommended slope ratio table.

[0036] Specifically, the internal friction angle φ' represents the mechanical strength, reflecting the frictional resistance of the rock mass under normal stress; cohesion c' represents the mechanical strength, reflecting the shear resistance of the rock mass under asymmetric stress; the rock mass integrity coefficient reflects the degree of joint and fracture development; the weathering degree reflects the degree of deterioration of the rock mass due to weathering; and the slope height reflects the potential energy scale and instability consequences of the slope. The weathering degree is determined comprehensively through on-site outcrop observation and wave velocity testing, and is classified into fully weathered, strongly weathered, moderately weathered, and slightly weathered levels according to specifications. The slope height is obtained through topographic mapping or on-site layout.

[0037] After obtaining the above five parameters, the rock mass quality is comprehensively evaluated according to the rock mass quality grading standards specified in the "Code for Geological Investigation of Hydropower Projects" GB 50287-2016, to obtain the rock mass quality grade. The evaluation logic is as follows: the higher the internal friction angle φ' and cohesion c' of the rock mass, the larger the rock mass integrity coefficient, the lower the weathering degree, and the smaller the slope height, the better the rock mass quality, and the steeper the required slope ratio can be (i.e., the smaller the slope ratio value m); conversely, the worse the rock mass quality, the gentler the required slope ratio should be (i.e., the larger the slope ratio value m).

[0038] After determining the rock mass quality grade, the recommended slope ratio value corresponding to the grade is obtained by consulting the preset standard slope ratio recommendation table, which is the initial slope ratio value. The standard slope ratio recommendation table is pre-established, as shown in Table 1, which records the mapping relationship between different rock mass quality grades and recommended initial slope ratio values.

[0039] Table 1: Recommended Standard Slope Ratio It is worth noting that in this application, the slope ratio is expressed in the form of 1:m, where m is the slope ratio value. The larger the slope ratio value m, the gentler the slope; the smaller the slope ratio value m, the steeper the slope. The initial slope ratio value, predicted slope ratio value, coupled slope ratio value, and recommended slope ratio value are all expressed in the form of m value and participate in the calculation, and finally the design output is in the form of a 1:m slope ratio.

[0040] In a preferred embodiment, the machine learning model in step S3 is obtained through the following steps: S31, obtain historical data of rock slopes of existing hydropower projects. Each historical data includes rock fracture angle, uniaxial compressive strength of rock mass, lithology, rock mass integrity coefficient, weathering degree, slope height, and the corresponding actual excavation slope ratio. First, historical data on rock slopes of existing hydropower projects were collected. The historical data came from completed hydropower project slopes that had been tested in operation. Each historical data record documented the key engineering geological parameters of an independent slope project and the actual excavation slope ratio adopted in the end.

[0041] S32, perform preprocessing on the historical data, including outlier removal and missing value completion; The collected historical data undergoes preprocessing to improve data quality and ensure the stability and reliability of subsequent model training. Preprocessing includes: (1) Outlier Removal: The 3σ principle (Laida criterion) is used to identify and remove data that deviates from the normal range. For each numerical parameter (rock fracture angle, rock uniaxial compressive strength, rock integrity coefficient, slope height), its mean μ and standard deviation σ are calculated. If the value of a data point exceeds the interval [μ-3σ, μ+3σ], it is determined to be an outlier and removed. The 3σ principle is based on the assumption of normal distribution and can retain normal data with a confidence level of 99.7%, making it a mature method in statistical data processing.

[0042] (2) Missing value completion: For fields with missing values ​​in the data records, the mean or interpolation method of the same type of engineering data is used to complete the missing values. Specifically, if a data point is missing a parameter value, the mean of the parameter is calculated as the completion value from other data with the same lithology and weathering degree as the data point; or linear interpolation is used to estimate the missing parameter based on the correlation between other known parameters of the data point and the missing parameter.

[0043] S33 uses lithology and weathering degree as the stratification basis to perform stratified sampling on the preprocessed historical data, dividing it into training and test sets. The specific operation of stratified sampling is as follows: all historical data are divided into multiple sub-layers based on a cross-combination of lithology (e.g., granite, limestone, sandstone, etc.) and weathering degree (e.g., completely weathered, strongly weathered, moderately weathered, slightly weathered). Then, within each sub-layer, samples are randomly selected at a preset ratio (e.g., 8:2) and assigned to the training and test sets respectively. Finally, the samples extracted from each sub-layer are merged to form the global training and test sets. Through stratified sampling, the distribution ratio of each lithology category and weathering degree is ensured to be consistent between the training and test sets, enabling the model evaluation indicators to truly reflect the model's predictive performance under various geological conditions, resulting in stable and reliable evaluation results.

[0044] S34, For the historical data in the training set, the internal friction angle and cohesion of the rock mass after standard reduction are calculated from the rock mass fracture angle and the uniaxial compressive strength of the rock mass. The internal friction angle, cohesion, rock mass fracture angle, lithology code, rock mass integrity coefficient, weathering degree, and slope height after standard reduction are used as input features, and the actual excavation slope ratio is used as the target variable to train the XGBoost regression model to obtain the initial machine learning model. First, for each historical data point in the training set, the internal friction angle φ' and cohesion c' of the rock mass are calculated using the rock mass fracture angle and uniaxial compressive strength, after standard reduction, to ensure consistency between the historical data and the target slope data. Second, an input feature vector is constructed. Categorical variables such as lithology and weathering degree are converted into numerical codes. Specifically, lithology is converted into a lithology code (e.g., granite is coded as 1, limestone as 2, sandstone as 3), and weathering degree is converted into a weathering degree code (e.g., slightly weathered as 1, moderately weathered as 2, strongly weathered as 3, and completely weathered as 4). The input feature vector consists of the following features: rock mass fracture angle, internal friction angle φ' (after standard reduction), cohesion c' (after standard reduction), lithology code, rock mass integrity coefficient, weathering degree code, and slope height.

[0045] Using the input feature vector as input and the corresponding actual excavation slope ratio as the target variable, the XGBoost regression model is trained. The training process of the XGBoost regression model is as follows: XGBoost employs a gradient boosting framework, iteratively adding decision trees to gradually reduce prediction error. In each iteration, the newly added decision tree fits the residual of the current model on the training set, and the objective function is optimized through gradient descent. The objective function consists of two parts: a loss function and a regularization term. The loss function measures the deviation between the predicted slope ratio and the actual excavation slope ratio, while the regularization term controls the model complexity to prevent overfitting. After training, a regression model capable of predicting slope ratio values ​​based on input features is obtained, denoted as the initial machine learning model.

[0046] S35, the initial machine learning model is evaluated using the test set, and when the evaluation metric meets the preset accuracy requirement, the initial machine learning model is used as the machine learning model.

[0047] The initial machine learning model is evaluated using a test set. The input feature vector of each data point in the test set is input into the initial machine learning model to obtain the predicted slope ratio. The predicted slope ratio is then compared with the actual excavation slope ratio recorded in the test set to calculate the preset evaluation index.

[0048] The evaluation index may be the coefficient of determination R. 2 At least one of the following: root mean square error (RMSE) or mean absolute error (MAE). For example, R 2 The closer the value is to 1, the stronger the model's ability to explain slope ratio variations; the smaller the RMSE, the smaller the deviation between the predicted slope ratio and the actual excavation slope ratio. Determine whether the evaluation index meets the preset accuracy requirements (e.g., R²). 2 ≥0.85, or RMSE≤0.10). If satisfied, the initial machine learning model is used as the pre-trained machine learning model; if not satisfied, the hyperparameters of XGBoost (such as the number of decision trees, maximum depth, and learning rate) are adjusted and the S34 training step is re-executed until the evaluation metric meets the preset accuracy requirement.

[0049] In a preferred embodiment, step S4 includes the following steps: S41, Determine the risk level of the target slope based on the weathering degree and slope height; The weathering degree reflects the extent to which the rock mass has deteriorated due to weathering. The more severe the weathering, the lower the rock mass strength, and the higher the risk of slope instability. Slope height reflects the potential energy scale of the slope and the consequences of instability. The higher the slope, the larger the affected area of ​​instability, and the higher the risk. The rules for classifying the risk levels are pre-established, based on industry engineering practice and relevant standards for classifying slope risks under different geological conditions. As an example, the correspondence between the risk levels, weathering degree, and slope height is as follows: Table 2: Correspondence between Risk Level, Weathering Degree Level, and Slope Height For situations where the weathering degree and slope height belong to different risk levels (e.g., moderately weathered but H>50m, or strongly weathered but H<20m), the final risk level can be determined according to preset comprehensive evaluation rules. For example, the higher risk level can be used, or a weighted evaluation can be performed based on preset weights for weathering degree and slope height.

[0050] S42, determine the weight ω1 of the initial slope ratio and the weight ω2 of the predicted slope ratio based on the risk level, where ω1 + ω2 = 1, and the higher the geological risk indicated by the risk level, the larger the weight ω1. The initial slope ratio is derived from the industry standard recommendation table and is a conservative empirical value summarized from a large amount of engineering practice, leaning towards safety. The predicted slope ratio is derived from the learning of historical data by the machine learning model and can reflect the optimal slope ratio actually used under similar geological conditions, leaning towards economy. When the geological risk is high, safety should be ensured first, and the proportion of the conservative value in the standard should be increased; when the geological risk is low, the rock mass conditions are good, and the safety margin is sufficient, the data-driven optimization results can be fully adopted to reduce the engineering cost. As a preferred example, the correspondence between the risk level and the weight is shown in Table 3: Table 3: Correspondence between Risk Level and Weight S43, according to formula Calculate the coupling slope ratio ,in The initial slope ratio value is... The predicted slope ratio is denoted as .

[0051] In a preferred embodiment, step S5 includes the following steps: S51, according to the formula α=arctan(1 / Calculate the slope angle α; S52, under natural working conditions, sudden drop in water level working conditions and earthquake working conditions, respectively, the safety factor for each working condition is calculated based on the values ​​of pore water pressure, water weight and horizontal seismic force corresponding to each working condition; The preset safety factor threshold for the natural working condition is 1.30, the preset safety factor threshold for the sudden drop in water level working condition is 1.25, and the preset safety factor threshold for the earthquake working condition is 1.25.

[0052] The limit equilibrium method is the most widely used and industry-recognized mature method in slope stability analysis. Its basic principle is as follows: assuming a potential sliding surface, treating the sliding body as a rigid body, analyzing the balance between the anti-sliding force (or moment) and the sliding force (or moment) acting on the sliding body, and defining the safety factor Fs as the ratio of the two. Fs > 1 indicates that the slope is in a stable state, Fs < 1 indicates that the slope will become unstable, and Fs = 1 indicates that the slope is in a limit equilibrium state.

[0053] The three working conditions are: natural working condition, which refers to the long-term working state during normal slope operation, considering only the self-weight of the rock mass and the hydrostatic pressure at the normal groundwater level, without earthquakes; sudden drop in water level working condition, which is a temporary dangerous state caused by the rapid drop in reservoir water level, where groundwater in the slope cannot drain in time, the sliding surface has been drained, but the self-weight of the saturated part of the slope still acts on the sliding surface; and earthquake working condition, which is an extreme state where earthquakes and normal seepage act simultaneously, with an additional horizontal seismic inertial force applied on top of the hydrostatic pressure in the natural working condition. These three working conditions are the conventional and typical working conditions in this field.

[0054] The safety factor is calculated as follows: Angle of slope: ; Sliding surface length: ;in, The inclination angle of the sliding surface; Volume of sliding body (per unit width): Where γ is the unit weight of the rock mass; Weight of the sliding body: ; Anti-slip force: Where u is the pore water pressure and Vw is the weight of water; Sliding force: ;in, Seismic coefficient; Safety factor: ; Each working condition corresponds to a preset safety factor threshold, which serves as a quantitative standard for determining whether the slope meets safety requirements under that condition. The preset safety factor thresholds are set according to industry standards defined in the "Code for Geological Investigation of Hydropower Engineering" GB50287-2016 and the "Code for Design of Slopes in Hydropower Engineering"; specifically, the preset safety factor threshold for the natural working condition is 1.30, the preset safety factor threshold for the sudden drop in water level working condition is 1.25, and the preset safety factor threshold for the earthquake working condition is 1.25.

[0055] In a preferred embodiment, step S6 includes the following steps: S61, determine whether the safety factors calculated under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions are all greater than or equal to their respective preset safety factor thresholds; if not, increase the coupled slope ratio value by a preset fixed step size; the fixed step size is a preset slope ratio increment, and the fixed step size is a value in the range of 0.05~0.10, preferably 0.05. The principle for selecting the step size is: if the step size is too large, it may lead to an excessive increase in the coupled slope ratio value. Although the safety factor meets the requirements, the slope is too gentle, the excavation volume is unnecessarily increased, and the economy is damaged; if the step size is too small, the number of iterations increases and the convergence speed is slow. A step size of 0.05~0.10 is a reasonable trade-off between convergence speed and design accuracy in engineering practice.

[0056] S62, update the slope angle based on the increased coupling slope ratio; as the coupling slope ratio increases, the slope angle decreases accordingly. A smaller slope angle results in a gentler slope excavation surface, reduces the weight of the sliding body, and keeps the sliding surface length unchanged. This increases the anti-sliding force, reduces the sliding force, and consequently improves the safety factor.

[0057] S63, with the updated slope angle, the slope stability limit balance verification under the natural working condition, the sudden drop in water level working condition and the earthquake working condition is performed again to obtain the updated safety factor. S64. Repeat steps S61 to S63 until the safety factor under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions is greater than or equal to the corresponding preset safety factor threshold, and the coupled slope ratio value that meets the conditions at this time is used as the recommended slope ratio output.

[0058] The termination condition for this iterative process is that the safety factors for all working conditions simultaneously meet the requirements. Since the coupled slope ratio increases with each iteration, the safety factor monotonically increases. When the coupled slope ratio approaches infinity, the slope angle approaches 0°, the slope approaches horizontal ground, and the safety factor approaches infinity, thus meeting the threshold requirement. However, in engineering practice, the design requirement is to stop the iteration when the safety factor just exceeds the threshold to avoid excessive slowing down and causing unnecessary increases in excavation.

[0059] When the iteration termination condition is met, the coupling slope ratio at this point is output as the recommended slope ratio. The output form of the recommended slope ratio is a slope ratio value, that is, the final recommended design slope ratio is 1:recommended slope ratio, which ensures that the economy is optimized by utilizing historical data and passes the safety verification of various extreme working conditions.

[0060] As a preferred embodiment, the following steps are included before outputting the recommended slope: Determine whether the target slope has an outward-dipping weak structural surface; wherein, the outward-dipping weak structural surface is a structural surface that dips outward, has a dip angle smaller than the slope angle corresponding to the recommended slope ratio, and has a mechanical strength lower than the surrounding rock mass; if so, obtain the dip angle of the control surface of the outward-dipping weak structural surface; the dip angle of the control surface is obtained by conducting on-site geological measurements on the identified outward-dipping weak structural surface, i.e., the true dip angle of the structural surface.

[0061] The dip of the structural surface is roughly consistent with the dip of the slope surface, meaning the angle between the structural surface dip and the slope surface dip is less than a preset angle (usually within 30°). When the structural surface dip is in the same direction or approximately in the same direction as the slope surface dip, the structural surface may be exposed on the slope excavation surface, forming a potential sliding bottom boundary.

[0062] If the dip angle of the structural surface is less than the slope angle of the currently recommended slope ratio, and the dip angle of the structural surface is greater than or equal to the slope angle, the structural surface will not be exposed on the slope surface and cannot form a continuous sliding surface, thus posing no controlling threat to the overall stability of the slope. Only when the dip angle of the structural surface is less than the slope angle can the structural surface be exposed on the slope surface, forming a potential sliding channel.

[0063] The cohesion and internal friction angle of the structural plane are significantly lower than those of the surrounding rock mass. Structural planes that meet this condition typically include argillaceous interlayers, inter-layer shear zones, fault gouge, and densely jointed zones. These weak structural planes are the weak points in the rock mass and are prone to sliding failure under engineering loads and external environmental influences. Among them, argillaceous interlayers are common weak interlayers in layered rock masses, and their strength is extremely low due to their high clay mineral content; inter-layer shear zones are shear fracture zones generated between bedding planes by tectonic movements, where the original structure has been destroyed; fault gouge is fine-grained infill formed by fault activity, with cohesion close to zero; and densely jointed zones are banded areas with highly developed joints and extremely fractured rock masses.

[0064] The cohesion and internal friction angle of the structural surface obtained through field exploration and indoor tests are compared with the rock mass cohesion c' and internal friction angle φ' of the same target slope determined in step S1 after standard reduction. If both are lower than 60% of the corresponding values ​​of the surrounding rock, the structural surface is determined to be a weak structural surface.

[0065] Determine whether the slope angle corresponding to the recommended slope ratio is greater than the control surface inclination angle; if so, increase the recommended slope ratio, update the slope angle based on the increased recommended slope ratio, and return to step S5 to recalculate the slope stability limit balance until the updated slope angle is not greater than the control surface inclination angle and the safety factor of all working conditions is greater than or equal to the corresponding preset safety factor threshold.

[0066] This implementation method applies a geometric control criterion based on outward-dipping weak structural planes before outputting the recommended slope ratio. This ensures that the final recommended slope ratio not only meets the limit equilibrium safety requirements based on rock mass strength parameters but also satisfies the geometric safety constraints controlled by the outward-dipping weak structural planes. This dual-protection mechanism ensures that the safety margin of the slope design is truly sufficient under special geological conditions, considering both the overall stability controlled by rock mass strength and the geometric stability controlled by the attitude of the structural planes. In slope engineering, bedding-parallel sliding controlled by outward-dipping weak structural planes is one of the most common instability modes. Because the sliding surface is an existing weak surface with shear strength far lower than the rock mass itself, the consequences of instability are often very serious. This step avoids the possibility of the recommended slope ratio entering this dangerous range by ensuring that the slope angle is not greater than the dip angle of the structural plane.

[0067] Furthermore, before outputting the recommended slope, the following steps are also included: When the slope height of the target slope is greater than 50 meters, or the recommended slope ratio is greater than 1.0, the target slope shall be set up with graded slope, with each platform width not less than 2 meters and the number of grades not less than 3.

[0068] By setting up graded slopes, single-level high slopes or single-level large-scale gentle slopes are transformed into multi-level slopes, which improves the stress distribution within the slope body, reduces the stress concentration at the toe of a single slope, provides convenient conditions for construction and maintenance, and enhances the long-term stability of the slope.

[0069] The present invention also provides a system for determining the recommended slope ratio of rock slopes in hydropower projects, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for determining the recommended slope ratio of rock slopes in hydropower projects as described above.

[0070] The above are merely preferred embodiments of the present invention and do not limit the scope of protection of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention’s specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for determining the recommended slope ratio for rock slopes in hydropower projects, characterized in that, Includes the following steps: S1, obtain the rock mass fracture angle, internal friction angle and cohesion of the target slope after standard reduction, as well as basic geological parameters including lithology, rock mass integrity coefficient, weathering degree and slope height, and potential sliding surface dip angle and sliding surface length; S2. Based on the friction angle, cohesion and basic geological parameters of the rock mass, and in accordance with the slope design specifications, determine the initial slope ratio. S3, the rock mass fracture angle, the rock mass internal friction angle, the cohesion and the basic geological parameters are used as input features and input into a pre-trained machine learning model to obtain the predicted slope ratio; S4. Based on the risk level of the target slope, determine the weights of the initial slope ratio and the predicted slope ratio, and perform weighted fusion of the initial slope ratio and the predicted slope ratio to obtain the coupled slope ratio. S5, using the slope angle corresponding to the coupled slope ratio and the potential sliding surface inclination angle and sliding surface length information as input, perform slope stability limit equilibrium verification under at least one preset working condition to obtain a safety factor; wherein, each preset working condition corresponds to a preset safety factor threshold. S6. When at least one of the safety factors is less than the preset safety factor threshold for the corresponding working condition, the coupling slope ratio is increased, and the slope angle is updated based on the increased coupling slope ratio. The slope stability limit balance is recalculated until the safety factors for all working conditions are greater than or equal to the corresponding preset safety factor threshold. The coupling slope ratio that finally meets the conditions is then output as the recommended slope ratio.

2. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 1, characterized in that, The friction angle and cohesion of the rock mass after standard reduction in step S1 include the following steps: Obtain the rock mass fracture angle of the target slope. and the uniaxial compressive strength σ of the rock mass n ; Based on the Mohr-Coulomb failure criterion, the friction angle φ within the rock mass is calculated using the formula φ=2×(β-45°). According to the formula c=σ n The cohesive force c is calculated using (1-sinφ) / (2·cosφ). The basic reduction coefficient is determined based on the weathering degree level. The basic reduction coefficient is then adjusted based on the rock mass integrity coefficient to obtain a comprehensive reduction coefficient. The comprehensive reduction coefficient is multiplied by the internal friction angle φ and cohesion c of the rock mass to obtain the internal friction angle φ' and cohesion c' of the rock mass after standard reduction.

3. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 2, characterized in that, Step S2 includes the following steps: Using the reduced internal friction angle φ', cohesion c', rock mass integrity coefficient, weathering degree, and slope height as query conditions, the initial slope ratio value is obtained by querying the preset recommended slope ratio table.

4. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 3, characterized in that, The machine learning model in step S3 is obtained through the following steps: S31, obtain historical data of rock slopes of existing hydropower projects. Each historical data includes rock fracture angle, uniaxial compressive strength of rock mass, lithology, rock mass integrity coefficient, weathering degree, slope height, and the corresponding actual excavation slope ratio. S32, perform preprocessing on the historical data, including outlier removal and missing value completion; S33 uses lithology and weathering degree as the stratification basis to perform stratified sampling on the preprocessed historical data, dividing it into training set and test set; S34, For the historical data in the training set, the internal friction angle and cohesion of the rock mass after standard reduction are calculated from the rock mass fracture angle and the uniaxial compressive strength of the rock mass. The internal friction angle, cohesion, rock mass fracture angle, lithology code, rock mass integrity coefficient, weathering degree, and slope height after standard reduction are used as input features, and the actual excavation slope ratio is used as the target variable to train the XGBoost regression model to obtain the initial machine learning model. S35, the initial machine learning model is evaluated using the test set, and when the evaluation metric meets the preset accuracy requirement, the initial machine learning model is used as the machine learning model.

5. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 1, characterized in that, Step S4 includes the following steps: S41, Determine the risk level of the target slope based on the weathering degree and slope height; S42, determine the weight ω1 of the initial slope ratio and the weight ω2 of the predicted slope ratio based on the risk level, where ω1+ω2=1, and the higher the geological risk indicated by the risk level, the larger the weight ω1; S43, according to formula Calculate the coupling slope ratio ,in The initial slope ratio value is... The predicted slope ratio is denoted as .

6. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 5, characterized in that, Step S5 includes the following steps: S51, according to the formula α=arctan(1 / Calculate the slope angle α; S52, under natural working conditions, sudden drop in water level working conditions and earthquake working conditions, respectively, the safety factor for each working condition is calculated based on the values ​​of pore water pressure, water weight and horizontal seismic force corresponding to each working condition; The preset safety factor threshold for the natural working condition is 1.30, the preset safety factor threshold for the sudden drop in water level working condition is 1.25, and the preset safety factor threshold for the earthquake working condition is 1.

25.

7. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 6, characterized in that, Step S6 includes the following steps: S61, determine whether the safety factors calculated under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions are all greater than or equal to their respective preset safety factor thresholds; if not, increase the coupling slope ratio value by a preset fixed step size. S62, Update the slope angle based on the increased coupling slope ratio; S63, with the updated slope angle, the slope stability limit balance verification under the natural working condition, the sudden drop in water level working condition and the earthquake working condition is performed again to obtain the updated safety factor. S64. Repeat steps S61 to S63 until the safety factor under natural working conditions, sudden drop in water level working conditions, and earthquake working conditions is greater than or equal to the corresponding preset safety factor threshold, and the coupled slope ratio value that meets the conditions at this time is used as the recommended slope ratio output.

8. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 1, characterized in that, Before outputting the recommended slope, the following steps are also included: Determine whether the target slope has an outward-dipping weak structural surface; wherein, the outward-dipping weak structural surface is a structural surface that dips outward, has a dip angle smaller than the slope angle corresponding to the recommended slope ratio, and has a mechanical strength lower than the surrounding rock mass; if so, obtain the dip angle of the control surface of the outward-dipping weak structural surface; Determine whether the slope angle corresponding to the recommended slope ratio is greater than the control surface inclination angle; if so, increase the recommended slope ratio, update the slope angle based on the increased recommended slope ratio, and return to step S5 to recalculate the slope stability limit balance until the updated slope angle is not greater than the control surface inclination angle and the safety factor of all working conditions is greater than or equal to the corresponding preset safety factor threshold.

9. The method for determining the recommended slope ratio for rock slopes in hydropower projects according to claim 1, characterized in that, Before outputting the recommended slope, the following steps are also included: When the slope height of the target slope is greater than 50 meters, or the recommended slope ratio is greater than 1.0, the target slope shall be set up with graded slope, with each platform width not less than 2 meters and the number of grades not less than 3.

10. A system for determining the recommended slope ratio for rock slopes in hydropower projects, characterized in that, The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for determining the recommended slope ratio for rock slopes in hydropower projects as described in any one of claims 1 to 9.

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