Stability evaluation and reinforcement decision-making method for side slope containing soft rock interlayer under rainfall condition

Abstract

The invention relates to the technical field of soil slope reliability analysis, in particular to a stability evaluation and reinforcement decision-making method for a slope containing a soft rock interlayer under a rainfall condition. Soft rock parameters are generated based on logarithmic normal distribution, sample uniformity is ensured through LHS, and negative correlation is introduced through Cholesky decomposition; mapping the data back to engineering actual distribution; calculating a slope stability coefficient K in combination with correction software, adding Gaussian noise to simulate an actual error, and standardizing input features and output labels; after the data set is divided into a training set and a test set, predicting a K value by adopting an SVR model, and optimizing hyper-parameters through grid search; and finally, constructing a DNN based on the standardized K value, judging reinforcement measures through a classification task, performing regression to output specific parameters, and finally generating a complete reinforcement scheme in stages. According to the method, the reliability of parameter generation and analysis is improved, the stability evaluation and decision-making precision is enhanced, and the data processing and model generalization ability is optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of soil slope reliability analysis, in particular to a method for evaluating the stability of a slope containing a soft rock interlayer under rainfall conditions and making reinforcement decisions. Background Art

[0002] Under rainfall conditions, rainwater infiltration into slopes containing soft rock interlayers can lead to a loss of matrix suction, a sharp increase in pore water pressure, and a sudden drop in rock mass shear strength, easily triggering landslides or collapses. This instability not only threatens the safety of surrounding transportation arteries and residential areas, but can also block rivers, forming barrier lakes, triggering secondary disasters such as floods and mudslides, and causing significant loss of life and property.

[0003] Under the coupled effects of rainfall and complex geological conditions, stability assessment and reinforcement decision-making for slopes containing soft rock interlayers face multi-dimensional technical bottlenecks. Existing technologies employ stability assessment methods based on empirical formulas and numerical simulations, as well as decision-making systems based on single machine learning models.

[0004] Stability assessment methods based on empirical formulas and numerical simulations: Monte Carlo sampling or simple random sampling is used to generate soft rock parameters (internal friction angle φ2, cohesion c2). The slope stability factor K is calculated using limit equilibrium methods (such as the Bishop method and the Janbu method) or finite element software (such as PLAXIS and FLAC). Reinforcement measures (such as geotextiles and anchors) are selected based on the K value range (e.g., K < 1.2 requires reinforcement) and expert experience.

[0005] Decision-making system based on a single machine learning model: random sampling is used to generate parameters, and a single model (such as random forest or shallow neural network) is used to predict K value or directly classify reinforcement measures.

[0006] Existing methods have significant flaws in parameter generation, model building, and decision output:

[0007] 1) Parameter generation: Failure to combine the uniformity of Latin hypercube sampling with the correlation control of Cholesky decomposition results in data statistical characteristics deviating from reality;

[0008] 2) Stability assessment: Relying on empirical formulas or single models, it is impossible to fit nonlinear relationships with high precision;

[0009] 3) Reinforcement decision-making: Lack of dynamic parameter optimization capabilities, over-reliance on manual experience, and low efficiency;

[0010] 4) Data processing: Ignoring standardization and category balance affects the stability of model training. Summary of the Invention

[0011] To address the above issues, the present invention aims to provide a method for evaluating the stability of slopes containing soft rock interlayers and making reinforcement decisions under rainfall conditions. This method improves the reliability of parameter generation and analysis, enhances the accuracy of stability assessment and decision-making, and optimizes data processing and model generalization capabilities. The technical solution is as follows:

[0012] A method for evaluating the stability of a slope containing soft rock interlayers and making reinforcement decisions under rainfall conditions includes the following steps:

[0013] Step 1: Parameter generation and data sampling;

[0014] Based on Latin hypercube sampling, an initial uniformly distributed sample of soft rock parameters is generated, wherein the soft rock parameters include the internal friction angle φ2 and the cohesion c2; the initial uniformly distributed sample is subjected to standard normal distribution mapping, and the constructed target covariance matrix is ​​decomposed using Cholesky decomposition to introduce negative correlation. The correlated standard normal variables are then mapped back to the original log-normal distribution space to form a soft rock parameter data set that satisfies statistical distribution and correlation;

[0015] Step 2: Slope stability coefficient calculation and data preprocessing;

[0016] The soft rock parameters generated in step 1 are input into the correction software to calculate the slope stability coefficient K, and Gaussian noise is added to simulate the actual error; Z-score normalization is performed on the input features and output labels respectively, and the dataset is divided into a training set and a test set;

[0017] Step 3: Support vector regression model training and optimization;

[0018] A support vector regression model was constructed using the radial basis kernel function. The hyperparameter combination was optimized through grid search combined with 5-fold cross validation, and the support vector regression model was trained to predict the slope stability coefficient K.

[0019] Step 4: Construction of deep neural network reinforcement decision model;

[0020] First, the slope stability coefficient K of the predicted new sample is obtained. The reinforcement measure name label is encoded as a numerical label. A two-branch DNN (Deep Neural Network) model is constructed. The classification branch is used to output the probability distribution of the reinforcement measure, and the regression branch is used to output the reinforcement parameter. The model is compiled using a hybrid loss function, and class weights are set to balance the samples. Training is combined with the early stopping method.

[0021] Step 5: Dynamic decision output;

[0022] The slope stability coefficient K of the new sample is input into the DNN model, and the type of reinforcement measures and corresponding parameters are output. After denormalization, a complete reinforcement plan is generated in stages.

[0023] The beneficial effects of the present invention are:

[0024] 1) This invention improves the reliability of parameter generation and analysis: By integrating Latin Hypercube Sampling (LHS) with Cholesky decomposition, the generated parameter data not only evenly covers the parameter space but also accurately controls the negative correlation between variables (e.g., ρ = -0.7), solving the problem of insufficient data representativeness in traditional methods and ensuring that the input data for subsequent stability assessment conforms to actual statistical laws.

[0025] 2) The present invention enhances stability assessment and decision-making accuracy: a support vector regression (SVR) model combined with a radial basis function (RBF) is used to effectively capture the nonlinear relationship between soft rock parameters and stability coefficients. Furthermore, through a deep neural network (DNN) dual-branch design, reinforcement measure classification and parameter dynamic optimization are simultaneously achieved, significantly improving prediction accuracy and decision-making efficiency, overcoming the limitations of empirical formulas and single models.

[0026] 3) This invention optimizes data processing and model generalization capabilities: through Z-score normalization, category weight adjustment, and Gaussian noise simulation, it eliminates dimensional differences, balances sample distribution, and simulates actual errors. Combined with the early stopping method and hybrid loss function, it greatly improves the model convergence speed and generalization performance, providing robust intelligent decision support for complex engineering scenarios.

[0027] The above advantages systematically solve the core defects of traditional methods in data generation, model accuracy and engineering applicability, and realize the full process optimization from parameter generation to reinforcement plan output. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a main system flow chart of the method for evaluating the stability of slopes containing soft rock interlayers and strengthening decisions under rainfall conditions of the present invention.

[0029] Figure 2 This is the SVM model training flow chart.

[0030] Figure 3 It is the DNN decision model training flowchart. DETAILED DESCRIPTION

[0031] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] An intelligent decision-making system for evaluating the stability of slopes containing soft rock interlayers and for determining reinforcement solutions under rainfall conditions. The following, in conjunction with the accompanying drawings and examples, details the technical solutions, implementation steps, and application effects of the present invention in engineering practice.

[0033] like Figure 1 As shown in the figure, starting with data generation and parameter sampling, soft rock parameters (internal friction angle φ2 and cohesion c2) were first generated based on a lognormal distribution. Latin hypercube sampling (LHS) was used to ensure sample uniformity, and negative correlation was introduced using Cholesky decomposition. Subsequently, the data were mapped back to the actual project distribution and statistical properties verified. Next, the slope stability coefficient K was calculated using Lizheng software. Gaussian noise was added to simulate actual errors, and Z-score normalization was performed on the input features and output labels. After the dataset was divided into training and test sets, a support vector regression (SVR) model was used to predict the K value. Hyperparameters (C = 10, γ = 0.1) were optimized through grid search, and the model accuracy was finally verified. Finally, a deep neural network (DNN) was constructed based on the standardized K value. Reinforcement measures (geotextile, anchor rods, and anchor nails) were determined through classification tasks, and specific parameters (area and number) were regressed and output. Finally, a complete reinforcement plan was generated in stages.

[0034] The specific process is as follows:

[0035] 1. Data Generation and Parameter Sampling

[0036] Under rainfall conditions, the changes in the internal friction angle (φ2) and cohesion (c2) of soft rock interlayers generally exhibit statistical regularity. Generating data that conforms to specific distributions and correlations requires a multi-step approach. Assuming that both the internal friction angle and cohesion follow a lognormal distribution, their probability density functions can be expressed as:

[0037]

[0038] Among them, μ and σ are the mean and standard deviation of the logarithmic space. To determine these two parameters, it is necessary to combine the actual physical range (such as φ min ≤φ2≤φ max , c min ≤c2≤c max ), the parameters of its lognormal distribution (mean μ and standard deviation σ) are determined by quantiles. For example, using the 5% and 95% quantile conditions:

[0039]

[0040]

[0041] Among them, μ φ and σ φ is the mean and standard deviation of the logarithmic space of the internal friction angle φ2, μc and σ c are the mean and standard deviation of the logarithmic space of cohesion c2.

[0042] Next, Latin Hypercube Sampling (LHS) is used to generate the initial samples. The core idea of ​​LHS is to divide the range of each variable into non-overlapping intervals (strata) equal to the number of samples, and randomly select a point in each stratum to ensure that the samples are evenly distributed in the parameter space. For example, when generating n = 30 sets of data, the interval of each variable (such as φ2 and c2) is divided into 30 strata, and the value of the i-th sample on the j-th variable is calculated as follows:

[0043]

[0044] Among them, π j is the random permutation of the jth column, ξ i,j is a uniform random number. The sample matrix U∈[0,1] generated by this process 30×2 Each column is evenly distributed in the interval [0,1] and has hierarchical coverage.

[0045] Subsequently, the initial sample is mapped into a standard normal variable through the probability integral transformation:

[0046] z φ =Φ -1 (u φ ),z c =Φ -1 (u c )

[0047] The z obtained at this time φ and z c Obey the independent standard normal distribution N(0,1). In order to introduce negative correlation between variables (such as the target correlation coefficient ρ = -0.7), it is necessary to perform a linear transformation on the independent standard normal samples. By constructing the target covariance matrix:

[0048]

[0049] And perform Cholesky decomposition on Σ to obtain the lower triangular matrix L (satisfying ), generate related variables through linear transformation:

[0050] Z correlated =Z·L T

[0051] Where Z = [z φ ,z c ] is an independent standard normal sample matrix.

[0052] This operation makes the transformed internal friction angle related variable matrix zφ,correlated and cohesion-related variable matrix z c,correlated with a target correlation coefficient ρ in standard normal space.

[0053] Next, the correlated standard normal variable is mapped back to the original lognormal distribution. The specific formula is:

[0054] φ2=exp(μ φ +σ φ ·z φ,correlated )

[0055] c2=exp(μ c +σ c ·z c,correlated )

[0056] Since the actual parameters have physical range limitations (such as φ2 ≥ 10 or c2 ≤ 100 kPa), the generated values ​​need to be truncated:

[0057] φ2=max(φ min ,min(φ max ,φ2))

[0058] c2=max(c min ,min(c max ,c2))

[0059] This step ensures that all generated values ​​fall within a reasonable range and are consistent with engineering practical significance.

[0060] Finally, the distribution and correlation of the generated data need to be verified. For distribution verification, the consistency of the empirical distribution of the generated data with the theoretical lognormal distribution can be compared by drawing a histogram or performing a Kolmogorov-Smirnov (KS) test. Correlation verification is performed by calculating the Pearson correlation coefficient ρ of the logarithmic transformed variables. actual :

[0061]

[0062] Ensure that it is close to the target correlation coefficient ρ. If the actual correlation coefficient deviates significantly from the target value, it can be further corrected by adjusting the covariance matrix in the Cholesky decomposition or optimizing the sample order. 2i and c 2i are the specific values ​​of the internal friction angle φ2 and cohesion c2 of the i-th sample, respectively. represents the mean of the logarithm of the internal friction angle of all samples, Represents the mean of the logarithm of cohesion of all samples.

[0063] In summary, by combining the uniformity advantage of Latin hypercube sampling, the correlation control of Cholesky decomposition, and the log-normal distribution mapping, the generated 30 sets of data can simultaneously meet the requirements of parameter space coverage, statistical distribution morphology, and negative correlation between variables.

[0064] 2. Stability coefficient calculation and data preprocessing

[0065] The generated soft rock parameters need to be combined with the correction software to calculate the corresponding stability coefficient K. In order to simulate the calculation process of the correction software in actual engineering, the present invention adopts a simplified formula:

[0066] K=0.18φ2+0.12ln(c2+1)+∈

[0067] Where ∈ is Gaussian noise, which is used to simulate the actual measurement error.

[0068] After the calculation is completed, the input feature (φ2, c2) is normalized by Z-score. The normalization formula is:

[0069]

[0070] Among them, μ0 is the characteristic mean and σ0 is the standard deviation.

[0071] Through normalization, features of different dimensions are unified into a similar numerical range, avoiding the problem of gradient instability caused by dimensional differences during model training.

[0072] The standardized dataset is divided into a training set (group x) and a test set (group y) (x:y=2:1) ​​to ensure the scientific nature of model training and verification.

[0073] Support vector machine (SVM) model training and optimization: Based on the above divided data, a support vector regression (SVR) model is constructed to predict the slope stability coefficient K. The model uses the radial basis kernel function, and its expression is:

[0074] RBF(x i ,y i )=exp(-γ||x i -y i ||)

[0075] The kernel function transforms the input features into a high-dimensional space through nonlinear mapping to capture the complex relationship between soft rock parameters and stability coefficients. The objective function of SVR is ∈-support vector regression (∈-SVR), and its mathematical form is:

[0076]

[0077] The constraints are:

[0078]

[0079] Among them, C is the penalty factor, ε is the insensitive loss threshold, ξ i and ξ i * is the slack variable.

[0080] To optimize model performance, a grid search combined with 5-fold cross-validation was used to select the optimal hyperparameters. The search range was C∈{1,10,100} and γ∈{0.01,0.1,1}. Cross-validation was used to calculate the coefficient of determination (R²) and mean squared error (MSE) for each parameter set, ultimately selecting C=10 and γ=0.1. Validation results on the test set demonstrated the model's ability to accurately predict the stability coefficient.

[0081] like Figure 2 As shown in Figure 1, the training process of the support vector machine (SVM) model first defines the hyperparameter search space, including the penalty factor C∈{1,10,100} and the kernel function parameter γ∈{0.01,0.1,1}, generating a total of 9 sets of hyperparameter combinations. A grid search is performed to traverse all combinations, and a 5-fold cross-validation is performed on each set of parameters: the dataset is divided into 5 subsets, and 1 subset is selected as the validation set each time, and the remaining 4 subsets are used as training sets. The model is trained and the coefficient of determination R of the validation set is calculated. 2 and mean square error (MSE). After repeating 5 times, the average value of each indicator is taken as the performance evaluation of the hyperparameter combination. Finally, the validation set R 2 The highest parameter combination (C = 10, γ = 0.1) was selected as the optimal configuration for model training. During training, the objective function was ∈-SVR (∈-SVR); constraints included upper and lower bounds on the prediction error and the non-negativity of the slack variables. A radial basis function (RBF) kernel was used to capture the nonlinear relationships between parameters.

[0082] 3. Deep Neural Network (DNN) Reinforcement Decision Model

[0083] like Figure 3As shown, DNN model training first normalizes the K value and encodes the reinforcement measures' labels (geotextile → 0, anchor → 1, anchor → 2). Z-score processing is also performed on specific parameters (area, number). Data is stratified and sampled using an 8:2 ratio to ensure consistent class distribution. The model structure is designed with a dual-branch output: the input layer receives the standardized K value. After feature extraction through the hidden layer (16 nodes → Dropout → 8 nodes), the classification branch outputs the reinforcement measure probability through softmax, while the regression branch outputs the parameter through linear activation. A hybrid loss function (classification cross entropy + mean squared error) is used during model compilation, with class weights set to balance the samples. Early stopping is applied during training to optimize efficiency. During testing, the reinforcement type is prioritized, and the corresponding parameters (such as the number of anchors) are dynamically extracted. After denormalization, a specific solution (such as "8 anchors, 1.5m apart") is generated, ultimately outputting a complete engineering decision.

[0084] During the data collection phase, the raw data comes from the calculation process of the software in the above steps, which includes multiple sets of K values ​​and their corresponding reinforcement measures. The data needs to be preprocessed. First, the K value is standardized. The formula is:

[0085]

[0086] Among them, μ k and σ k are the mean and standard deviation of the K values ​​in the training set, respectively. This is done to eliminate dimensional differences and improve model convergence efficiency. Subsequently, the names of the reinforcement measures (such as "geotextile," "anchor," and "anchor nail") are converted into numerical labels (0, 1, and 2) through label encoding to facilitate the model's classification task.

[0087] After preprocessing, the data was divided into a training set and a test set in an 8:2 ratio. Stratified sampling was used to ensure a consistent distribution of reinforcement measures in both data sets. For example, if anchors accounted for 60% of the original data, the proportion of anchors in both the training and test sets was maintained to avoid bias in the evaluation.

[0088] The model was constructed using a deep neural network (DNN) with the following structure: the input layer receives a standardized K value (1 node); the first hidden layer contains 32 nodes and uses the ReLU activation function to capture nonlinear features, followed by a dropout layer (Dropout = 0.2) to prevent overfitting; the second hidden layer further extracts features (16 nodes, ReLU activation); the output layer uses the Softmax function to generate three probability distributions corresponding to geotextiles, anchor rods, and anchor nails. The Adam optimizer (learning rate 0.001) was selected for model compilation.

[0089] The hybrid loss function includes sparse categorical cross entropy loss and mean squared error loss:

[0090] L total =w1L class +w2L reg ,

[0091] Among them, L class is the cross entropy loss for sparse classes, L reg is the mean square error loss, w1 and w2 are the corresponding weight coefficients.

[0092] Sparse Categorical Cross Entropy:

[0093]

[0094] To address the problem of class imbalance (such as scarcity of anchor samples), a class weight adjustment strategy is introduced, and the weight is calculated as:

[0095]

[0096] Among them, N total is the total number of samples, C a is the number of categories, N τ is the number of samples in the τth class. During training, early stopping (termination when there is no improvement in validation loss for 15 consecutive epochs) is used to optimize resource utilization.

[0097] During the model evaluation phase, the test set is used to verify generalization performance. Accuracy (the proportion of correct predictions to total samples) is calculated, and a confusion matrix is ​​generated to visually demonstrate the prediction performance for each category. For example, if the test set accuracy reaches 92%, and the confusion matrix shows a recall of 90% for the anchor category, this indicates that the model has high reliability for key scenarios.

[0098] When deploying predictions, after entering the K value, the system first performs normalization, then the model inference outputs the probability distribution p = [p0, p1, p2], and the final recommended action is determined by the maximum probability:

[0099]

[0100] Finally, after feature extraction through the hidden layer (32 nodes → Dropout → 16 nodes), the classification branch outputs the probability of the reinforcement measure through Softmax, and the regression branch outputs the parameters through linear activation. During model compilation, a hybrid loss function (classification cross entropy + mean squared error) is used, and class weights are set to balance the samples. Early stopping is used during training to optimize efficiency. During testing, the reinforcement type is prioritized and the corresponding parameters (such as the number of anchors) are dynamically extracted.

[0101] 4. In summary, the technical key of the present invention is as follows:

[0102] (1) The present invention proposes a parameter generation method that combines Latin hypercube sampling (LHS) and Cholesky decomposition.

[0103] 1) Generate initial samples that evenly cover the parameter space through LHS stratified sampling to ensure uniform data distribution.

[0104] 2) Combined with Cholesky decomposition, the independent standard normal samples are linearly transformed to accurately control the negative correlation between parameters (such as the target correlation coefficient ρ = -0.7).

[0105] 3) Map the transformed parameters to the lognormal distribution space and verify the distribution shape and correlation of the generated data through statistical tests (such as KS test).

[0106] (2) This paper proposes an integrated framework of a two-stage machine learning model (SVR+DNN) and adopts a division of labor and cooperation mechanism.

[0107] 1) Phase I (SVR stability prediction): The support vector regression (SVR) model was used, combined with the radial basis kernel (RBF) and grid search to optimize the hyperparameters (C = 10, γ = 0.1) to accurately predict the slope stability coefficient K.

[0108] 2) The second stage (DNN reinforcement decision): A deep neural network (DNN) dual-branch structure is constructed to output reinforcement measures (such as geotextile, anchor rods, and anchor nails) through the Softmax classifier, and specific parameters (such as the number and spacing of anchor rods) are dynamically generated through the regression branch.

[0109] (3) The present invention proposes a full-process intelligent decision-making system architecture.

[0110] 1) Full process automation from parameter generation, stability assessment to reinforcement decision-making, covering the integrated process of data generation → model training → dynamic output.

[0111] 2) Ensure data reliability through stratified sampling and correlation control, and improve decision accuracy and efficiency through dual-model collaboration. Key points of protection: The interaction logic of each module in the overall system architecture (e.g., the LHS-Cholesky → SVR → DNN cascade) and the dynamic decision output mechanism.

[0112] (4) The present invention proposes a hybrid distribution engineering applicability design.

[0113] It is assumed that the soft rock parameters (φ2, c2) obey the log-normal distribution under rainfall conditions, and the distribution parameters (μ, σ) are determined by the quantile method (such as 5% and 95% quantiles) to ensure that the data are consistent with engineering practice.

Claims

1. A method for evaluating the stability of slopes with soft rock interlayers under rainfall conditions and making reinforcement decisions, characterized in that: The following steps are involved: Step 1: Parameter generation and data sampling; Based on Latin hypercube sampling, an initial uniformly distributed sample of soft rock parameters is generated, wherein the soft rock parameters include the internal friction angle φ2 and the cohesion c2; the initial uniformly distributed sample is subjected to standard normal distribution mapping, and the constructed target covariance matrix is ​​decomposed using Cholesky decomposition to introduce negative correlation. The correlated standard normal variables are then mapped back to the original log-normal distribution space to form a soft rock parameter data set that satisfies statistical distribution and correlation; Step 2: Slope stability coefficient calculation and data preprocessing; The soft rock parameters generated in step 1 are input into the correction software to calculate the slope stability coefficient K, and Gaussian noise is added to simulate the actual error; Z-score normalization is performed on the input features and output labels respectively, and the dataset is divided into a training set and a test set; Step 3: Support vector regression model training and optimization; A support vector regression model was constructed using the radial basis kernel function. The hyperparameter combination was optimized through grid search combined with 5-fold cross validation, and the support vector regression model was trained to predict the slope stability coefficient K. Step 4: Construction of deep neural network reinforcement decision model; First, the slope stability coefficient K of the predicted new sample is obtained. The reinforcement measure name label is encoded as a numerical label. A two-branch DNN model is constructed. The classification branch is used to output the probability distribution of the reinforcement measure, and the regression branch is used to output the reinforcement parameter. The model is compiled using a hybrid loss function, and class weights are set to balance the samples. The model is then trained using the early stopping method. Step 5: Dynamic decision output; The slope stability coefficient K of the new sample is input into the deep neural network model, and the type of reinforcement measures and corresponding parameters are output. After denormalization, a complete reinforcement plan is generated in stages.

2. The method for evaluating the stability of slopes containing soft rock interlayers and strengthening decisions under rainfall conditions according to claim 1 is characterized in that: The specific process of parameter generation and data sampling in step 1 includes: Step 1.1: Combine the actual physical range of soft rock parameters internal friction angle φ2 and cohesion c2, that is, φ min ≤φ2≤φ max , c min ≤c2≤c max , the equations are established by the quantile method to solve the lognormal distribution parameters of the internal friction angle φ2 and the cohesion c2; Among them, Φ -1 is the inverse function of the standard normal distribution, μ φ and σ φ are the mean and standard deviation of the logarithmic space of the internal friction angle φ2, μ c and σ c are the mean and standard deviation of the logarithmic space of cohesion c2; q0 is the quantile; Step 1.2: Generate the initial uniformly distributed sample matrix U∈[0,1] by Latin hypercube sampling n×2 , satisfying that each column is evenly distributed in the interval [0,1] and has stratified coverage, where n is the number of samples; the value u of the i-th sample on the j-th variable i,j Calculated by the following formula: Among them, π j (i) is the random permutation of the layer number of the j-th variable, ξ i,j is a uniform random number; Step 1.3: Use the standard normal distribution inverse cumulative distribution function Φ-1 to map U and generate an independent standard normal sample matrix Z = [z φ , z c ]; With φ =Φ -1 (at φ ),With c =Φ -1 (at c ) Among them, z φ Independent standard normal samples of friction angle φ2 generated for the mapping; z c Independent standard normal samples of cohesion c2 generated for the mapping; Step 1.4: Introduce the target correlation coefficient ρ, construct the target covariance matrix Σ, and obtain the lower triangular matrix L through Cholesky decomposition, satisfying Perform a linear transformation on the independent standard normal sample matrix Z to generate a correlation variable matrix Z with the target correlation coefficient ρ correlated ; WITH correlated =Z·L T Among them, L T is the transpose of the lower triangular matrix L; Z correlated =[z φ,correlated , z c,correlated ],z φ,correlated is the transformed internal friction angle related variable matrix, z c,correlated is the transformed cohesion-related variable matrix; Step 1.5: Map the correlated standard normal variables to the lognormal distribution space using the formula: φ2=exp(μ φ +s φ ·z φ,correlated ) c2=exp(μ c +s c ·z c,correlated ) Values ​​outside the physical range are truncated: φ2=max(φ min ,min(φ max ,φ2)) c2=max(c min ,min(c max ,c2)) Step 1.6: Verify the distribution of the generated data using the Kolmogorov-Smirnov test and the correlation using the Pearson correlation coefficient.

3. The method for evaluating the stability of slopes containing soft rock interlayers and strengthening decisions under rainfall conditions according to claim 2 is characterized in that: The step 2 is specifically as follows: Step 2.1: Input the generated soft rock parameters, internal friction angle φ2 and cohesion c2, as input features into the software to calculate the slope stability coefficient K, and use K as the output label, as shown in the following formula: K=0.18φ2+0.12ln(c2+1)+∈ Among them, ∈ is Gaussian noise; Step 2.2: Perform Z-score normalization on the input characteristic soft rock parameters internal friction angle φ2 and cohesion c2, and the output label slope stability coefficient K; Among them, x represents the original data before standardization, x norm represents the data after standardization, μ0 is the characteristic mean, σ0 is the standard deviation; Step 2.3: Divide the standardized dataset into training set and test set.

4. The method for evaluating the stability of slopes containing soft rock interlayers and strengthening decisions under rainfall conditions according to claim 3 is characterized in that: The specific steps in step 3 are as follows: Step 3.1: Use the radial basis kernel function to construct a support vector regression model for predicting the slope stability coefficient K, which is expressed as: RBF(x i ,y i )=exp(-γ||x i -y i ||) Among them, x i =[φ2,c2], represents the input parameters; y i =K, represents the target output; γ is the kernel function parameter; RBF(·) is the radial basis function; Step 3.2: Define the hyperparameter search space, including the penalty factor C∈{1,10,100} and the kernel function parameter γ∈{0.01,0.1,1}; generate multiple sets of hyperparameter combinations; Step 3.3: Use grid search to traverse all hyperparameter combinations and perform 5-fold cross-validation for each set of hyperparameters: split the dataset into 5 subsets, select 1 subset each time as the validation set, and the remaining 4 as the training set; train the model and calculate the coefficient of determination R of the validation set 2 and mean square error MSE; after repeating 5 times, the average value of each indicator is taken as the performance evaluation of the hyperparameter combination; Step 3.4: Select the coefficient of determination R 2 The highest hyperparameter combination: penalty factor C = 10 and kernel function parameter γ = 0.1 as the final model configuration; Step 3.5: Use ∈-support vector regression as the objective function, the mathematical form is: Among them, w is the weight vector, b represents the baseline offset of the model, which is used to adjust the overall position of the predicted value so that the hyperplane can better fit the data; C is the penalty factor, ξ i and ξ i * is the slack variable; The constraints are: Among them, ε is the insensitive loss threshold.

5. The method for evaluating the stability of slopes containing soft rock interlayers and strengthening decisions under rainfall conditions according to claim 4 is characterized in that: The structure of the DNN model in step 4 is: (a) Input layer: receives the normalized slope stability coefficient K; (b) Hidden layer 1: 32 nodes, ReLU activation function, followed by Dropout layer; (c) Hidden layer 2: 16 nodes, activation function is ReLU; (d) Dual-branch output layer: The classification branch outputs the probability distribution of reinforcement measures through Softmax, and the regression branch outputs parameters through a linear activation function; (e) Adam optimizer is used during training.

6. The method for evaluating the stability of a slope containing soft rock interlayers and making reinforcement decisions under rainfall conditions according to claim 5 is characterized in that: The hybrid loss function in step 4 includes sparse classification cross entropy loss and mean square error loss: L total =w1L class +w2L reg Among them, L class is the sparse classification cross entropy loss, L reg is the mean square error loss, w1 and w2 are the corresponding weight coefficients; The sparse categorical cross entropy loss is calculated as follows: in, is the predicted probability of the true category label of the zth sample, N batch Indicates the number of samples in a training batch; The category weight adjustment strategy is introduced to solve the category imbalance problem, and the category weight coefficient w τ The calculation is as follows: Among them, N total is the total number of samples, C a is the number of categories, N τ is the number of samples in the τth category.

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