A method for slope reliability analysis and reinforcement region identification considering spatial variability of soil

Abstract

The application provides a slope reliability analysis and reinforcement region identification method considering spatial variability of soil bodies, and relates to the technical field of slope reliability analysis. A numerical model of a slope is established, a soil parameter random field sample is generated, and an image dataset is constructed by extracting a safety factor and a maximum shear strain increment field through numerical simulation; a numerical regression proxy model fused with an adaptive attention module is constructed and trained to predict the safety factor of the slope, and an image conversion proxy model based on a conditional generative adversarial network is used to reconstruct the maximum shear strain increment field image; a global sensitivity index is calculated based on a deep learning explainability method to identify a parameter high sensitivity region; a spatial cost field is constructed to search for a potential sliding surface and a high frequency sliding region is counted; the parameter high sensitivity region and the high frequency sliding region are spatially coupled to determine a key reinforcement region of the slope and verify it. The application breaks through the calculation efficiency bottleneck of traditional numerical simulation, realizes efficient prediction of the full-field mechanical response and failure mode of the slope, and significantly enhances the explainability of the deep learning model in the application of geotechnical engineering.

Description

Technical Field

[0001] This invention relates to the application of deep learning algorithms in geotechnical engineering and the field of slope reliability analysis technology, and in particular to a method for slope reliability analysis and reinforcement area identification that considers the spatial variability of soil. Background Technology

[0002] In the field of slope reliability analysis, the spatial variability of soil parameters is crucial for slope stability assessment and safe construction design. Traditional slope reliability analysis methods include first-order reliability analysis (FORM) and Monte Carlo simulation (MCSM), which use stochastic finite element methods to perform numerous simulations to obtain the slope reliability index β. However, these methods are limited by the nonlinearity of the limit state surface and the computational efficiency of numerical simulation for single samples, resulting in bottlenecks in computational efficiency and accuracy. Therefore, surrogate model methods based on machine learning are widely used in slope reliability analysis due to their small sample requirements and high computational efficiency. Among them, surrogate models that use digital images as input retain spatial correlation information and avoid the loss of feature information after data dimensionality reduction, making them a hot research direction in recent years. However, most existing surrogate models only output scalar results such as the safety factor FoS or failure probability, making it difficult to simultaneously reflect the maximum shear strain increment field, potential slip surface morphology, and instability mode within the slope.

[0003] For example, in reference 1, "Ji Jian, Jiang Zhen, Yin Xin, Wang Tao, Cui Hongzhi, Zhang Weijie, Deep learning and reliability analysis of digital image features of random field slope, Chinese Journal of Geotechnical Engineering, 2022, 44(8), 1463-1473", the discrete results of random field of soil are transformed into digital images. A convolutional neural network (CNN) surrogate model between random field image and slope function function is established to accurately approximate the real slope stability calculation results and significantly improve the efficiency of detailed calculation of slope reliability analysis. Reference 2, "Huang N, Han Y, Xie W, Hu R, Peng H, Song G, Wu M, Zhu M, Wei H, Liang M, An innovative and efficient approach for slope reliability analysis: Machine learning based surrogate modeling with advanced attention mechanisms, Engineering Geology, 2025, 354, 108194", utilizes Convolutional Block Attention Module (CBAM) to improve the global feature extraction capability of CNNs and demonstrates the enhancement of model interpretability through Gradient Weighted Class Activation Mapping (Grad-CAM). Reference 3, "Lin W, Ma G, Jiang M, Xu J, Rezania M, Zhu H, An efficient graph neural networks surrogate model for slope reliability analysis considering soil spatial variability," *Reliability Engineering and System Safety*, 2026, 267, 111924, proposes an alternative model based on graph attention networks (GAT). This model converts image pixels into graph nodes, mapping conventional image data to a graph structure containing topological information to facilitate efficient reliability analysis. In terms of predicting field information, the surrogate model method based on digital images can replace complex numerical simulation calculations to highly approximate simulation results of real mechanics, seepage, and heat conduction.Reference 4, "Wang Z, Zhang J, Huang H, Interpreting random fields through the U-Net architecture for failure mechanism and deformation predictions of geosystems, Geoscience Frontiers, 2024, 15, 101720", proposes a deep learning proxy model based on the U-Net architecture. It takes the random field of soil parameters as input and can efficiently and accurately predict the failure mechanism, sliding surface distribution and deformation field of spatially variable soil slopes.

[0004] However, the above studies lacked a connection between slope stability and its failure modes. The research content was limited to improving the accuracy and computational efficiency of the surrogate model, with insufficient analysis of the interpretability of the surrogate model, and failed to further delve into the engineering design and construction planning of slopes. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a method for slope reliability analysis and reinforcement area identification that considers the spatial variability of soil. This method not only predicts the safety factor, but also predicts the location of the potential sliding surface of the slope, and can identify the high-sensitivity area and high-frequency sliding area of ​​the slope, thereby determining the important reinforcement area of ​​the slope.

[0006] To achieve the above objectives, the present invention adopts the following technical solution, including: A method for slope reliability analysis and reinforcement zone identification considering the spatial variability of soil includes the following steps: Step 1: Establish a finite difference numerical model of the slope, divide it into discrete grids, and extract grid coordinate information; Step 2: Construct a random field probability distribution model of soil shear strength parameters, generate random field samples of soil parameters, and map them to the discrete grid. Step 3: Calculate the slope safety factor of the random field sample using the strength reduction method based on numerical simulation software, and extract the maximum shear strain increment field under critical conditions; Step 4: Convert the discrete values ​​of the soil parameter random field samples into a multi-channel soil parameter random field image, convert the maximum shear strain increment field into a single-channel grayscale image, and construct the training dataset for the surrogate model together with the corresponding slope safety factor. Step 5: Construct and train a numerical regression surrogate model that integrates an adaptive convolutional block attention module to predict the slope safety factor; Step 6: Construct and train an image transformation proxy model based on conditional generative adversarial network (cGAN), taking the multi-channel soil parameter random field image as input and outputting a single-channel maximum shear strain increment field grayscale image. Step 7: Based on the SHAP interpretability method, calculate the normalized global sensitivity index (NGSI) of the safety factor prediction results to spatial input features, and identify areas with high parameter sensitivity. Step 8: Construct a spatial cost field that is inversely proportional to the maximum shear strain increment field, perform a potential sliding surface search on the output single-channel maximum shear strain increment field grayscale image, and count the spatial occurrence frequency of the sliding surface to obtain the high-frequency sliding region. Step 9: Perform spatial coupling analysis on the high-sensitivity region of the parameters and the high-frequency sliding region to determine the key reinforcement region of the slope, and take the key reinforcement region as the preferred layout region of the slope support structure. The safety factor is predicted by the numerical regression surrogate model and the reliability index and failure probability before and after reinforcement are calculated for verification.

[0007] Preferably, the specific method for generating the random field samples of soil parameters in step 2 is as follows: remember and Let represent the coordinates of the center points of any two discrete grid cells in the slope numerical model, and let represent the random field of soil parameters. Its probability distribution type is log-normal; autocorrelation function It is a quadratic exponential function, and its expression is:

[0008] In the formula, The horizontal autocorrelation distance. The vertical autocorrelation distance is calculated based on the grid coordinates and eigenvalue decomposition is performed. Discrete random field samples of soil parameters are obtained by solving the KL expansion method.

[0009] Preferably, the numerical regression surrogate model described in step 5 includes a convolutional neural network and a fully connected layer; The convolutional neural network is used to extract the random field image features of the multi-channel soil parameters; the fully connected layer receives the image features extracted by the convolutional neural network and outputs a safety coefficient; the numerical regression surrogate model consists of the following structure connected in series along the network input-output direction: The system consists of a first convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, a residual structure containing an adaptive convolutional block attention module, an average pooling layer, a second convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, an average pooling layer, a flattening structure, and a fully connected layer, a PReLU activation layer, a dropout layer, and an output fully connected layer connected in sequence.

[0010] Preferably, the image transformation proxy model in step 6 is constructed as a conditional generative adversarial network (cGAN), wherein the conditional generative adversarial network includes a generator. and discriminator : The conditional generative adversarial network uses the multi-channel soil parameter random field image as conditional input. The corresponding single-channel maximum shear strain increment field grayscale image is used as the target output. ; The generator A lightweight U-shaped module with embedded adaptive convolutional block attention module is used. 2 The -Net architecture, whose overall network topology includes an encoding unit, a bridging unit, a decoding unit, and an output unit connected in sequence; wherein, the encoding unit and the decoding unit both adopt a structure of residual U-block RSU and adaptive convolutional block attention module cascaded together.

[0011] Preferably, the specific feature extraction and channel mapping process of the encoding unit and the bridging unit is as follows: Encoding phase: Conditional input Enter the encoding unit; In the first level of encoding, the input features are mapped to 64 feature channels by the first residual U block RSU1. Then, spatial and channel attention recalibration is performed by the first level of encoding adaptive convolutional block attention module, and the resolution is halved by the first max pooling layer downsampling. In the second-level encoding, the downsampled features are entered into the second residual U block RSU2 and mapped to 128 feature channels. Then, spatial and channel attention recalibration is performed through the second-level encoding adaptive convolutional block attention module, and then the resolution is halved by the second max pooling layer. Bridging phase: Deep features after secondary downsampling enter the bridging unit; The deep features are first input into the third residual U block RSU3 to further expand and map the feature channels to 256 feature channels, and then bridged by the adaptive convolutional block attention module.

[0012] The skip connection and multi-scale feature splicing and recovery process of the decoding unit is as follows: First-level decoding and reconstruction: The 256-channel features output by the bridging unit are first upsampled through the first transposed convolutional layer to double the spatial resolution and reduce the number of feature channels to 128. Subsequently, these 128-channel features are spliced ​​together with the 128-channel attention features output by the second-level encoding adaptive convolutional block attention module in the encoding stage through a skip connection feature concatenation in the channel dimension, and fused into a 256-channel composite feature tensor. This 256-channel composite feature tensor is then subjected to dimensionality reduction and multi-scale feature extraction by the second-level decoding adaptive convolutional block attention module and the second-level decoding RSU, outputting 128-channel deep recovery features. Second-level decoding and reconstruction: The 128-channel deep recovery features are upsampled again through the second transposed convolutional layer, doubling the spatial resolution and reducing the number of channels to 64. Subsequently, the 64-channel features are concatenated with the 64-channel attention features output by the first-level encoding adaptive convolutional block attention module in the encoding stage, and fused into a 128-channel composite feature tensor. The 128-channel composite feature tensor is then passed through the first-level decoding adaptive convolutional block attention module and the first-level decoding RSU in sequence, finally outputting 64-channel shallow recovery features, which are then sent to the output unit for single-channel mapping.

[0013] The micro-feature extraction process for RSU1 and RSU2 in the encoding unit, and RSU3 in the bridging unit, is as follows: RSU1 Internal Feature Extraction: Input features are first mapped locally through an input convolutional layer, then sequentially passed through a first internal downsampling chain consisting of three cascaded encoding convolutional layers and two max-pooling layers to extract multi-scale local features step by step. After transitioning to global context information through a dilated convolutional layer at the bottom layer, the features sequentially pass through a first internal upsampling chain consisting of three cascaded decoding convolutional layers and two upsampling layers, and are concatenated with the features of the corresponding resolution in the first internal downsampling chain. Finally, the output is passed through an output convolutional layer and added element-wise with the input features of RSU1 through local residual connections. RSU2 internal feature extraction: A shallow nesting depth is used to adapt to the feature domain after the resolution reduction. The input features are first mapped locally through the input convolutional layer, and then passed through a second internal downsampling chain consisting of two encoding convolutional layers and one max pooling layer in alternating concatenation. After global context information transition through a dilated convolutional layer with an inflation rate of 2 at the bottom layer, the features are passed through a second internal upsampling chain consisting of two decoding convolutional layers and one upsampling layer in alternating concatenation, and channel concatenation is performed with the features of the corresponding resolution in the second internal downsampling chain. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU2 through local residual connections. RSU3 internal feature extraction: The input features are first mapped locally through the input convolutional layer, and then extracted into deep local features through only one encoding convolutional layer, while maintaining the spatial resolution of the feature map throughout. After transitioning to global context information through a dilated convolutional layer with a dilation rate of 2 at the bottom layer, the features are directly mapped through a decoding convolutional layer and concatenated with the equal-resolution features output by the encoding convolutional layer. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU3 through local residual connections.

[0014] Preferably, the adaptive convolutional block attention module sequentially performs feature recalibration on the input feature map through the adaptive channel attention submodule and the adaptive spatial attention submodule. The specific feature extraction process and formula are as follows; Let the input feature map be ,in , , These represent the number of channels, height, and width of the feature map, respectively. First, the input feature map Global average pooling and global max pooling based on spatial dimensions are performed separately to obtain the average pooling channel features. and maximum pooling channel features Subsequently, adaptive one-dimensional convolution was used. Enable local cross-channel interaction and generate channel attention weights. The calculation formula is as follows:

[0015] In the formula, Sigmoid activation function; one-dimensional convolution The adaptive convolution kernel size is determined by the number of input channels. Nonlinear mapping is dynamically determined; Then, the channel attention weights With input feature map Element-wise multiplication yields the feature map after channel recalibration. ,Right now ; Then, using the aforementioned feature map As input, firstly, average pooling and max pooling are performed along the channel dimension to generate two-dimensional average pooling spatial features. and max pooling space features The two are then concatenated along the channel dimension to obtain the concatenated feature. Subsequently, parallel convolutional kernels are used to extract multi-scale spatial features, and learnable parameters are introduced for fusion to generate spatial attention weights. The calculation formula is as follows:

[0016] In the formula, These represent the kernel size as follows: and Two-dimensional convolution operation; These are learnable fusion weight parameters that are dynamically updated during network training. Finally, the spatial attention weights are... With feature map Element-wise multiplication outputs the final fused feature map after channel and spatial attention weighting. ,Right now .

[0017] Preferably, the specific calculation formula and evaluation process of the Normalized Global Sensitivity Index (NGSI) mentioned in step 7 are as follows: Using the SHAP interpretability method, compute the first... In the multi-channel soil parameter random field sample, the first The local marginal contribution of input features at each spatial grid location to the slope safety factor prediction result is denoted as the local SHAP value. ; The absolute cumulative value of local SHAP values ​​of multiple random field samples at the same spatial grid location is calculated, as well as the absolute cumulative value of the input feature deviation from the baseline value at that spatial grid location. Extract the first The multi-channel soil parameter random field sample is in the _ ... The absolute value of the deviation of the input feature from the baseline value at each spatial grid location is denoted as . ; The formula for calculating the Normalized Global Sensitivity Index (NGSI) is as follows:

[0018] In the formula, The total number of random field samples used for global interpretation; To prevent numerical stability constants with a denominator of zero; The normalized global sensitivity index (NGSI) is used to decouple the inherent sensitivity of the model from the amplitude of input fluctuations, and the high-sensitivity region of the parameters is extracted based on the spatial numerical distribution of NGSI.

[0019] Preferably, the specific algorithm and physical conversion formula for searching the potential sliding surface of the output single-channel maximum shear strain increment field grayscale image in step 8 include: Mapping pixel values ​​from a single-channel maximum shear strain increment field image to physical space, and denoteing spatial grid cells. The normalized maximum shear strain increment at is ,in Construct a maximum nonlinear spatial cost function based on the exponentially decaying increment of shear strain. Its formula is:

[0020] In the formula, For sensitivity parameters; Traverse the geometric boundary nodes of the slope numerical model, identify and extract the local maxima of the maximum shear strain increment field, and select the two maxima with the greatest spatial distance as the start and end anchor points of the potential sliding surface. In the spatial cost field, A is used The heuristic search algorithm uses the start and end anchor points as the starting and ending points to solve for the minimum cumulative cost path, thereby forcing the search path to converge to the trajectory of the maximum shear strain increment and extracting the discrete sliding surface path. The discrete sliding surface path is subjected to curve fitting and geometric smoothing using a cubic B-spline interpolation algorithm, resulting in a potential sliding surface with geometric continuity.

[0021] Preferably, the spatial coupling criteria for determining the key reinforcement area and the preferred layout area in step 9 are as follows: Construct a spatial coordinate system to map the areas with high sensitivity to soil parameters and high-frequency sliding areas into the same spatial coordinate system; The geometric intersection of the high-sensitivity region and the high-frequency sliding region in spatial location is calculated, and this overlapping region is defined as the key reinforcement region of the slope. Using this key reinforcement area as the preferred location for the lateral layout of anti-slide piles or anti-slide retaining walls, the vertical main body of the support structure penetrates the highly sensitive area of ​​the parameters and cuts off the high-frequency sliding area, so as to achieve spatial coupling reinforcement of local shear strength enhancement and macroscopic sliding surface blockage.

[0022] Preferably, step 9 involves using a numerical regression surrogate model to predict the safety factor and calculating reliability indicators and failure probabilities before and after reinforcement for verification. Specifically, this includes: Using the same random field samples, numerical simulation software was used to calculate results including both reinforced and unreinforced samples, and these results were combined into a dataset. A numerical regression surrogate model was then trained, and predictions were made based on Monte Carlo simulation. The safety factor of the sub-random samples is used to form a data pool, and limit state conditions are applied. As a criterion for determining instability, failure probability Directly calculate as the number of instabilities in the Monte Carlo data pool With data pool size The ratio:

[0023] Based on the calculated failure probability Slope reliability index The following can be calculated:

[0024] In the formula, This represents the inverse cumulative distribution function of the standard normal distribution.

[0025] The advantages of this invention are: (1) This invention overcomes the limitation of traditional reliability analysis, which usually only focuses on a single safety factor, and realizes the paradigm shift to "full-field mechanical response and failure mode prediction". Existing slope reliability analysis methods usually only focus the calculation target on a single "safety factor" scalar, which is difficult to intuitively and comprehensively reflect the internal failure evolution process of the slope under complex conditions. Based on a deep network architecture, this invention extends the prediction dimension from a one-dimensional scalar to a two-dimensional field variable. While outputting the safety factor, this framework can simultaneously and intuitively predict the maximum shear strain increment field information of the slope and extract the potential sliding surface location. This multi-dimensional prediction result provides a richer and more physically meaningful scientific basis for comprehensively assessing slope stability and revealing the instability evolution mechanism.

[0026] (2) This invention has made a great breakthrough in the computational efficiency bottleneck of complex random field sampling and reliability analysis. In the reliability analysis of systems considering the spatial variability of soil and rock, traditional methods require tens of thousands of repeated calls to time-consuming numerical simulation programs, resulting in a serious computational bottleneck. This invention constructs an efficient deep learning proxy model to transform the solution of complex nonlinear physical field evolution into the fast forward propagation calculation of neural networks. While ensuring that the prediction accuracy is highly consistent with traditional numerical methods, the single calculation time is shortened exponentially, making large-scale random sampling and refined risk assessment highly timely and feasible in engineering practice.

[0027] (3) This invention significantly enhances the physical perception capability and strong interpretability of deep learning models in geotechnical engineering applications. Traditional pure data-driven deep learning models are often regarded as "black boxes" and lack clear physical logic, making it difficult to gain widespread trust in rigorous engineering fields. This invention constructs a deep learning framework with interpretability. This method not only integrates the underlying physical and mechanical laws of soil and rock without loss during the learning process, but also is easy to combine with interpretable artificial intelligence technology. It can quantitatively reveal and trace the contribution and sensitivity of input variables to the final stability prediction results. This effectively breaks the black box characteristics of the model and greatly improves the transparency, scientific credibility and practical value of the prediction results in engineering risk decision-making. Attached Figure Description

[0028] Figure 1 This is a flowchart of a slope reliability analysis and reinforcement area identification method that considers the spatial variability of soil according to the present invention.

[0029] Figure 2 This is a schematic diagram of the slope model and discrete mesh in an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram illustrating the process of generating a digital image dataset using a proxy model according to an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram of the numerical regression proxy model architecture in an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram comparing the prediction effect of the numerical regression surrogate model with the actual value in an embodiment of the present invention.

[0033] Figure 6 This is a schematic diagram of the architecture based on the lightweight U2-Net generator in an embodiment of the present invention.

[0034] Figure 7 This is a schematic diagram illustrating how the loss function of the image conversion proxy model changes during the training process in an embodiment of the present invention.

[0035] Figure 8 This is a schematic diagram of the maximum shear strain increment field prediction results of the image conversion proxy model in an embodiment of the present invention.

[0036] Figure 9 This is a schematic diagram of the highly sensitive region of the random field parameters of cohesion and internal friction angle calculated based on NGSI in an embodiment of the present invention.

[0037] Figure 10 This is a schematic diagram of the spatial distribution and spatial frequency distribution of the potential sliding surface extracted by the model in an embodiment of the present invention, based on the prediction of the maximum shear strain increment field.

[0038] Figure 11 This is a schematic diagram of an important slope reinforcement area in an embodiment of the present invention.

[0039] Figure 12 This is a schematic diagram of the anti-slide pile reinforcement scheme in an embodiment of the present invention. Detailed Implementation

[0040] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Figure 1This is a flowchart of a slope reliability analysis and reinforcement zone identification method considering the spatial variability of soil, according to the present invention. Figure 1 As can be seen, it includes the following steps: Step 1: Establish a finite difference numerical model of the slope, divide it into discrete grids, and extract grid coordinate information.

[0042] The slope model established in this embodiment is shown in [reference needed]. Figure 2 In this embodiment of the invention, the slope model is 30m long, with a bottom height of 10m, a top height of 15m, and a slope angle of 45°. The slope soil parameters are shown in Table 1. In this embodiment, the slope model uses a discrete grid of 1210 grid cells, with the slope body using a regular rectangular grid and the slope surface using a regular triangular grid. The coordinate information file and area information file of the grid are exported.

[0043] Table 1. Slope Soil Parameter Values

[0044] Step 2: Construct a random field probability distribution model of soil shear strength parameters, generate random field samples of soil parameters, and map them to the discrete grid.

[0045] The specific method for generating the random field samples of soil parameters in step 2 is as follows: remember and Let represent the coordinates of the center points of any two discrete grid cells in the slope numerical model, and let represent the random field of soil parameters. Its probability distribution type is log-normal; autocorrelation function It is a quadratic exponential function, and its expression is:

[0046] In the formula, The horizontal autocorrelation distance. The vertical autocorrelation distance is calculated based on the grid coordinates and eigenvalue decomposition is performed. Discrete random field samples of soil parameters are obtained by solving the Karhunen-Loève (KL) expansion method.

[0047] Step 3: Calculate the slope safety factor of the random field sample using the strength reduction method based on numerical simulation software, and extract the maximum shear strain increment field under critical conditions.

[0048] Step 4: Convert the discrete values ​​of the soil parameter random field samples into a multi-channel soil parameter random field image, convert the maximum shear strain increment field into a single-channel grayscale image, and construct the training dataset for the surrogate model together with the corresponding slope safety factor.

[0049] In this embodiment, the process for generating input and output images for the proxy model is as follows: Figure 3 Specifically, the discrete values ​​of the random field parameters of each unit in the model input image are mapped to pixel values ​​in the range of [0-255]. In this embodiment, the random field of soil parameters includes a cohesion random field and an internal friction angle random field. The cohesion random field is mapped to the red channel, and the internal friction angle random field is mapped to the green channel. The input image is a dual-channel cohesion and internal friction angle random field image with spliced ​​channels and an image size of 2×30×60. The maximum shear strain increment value of each unit in the model output image is mapped to pixels in the range of [0-255]. The output image is a single-channel grayscale image with an image size of 1×30×60.

[0050] Step 5: Construct and train a numerical regression surrogate model that incorporates an adaptive convolutional block attention mechanism, see... Figure 4 It is used to predict the safety factor of slopes.

[0051] The numerical regression proxy model described in step 5 includes a convolutional neural network and a fully connected layer; wherein, the convolutional neural network is used to extract the random field image features of the multi-channel soil parameters; the fully connected layer receives the image features extracted by the convolutional neural network and outputs a safety coefficient; the numerical regression proxy model consists of the following structure connected in series along the network input-output direction: a first convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, a residual structure containing an adaptive convolutional block attention module, an average pooling layer, a second convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, an average pooling layer, a flattening structure, and a fully connected layer, a PReLU activation layer, a dropout layer, and an output fully connected layer connected in sequence.

[0052] The convolutional neural network and fully connected layer described in step 5 are used to extract features from the multi-channel random field image of soil parameters and output a safety factor. Specifically, the dual-channel random field image of soil parameters is processed by a mean decentering layer based on the random field mean image and then input into the first convolutional layer. It is then input into the adaptive convolutional block attention module for feature selective processing to increase the weights of key channels and key regions of the image input features. The processed enhanced features are input into the first average pooling layer, the second convolutional layer, and the second average pooling layer, and then expanded and input into the fully connected layer, finally outputting the safety factor.

[0053] Specifically, a random field dual-channel image of size 2×30×60 is input into the first feature extraction block of the model. A 13×23 asymmetric convolution with stride 1 and padding 1 extracts anisotropic features of the image, outputting a feature map of size 16×20×40. Subsequently, the feature map is processed by PReLU nonlinear mapping and input into the adaptive convolutional block attention module. While maintaining the feature map size of 16×20×40, the response weights for different channels and spatial locations are recalibrated, and features are superimposed with the original features through residual connections. Then, the feature map is passed through a 2×2 average pooling downsampling layer, outputting a feature map of size 16×10×20. The feature map is then input into the second... The second feature extraction block uses a 7×11 asymmetric convolution with a stride of 1 and padding of 1 to extract features, outputting a feature map of size 32×16×12. The feature map then passes through a PReLU nonlinear mapping and a 2×2 average pooling downsampling layer, outputting a feature map of size 32×3×6. Next, the feature map is input to a fully connected module. First, the feature map is reshaped into a 1×576 one-dimensional vector through a flattening layer. This one-dimensional vector is connected to a fully connected layer containing 256 hidden nodes, and then passes through a PReLU nonlinear mapping and Dropout regularization. Finally, the 256 hidden features are linearly mapped to a single output node, outputting the slope safety factor.

[0054] Specifically, the adaptive convolutional block attention mechanism sequentially recalibrates the input feature map through an adaptive channel attention submodule and an adaptive spatial attention submodule. The specific feature extraction process and formulas are as follows: The input feature map is ,in , , These represent the number of channels, height, and width of the feature map, respectively. Specifically, the input feature map is a feature map with dimensions of 16×20×40, which is the output of the first feature extraction block. First, the input feature map... Global average pooling and global max pooling based on spatial dimensions are performed separately to obtain the average pooling channel features. and maximum pooling channel features Subsequently, adaptive one-dimensional convolution was used. Enable local cross-channel interaction and generate channel attention weights. The calculation formula is as follows:

[0055] In the formula, Sigmoid activation function; one-dimensional convolution The adaptive convolution kernel size is determined by the number of input channels. Nonlinear mapping is dynamically determined; The channel attention weights With input feature map Element-wise multiplication yields the feature map after channel recalibration. ,Right now ; With the feature map As input, average pooling and max pooling are first performed along the channel dimension to generate two-dimensional average pooling spatial features. and max pooling space features The two are then concatenated along the channel dimension to obtain the concatenated feature. ; Subsequently, parallel convolutional kernels are used to extract multi-scale spatial features, and learnable parameters are introduced for fusion to generate spatial attention weights. The calculation formula is as follows:

[0056] In the formula, These represent two-dimensional convolution operations with kernel sizes of 7×7 and 3×3, respectively. These are learnable fusion weight parameters that are dynamically updated during network training. Finally, the spatial attention weights are... With feature map Element-wise multiplication outputs the final fused feature map after channel and spatial attention weighting. ,Right now .

[0057] In this example, 500 sets of random field dual-channel image samples of soil parameters are generated according to the method described in step 3, and the safety factor is calculated by numerical simulation to form a dataset for training the numerical regression surrogate model. 10,000 sets of samples that were not used in training are input into the numerical regression surrogate model to predict the safety factor. The error between the predicted safety factor and the safety factor calculated by numerical simulation is compared to evaluate the model's performance.

[0058] Figure 5 The diagram shows a scatter plot of the predicted safety factor and the safety factor calculated by numerical simulation. The model exhibits excellent performance and a high coefficient of determination. Mean absolute error and root mean square error The values ​​are 0.9914, 0.0167, and 0.0106, respectively.

[0059] Step 6: Construct and train an image translation proxy model based on a conditional generative adversarial network (cGAN), see... Figure 6 The multi-channel soil parameter random field image is used as input to reconstruct the corresponding single-channel maximum shear strain increment field image.

[0060] Specifically, conditional generative adversarial networks (cGANs) include generators. and discriminator generator Receive random field dual-channel images Output the generated grayscale image of maximum shear strain increment. Discriminator Receive real sample pairs Or generate sample pairs It determines whether the image is a result of a real numerical simulation or the output of the generator.

[0061] The generator U employs the embedded adaptive convolutional block attention module 2 The -Net architecture's overall network topology includes sequentially connected encoding units, bridging units, decoding units, and output units; wherein, both the encoding and decoding units adopt a structure of cascaded residual U-blocks (RSU) and adaptive convolutional block attention modules.

[0062] Specifically, the generator's input is a 2×30×60 dual-channel random field image of cohesive internal friction angle.

[0063] Encoding phase: The first-level encoder RSU1 has 2 input channels, 16 intermediate channels, and 64 output channels, with an internal depth of... RSU1 outputs a first encoded feature of 64×30×60, which is then recalibrated through the first encoded adaptive convolutional block attention module and subsequently downsampled to 64×15×30 by max pooling.

[0064] The second-level encoder RSU2 has 64 input channels, 32 intermediate channels, and 128 output channels, with an internal depth of... RSU2 outputs a second encoded feature of 128×15×30, which is then recalibrated through the second encoded adaptive convolutional block attention module and subsequently downsampled to 128×8×15 by max pooling.

[0065] Bridging phase: The bridging unit RSU3 has 128 input channels, 64 intermediate channels, and 256 output channels, with an internal depth of [missing information]. This unit outputs 256×8×15 bridging features, and further enhances deep semantics and spatial response through a bridging adaptive convolutional block attention module.

[0066] Decoding phase: First, the bridging attention features are upsampled and reduced to 128 channels using a first transposed convolution. This feature is then concatenated with the 128-channel feature output from the second encoding adaptive convolutional block attention module to form a 256-channel composite feature. The concatenated feature is then fused by the second decoding adaptive convolutional block attention module and input into the second decoding RSU module to output a 128-channel restored feature.

[0067] Subsequently, the 128-channel recovered features are upsampled and reduced to 64-channel features through a second transposed convolution. This feature is then concatenated with the 64-channel features output by the first encoding adaptive convolutional block attention module to form a 128-channel composite feature. The concatenated feature is first fused by the first decoding adaptive convolutional block attention module, and then input into the first decoding RSU to output the 64-channel recovered features.

[0068] Output phase: The output convolutional layer uses a 1×1 convolution to map the 64-channel recovered features to a 1-channel image, and then uses the tanh activation function to output a maximum shear strain increment field image normalized to [-1, 1]. After inference, this image can be denormalized to a grayscale image of 0 to 255 or the physical shear strain increment value.

[0069] Specifically, the Residual U-block (RSU) includes input convolution, internal coding chain, dilated convolution bridging layer, internal decoding chain, internal skip connections, and local residual connections.

[0070] The input convolution typically employs 3×3 convolutions, batch normalization, and ReLU activation to map the input channels to the output channels of RSU, serving as the baseline features for the local residual branch. The internal encoding chain consists of several 3×3 convolutions and max pooling operations, used to progressively extract multi-scale local features. The internal bridging layer uses dilated convolutions with a dilation rate of 2 to expand the receptive field without further reducing resolution. The internal decoding chain restores resolution through upsampling and concatenates channels with features of the same scale from the internal encoding chain. Finally, the internal decoding output of RSU is element-wise added to the input convolution output to form the local residual output.

[0071] For RSU1, the larger internal depth allows for the capture of shallow details and mid-scale shearing structures even with high input resolution. For RSU2, the spatial resolution is reduced, and the internal depth is correspondingly decreased to extract deeper features while controlling the number of parameters. For RSU3, located at the bridging position, it mainly undertakes the function of global context integration, therefore employing a shallower internal depth and dilated convolution to increase the receptive field.

[0072] Both RSU1 and RSU2 are constructed with a nested large U-shaped topology consisting of internal data flow operation surfaces, and their internal depth levels are different. The specific micro-feature extraction process includes: RSU1 Internal Feature Extraction: Input features are first mapped locally through an input convolutional layer, then sequentially passed through a first internal downsampling chain consisting of three cascaded encoding convolutional layers and two max-pooling layers to extract multi-scale local features step by step. After transitioning to global context information through a dilated convolutional layer at the bottom layer, the features sequentially pass through a first internal upsampling chain consisting of three cascaded decoding convolutional layers and two upsampling layers, and are concatenated with the features of the corresponding resolution in the first internal downsampling chain. Finally, the output is passed through an output convolutional layer and added element-wise with the input features of RSU1 through local residual connections. RSU2 internal feature extraction: A shallow nesting depth is used to adapt to the feature domain after the resolution reduction. The input features are first mapped locally through the input convolutional layer, and then pass through the second internal downsampling chain, which consists of two encoding convolutional layers and one max pooling layer in alternating concatenation. After global context information transition through a dilated convolutional layer with an inflation rate of 2 at the bottom layer, the features pass through the second internal upsampling chain, which consists of two decoding convolutional layers and one upsampling layer in alternating concatenation, and are concatenated with the features of the corresponding resolution in the second internal downsampling chain. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU2 through local residual connections.

[0073] The RSU3 in the bridging unit is constructed as a tiled residual topology structure without size scaling, consisting of internal data flow operation surfaces. Its specific micro-feature extraction process includes: RSU3 internal feature extraction: The input features are first mapped locally through the input convolutional layer, and then extracted into deep local features through only one encoding convolutional layer, while maintaining the spatial resolution of the feature map throughout. After transitioning to global context information through a dilated convolutional layer with a dilation rate of 2 at the bottom layer, the features are directly mapped through a decoding convolutional layer and concatenated with the equal-resolution features output by the encoding convolutional layer. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU3 through local residual connections.

[0074] The discriminator A PatchGAN fully convolutional structure is employed. Its input is a 3-channel tensor obtained by concatenating a two-channel random field image of cohesion and internal friction angle with a real or generated maximum shear strain increment field image in the channel dimension; the initial convolutional layer uses... The convolutional kernel has a stride of 2, outputting 64 channels followed by the LeakyReLU activation function; subsequently, the first convolutional discriminant block outputs 128 channels, with a kernel size of... The stride is 2, followed by batch normalization and LeakyReLU; the second convolutional discriminant block outputs 256 channels, and the kernel size is... The step size is 1, followed by batch normalization and LeakyReLU; the final convolutional layer outputs a local image patch authenticity discrimination map.

[0075] The advantage of PatchGAN lies in the fact that the discriminator does not just provide a single true / false label for the entire image, but rather distinguishes between multiple local image patches. This is beneficial for the generator to learn local high-value bands, edges, and texture structures in the maximum shear strain increment field.

[0076] Generator loss Including combating losses L1 loss SSIM structural similarity loss :

[0077] in, For L1 loss weights; For SSIM loss weights; The input to the generator is a two-channel random field image; The generator output is the grayscale image of the maximum shear strain increment field. A grayscale image mapped to the maximum shear strain increment field results obtained from numerical simulation; As a discriminator, it receives real sample pairs. Or generate sample pairs To determine whether the image is a real numerical simulation result or a generator output; As a generator, it receives two-channel images of a random field. The maximum shear strain increment field grayscale image is generated; L1 loss is used to ensure that the pixels are generally similar, SSIM loss is used to maintain structural similarity, and adversarial loss is used to improve the realism of local texture and high-value bands in the generated image.

[0078] Discriminator loss Using binary cross-entropy loss for real sample pairs and generated sample pairs:

[0079] In this embodiment, the input image and the target image are normalized to [-1, 1]; the Adam optimizer is used with a learning rate of Batch size is 16; L1 loss weights The SSIM loss weight is 100. The value is 20. After training, save the generator parameters that achieve the best overall performance on the validation set.

[0080] In this example, 500 sets of random field dual-channel image samples of soil parameters are generated according to the method described in step 3, and the maximum shear strain increment field is calculated by numerical simulation to form a dataset to train the image conversion proxy model. 100 sets of samples in the dataset are used as an independent test set to evaluate the model performance.

[0081] Figure 7 The training process of the image transformation surrogate model over 300 rounds is demonstrated. The losses of the generator and discriminator gradually decrease and tend to plateau, and the output grayscale image has high structural consistency with the numerically simulated maximum shear strain increment field. In this example, the average L1 loss on the test set is 0.0139, and the average SSIM is 0.973.

[0082] Figure 8 The test set shows three types of maximum shear strain increment fields selected from the test set, corresponding to shallow slip, deep slip, and deep non-circular slip, respectively. All three types of maximum shear strain increment fields maintain high prediction accuracy and structural similarity, and the position of the sliding surface of the reconstructed maximum shear strain increment field is basically consistent with the numerical simulation results.

[0083] Step 7: Based on the SHAP interpretability method, calculate the normalized global sensitivity index (NGSI) of the safety factor prediction results to spatial input characteristics, and identify the highly sensitive areas of parameters that have a significant control effect on slope stability.

[0084] Specifically, the pre-trained surrogate model is loaded, and the slope mean image is used as the baseline input. The GradientExplainer library in Python is used to calculate the SHAP value of the predicted safety factor for each input channel and each spatial location. For the first... The nth sample (multi-channel soil parameter random field sample) at the nth For each spatial location, the local SHAP value is denoted as . The marginal contribution of the reaction channel and location to the baseline input for predicting the safety factor is calculated. The cumulative absolute value of the local SHAP value of multiple random field samples at the same spatial grid location is statistically analyzed, as well as the cumulative absolute value of the input feature at that spatial grid location deviating from the baseline value.

[0085] Extract the first The sample at the th The absolute value of the deviation of the input feature from the baseline value at each spatial grid location is denoted as . Then, the normalized global sensitivity index (NGSI) was calculated:

[0086] In the formula, The total number of random field samples used for global interpretation; To prevent numerical stability constants with a denominator of zero.

[0087] By calculating the normalized global sensitivity index (NGSI) for the dual-channel random field images of soil parameters, the highly sensitive regions for cohesion and internal friction angle random field parameters can be obtained, as shown in [reference needed]. Figure 9 , Figure 9 (a) corresponds to the region with high sensitivity to the random field parameters of cohesion. Figure 9 (b) corresponds to the region with high sensitivity to random field parameters of internal friction angle. Furthermore, the cohesion and internal friction angle random fields are combined to obtain the comprehensive sensitivity region of slope shear strength parameters.

[0088] In this embodiment, the highly sensitive areas are typically located near the toe of the slope and the potential shear zone in the lower middle part of the slope. This result is consistent with the understanding in geotechnical mechanics; changes in shear strength near the toe of the slope and the shear zone are more likely to alter the overall stability.

[0089] Step 8: Construct a spatial cost field that is inversely proportional to the maximum shear strain increment field, perform a potential sliding surface search on the reconstructed maximum shear strain increment field, and statistically analyze the spatial occurrence frequency of the sliding surface to obtain the high-frequency sliding region.

[0090] Specifically, in this example, firstly, the pixel values ​​in the reconstructed single-channel maximum shear strain increment field image are mapped to physical space, and the spatial grid cell is denoted as... The normalized maximum shear strain increment at is ,in A larger increment of maximum shear strain indicates that the location is more likely to be within a shear localization zone. Based on this physical meaning, a nonlinear spatial cost function based on the exponential decay of the maximum shear strain increment is constructed. Its formula is:

[0091] In the formula, This is a sensitivity parameter.

[0092] when Approaching 1 o'clock A smaller value indicates a search path that is more likely to pass through the current location; when Approaching 0 The magnitude is so large that it forces the search path to avoid the current location.

[0093] Subsequently, local maxima of the maximum shear strain increment field are identified and extracted by traversing the slope surface, slope bottom, slope toe, slope shoulder, and slope top. Starting and ending anchor points are determined as the path search start and end points based on distance, location, and slope geometry constraints. For the starting point, high shear strain concentration points near the slope top or slope shoulder are preferred; for the ending point, high shear strain concentration points near the slope toe or slope foot are preferred. If multiple candidate points exist, the anchor point combination is determined by comprehensively considering the magnitude of the maximum shear strain increment, horizontal distance, and spatial connectivity.

[0094] A search graph is constructed using a pixel grid as the graph structure nodes and an eight-neighbor connection method. An eight-neighbor connection includes adjacent nodes in the horizontal, vertical, and diagonal directions. A... A heuristic search algorithm finds the path with the minimum cumulative cost between the starting point and the ending point. Its priority is determined by the current cumulative path cost and the heuristic distance to the ending point. The heuristic function can be Euclidean distance. Since node cost is negatively correlated with the maximum shear strain increment, the search path typically extends along the high-value band of the maximum shear strain increment, which can serve as a discrete trajectory of the potential slip surface.

[0095] Because A The searched paths are affected by the pixel grid and may contain polylines and local jagged edges. This embodiment further employs cubic B-spline interpolation to smooth the discrete paths. The smoothed curves are output as continuous potential slip surfaces and can be converted back to physical coordinates. Paths that are abnormally short, incomplete, or clearly do not conform to the slope geometry can be eliminated based on path length, endpoint location, and curvature threshold. After the maximum shear strain increment grayscale image of each soil parameter random field dual-channel image is predicted by the image transformation surrogate model, the potential slip surface is obtained through the slip surface search algorithm.

[0096] For each soil parameter, the random field dual-channel image is mapped to each slip surface corresponding to that slip surface, and the number of times each grid cell or pixel is traversed by the slip surface is counted. If the total number of samples is... , No. The number of times each grid is traversed by the sliding surface is Then the frequency of the sliding surface is: .

[0097] Will Regions exceeding a preset threshold are defined as high-frequency sliding regions. In this embodiment, the frequency threshold is set to 30%. High-frequency sliding regions reflect the spatial locations repeatedly traversed by potential sliding surfaces under the influence of random fields, representing soil regions more likely to participate in macroscopic instability paths. Compared to single deterministic sliding surfaces, high-frequency sliding regions contain statistical instability information under the uncertainty of random fields. The spatial distribution and spatial frequency distribution of potential sliding surfaces obtained from random field dual-channel image search of 1000 soil parameters are shown below. Figure 10 , Figure 10(a) corresponds to the spatial distribution of potential sliding surfaces. Figure 10 (b) Corresponds to the spatial frequency distribution of the potential sliding surface, and those exceeding the preset frequency threshold are defined as high-frequency sliding regions.

[0098] Step 9: Perform spatial coupling analysis on the high-sensitivity region of the parameters and the high-frequency sliding region to determine the key reinforcement region of the slope, and take the key reinforcement region as the preferred layout region of the slope support structure. Predict the safety factor before and after reinforcement and calculate the reliability index and failure probability through the numerical regression surrogate model.

[0099] The spatial coupling criteria for determining the key reinforcement area and the preferred layout area in step 9 are as follows: Construct a spatial coordinate system and map the high-sensitivity soil parameter region extracted in step 7 and the high-frequency sliding region obtained by multiple searches and statistics in step 8 into the same spatial coordinate system. Calculate the geometric intersection of the highly sensitive region of the parameter and the high-frequency sliding region in spatial location, and define the overlapping region as the key reinforcement region of the slope. Using this key reinforcement area as the preferred location for the lateral layout of anti-slide piles or anti-slide retaining walls, the vertical main body of the support structure penetrates the highly sensitive area of ​​the parameters and cuts off the high-frequency sliding area, so as to achieve spatial coupling reinforcement of local shear strength enhancement and macroscopic sliding surface blockage.

[0100] Specifically, the highly parameter-sensitive region is converted into a first binary mask. The high-frequency sliding region is converted into a second binary mask. Key reinforcement areas for:

[0101] In this embodiment, the critical reinforcement area is located in a localized region approximately 12m to 13m horizontally and 6m to 7m above ground level. This location is close to the shear development control zone above the slope toe, and thus falls within a parameter-sensitive area while intersecting with a high-frequency slip channel. Therefore, arranging the main resistance sections of anti-slide piles or retaining walls near this area can more effectively block the slip channel and improve overall stability.

[0102] To verify the engineering significance of the key reinforcement area, this embodiment uses anti-slide piles as the support structure for comparison. The parameters of the anti-slide piles are shown in Table 2. Anti-slide piles were arranged at multiple horizontal locations with horizontal distances of 11m, 12m, 13m, 14m, 15m, and 16m. The pile length at each location was uniformly 6m. The reinforcement scheme is shown in [Table 2]. Figure 12 .

[0103] Table 2 shows the parameters of the anti-slide piles.

[0104] Using the same 500 random field samples, numerical simulation software was used to calculate a dataset containing results for both reinforced and unreinforced anti-slide piles. Numerical regression surrogate models were then trained on each dataset, and predictions were made based on Monte Carlo simulation. The safety factor of the sub-random samples is used to form a data pool, and limit state conditions are applied. As a criterion for determining instability, failure probability It can be directly calculated as the number of instabilities in the Monte Carlo data pool. With data pool size The ratio:

[0105] Based on the calculated failure probability Slope reliability index The following can be calculated:

[0106] In the formula, This represents the inverse cumulative distribution function of the standard normal distribution.

[0107] The stability results of the slope after reinforcement are shown in Table 3. The results indicate that when the anti-slide piles are arranged near the critical reinforcement area at a horizontal distance of 12m to 13m, the average safety factor is higher than that of the location far from the critical reinforcement area, the failure probability is lower, and the reliability index is higher. This verifies that the critical reinforcement area determined by the method can be used as the preferred arrangement area for the slope support structure.

[0108] Table 3. Calculation results of slope stability after reinforcement

[0109] This invention can be implemented by an electronic device. The electronic device includes a processor, a memory, a data interface, and an optional graphics processing unit. The memory stores program instructions, and when the processor executes these instructions, it performs the following functions: reading grid coordinates; generating random fields of cohesion and internal friction angle; calling or receiving numerical simulation results; generating image datasets; training or loading numerical regression surrogate models; training or loading image transformation surrogate models; performing rapid prediction of the maximum shear strain increment field of the safety factor; calculating failure probability and reliability indices; calculating NGSI values ​​to statistically analyze highly sensitive areas of soil parameters; searching for potential sliding surfaces and statistically analyzing high-frequency sliding areas; and outputting key reinforcement areas and suggested layout ranges for support structures.

[0110] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for slope reliability analysis and reinforcement zone identification considering the spatial variability of soil, characterized in that, Includes the following steps: Step 1: Establish a finite difference numerical model of the slope, divide it into discrete grids, and extract grid coordinate information; Step 2: Construct a random field probability distribution model of soil shear strength parameters, generate random field samples of soil parameters, and map them to the discrete grid. Step 3: Calculate the slope safety factor of the random field sample using the strength reduction method based on numerical simulation software, and extract the maximum shear strain increment field under critical conditions; Step 4: Convert the discrete values ​​of the soil parameter random field samples into a multi-channel soil parameter random field image, convert the maximum shear strain increment field into a single-channel grayscale image, and construct the training dataset for the surrogate model together with the corresponding slope safety factor. Step 5: Construct and train a numerical regression surrogate model that integrates an adaptive convolutional block attention module to predict the slope safety factor; Step 6: Construct and train an image transformation proxy model based on conditional generative adversarial network (cGAN), taking the multi-channel soil parameter random field image as input and outputting a single-channel maximum shear strain increment field grayscale image. Step 7: Based on the SHAP interpretability method, calculate the normalized global sensitivity index (NGSI) of the safety factor prediction results to spatial input features, and identify areas with high parameter sensitivity. Step 8: Construct a spatial cost field that is inversely proportional to the maximum shear strain increment field, perform a potential sliding surface search on the output single-channel maximum shear strain increment field grayscale image, and count the spatial occurrence frequency of the sliding surface to obtain the high-frequency sliding region. Step 9: Perform spatial coupling analysis on the high-sensitivity region of the parameters and the high-frequency sliding region to determine the key reinforcement region of the slope, and take the key reinforcement region as the preferred layout region of the slope support structure. The safety factor is predicted by the numerical regression surrogate model and the reliability index and failure probability before and after reinforcement are calculated for verification.

2. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The specific method for generating the random field samples of soil parameters in step 2 is as follows: remember and Let represent the coordinates of the center points of any two discrete grid cells in the slope numerical model, and let represent the random field of soil parameters. Its probability distribution type is log-normal; autocorrelation function It is a quadratic exponential function, and its expression is: In the formula, The horizontal autocorrelation distance. The vertical autocorrelation distance is calculated based on the grid coordinates and eigenvalue decomposition is performed. Discrete random field samples of soil parameters are obtained by solving the KL expansion method.

3. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The numerical regression surrogate model described in step 5 includes a convolutional neural network and a fully connected layer; The convolutional neural network is used to extract the random field image features of the multi-channel soil parameters; the fully connected layer receives the image features extracted by the convolutional neural network and outputs a safety coefficient; the numerical regression surrogate model consists of the following structure connected in series along the network input-output direction: The system consists of a first convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, a residual structure containing an adaptive convolutional block attention module, an average pooling layer, a second convolutional layer with an asymmetric rectangular convolutional kernel, a PReLU activation layer, an average pooling layer, a flattening structure, and a fully connected layer, a PReLU activation layer, a dropout layer, and an output fully connected layer connected in sequence.

4. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The image transformation proxy model described in step 6 is constructed as a conditional generative adversarial network (cGAN), which includes a generator. and discriminator : The conditional generative adversarial network uses the multi-channel soil parameter random field image as conditional input. The corresponding single-channel maximum shear strain increment field grayscale image is used as the target output. ; The generator A lightweight U-shaped module with embedded adaptive convolutional block attention module is used. 2 The -Net architecture, whose overall network topology includes an encoding unit, a bridging unit, a decoding unit, and an output unit connected in sequence; wherein, the encoding unit and the decoding unit both adopt a structure of residual U-block RSU and adaptive convolutional block attention module cascaded together.

5. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 4, characterized in that, The specific feature extraction and channel mapping process of the encoding unit and bridging unit is as follows: Encoding phase: Conditional input Enter the encoding unit; In the first level of encoding, the input features are mapped to 64 feature channels by the first residual U block RSU1. Then, spatial and channel attention recalibration is performed by the first level of encoding adaptive convolutional block attention module, and the resolution is halved by the first max pooling layer downsampling. In the second-level encoding, the downsampled features are entered into the second residual U block RSU2 and mapped to 128 feature channels. Then, spatial and channel attention recalibration is performed through the second-level encoding adaptive convolutional block attention module, and then the resolution is halved by the second max pooling layer. Bridging phase: Deep features after secondary downsampling enter the bridging unit; The deep features are first input into the third residual U block RSU3 to further expand and map the feature channels to 256 feature channels, and then bridged by the adaptive convolutional block attention module; The skip connection and multi-scale feature splicing and recovery process of the decoding unit is as follows: First-level decoding and reconstruction: The 256-channel features output by the bridging unit are first upsampled through the first transposed convolutional layer to double the spatial resolution and reduce the number of feature channels to 128. Subsequently, these 128-channel features are spliced ​​together with the 128-channel attention features output by the second-level encoding adaptive convolutional block attention module in the encoding stage through a skip connection feature concatenation in the channel dimension, and fused into a 256-channel composite feature tensor. This 256-channel composite feature tensor is then subjected to dimensionality reduction and multi-scale feature extraction by the second-level decoding adaptive convolutional block attention module and the second-level decoding RSU, outputting 128-channel deep recovery features. Second-level decoding and reconstruction: The 128-channel deep recovery features are upsampled again through the second transposed convolutional layer, doubling the spatial resolution and reducing the number of channels to 64. Subsequently, these 64-channel features are concatenated with the 64-channel attention features output by the first-level encoding adaptive convolutional block attention module in the encoding stage, fusing them into a 128-channel composite feature tensor. This 128-channel composite feature tensor is then passed through the first-level decoding adaptive convolutional block attention module and the first-level decoding RSU, finally outputting 64-channel shallow recovery features, which are then sent to the output unit for single-channel mapping. The micro-feature extraction process for RSU1 and RSU2 in the encoding unit, and RSU3 in the bridging unit, is as follows: RSU1 Internal Feature Extraction: Input features are first mapped locally through an input convolutional layer, then sequentially passed through a first internal downsampling chain consisting of three cascaded encoding convolutional layers and two max-pooling layers to extract multi-scale local features step by step. After transitioning to global context information through a dilated convolutional layer at the bottom layer, the features sequentially pass through a first internal upsampling chain consisting of three cascaded decoding convolutional layers and two upsampling layers, and are concatenated with the features of the corresponding resolution in the first internal downsampling chain. Finally, the output is passed through an output convolutional layer and added element-wise with the input features of RSU1 through local residual connections. RSU2 internal feature extraction: A shallow nesting depth is used to adapt to the feature domain after the resolution reduction. The input features are first mapped locally through the input convolutional layer, and then passed through a second internal downsampling chain consisting of two encoding convolutional layers and one max pooling layer in alternating concatenation. After global context information transition through a dilated convolutional layer with an inflation rate of 2 at the bottom layer, the features are passed through a second internal upsampling chain consisting of two decoding convolutional layers and one upsampling layer in alternating concatenation, and channel concatenation is performed with the features of the corresponding resolution in the second internal downsampling chain. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU2 through local residual connections. RSU3 internal feature extraction: The input features are first mapped locally through the input convolutional layer, and then extracted into deep local features through only one encoding convolutional layer, while maintaining the spatial resolution of the feature map throughout. After transitioning to global context information through a dilated convolutional layer with a dilation rate of 2 at the bottom layer, the features are directly mapped through a decoding convolutional layer and concatenated with the equal-resolution features output by the encoding convolutional layer. Finally, the output is passed through the output convolutional layer and added element-wise with the input features of RSU3 through local residual connections.

6. A method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil, as described in claim 3, 4, or 5, is characterized in that... The adaptive convolutional block attention module sequentially performs feature recalibration on the input feature map through the adaptive channel attention submodule and the adaptive spatial attention submodule. The specific feature extraction process and formula are as follows; Let the input feature map be ,in , , These represent the number of channels, height, and width of the feature map, respectively. First, the input feature map Global average pooling and global max pooling based on spatial dimensions are performed separately to obtain the average pooling channel features. and maximum pooling channel features Subsequently, adaptive one-dimensional convolution was used. Enable local cross-channel interaction and generate channel attention weights. The calculation formula is as follows: In the formula, Sigmoid activation function; one-dimensional convolution The adaptive convolution kernel size is determined by the number of input channels. Nonlinear mapping is dynamically determined; Then, the channel attention weights With input feature map Element-wise multiplication yields the feature map after channel recalibration. ,Right now ; Then, using the aforementioned feature map As input, firstly, average pooling and max pooling are performed along the channel dimension to generate two-dimensional average pooling spatial features. and max pooling space features The two are then concatenated along the channel dimension to obtain the concatenated feature. Subsequently, parallel convolutional kernels are used to extract multi-scale spatial features, and learnable parameters are introduced for fusion to generate spatial attention weights. The calculation formula is as follows: In the formula, These represent the kernel size as follows: and Two-dimensional convolution operation; These are learnable fusion weight parameters that are dynamically updated during network training. Finally, the spatial attention weights are... With feature map Element-wise multiplication outputs the final fused feature map after channel and spatial attention weighting. ,Right now .

7. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The specific calculation formula and evaluation process of the Normalized Global Sensitivity Index (NGSI) mentioned in step 7 are as follows: Using the SHAP interpretability method, compute the first... In the multi-channel soil parameter random field sample, the first The local marginal contribution of input features at each spatial grid location to the slope safety factor prediction result is denoted as the local SHAP value. ; The absolute cumulative value of local SHAP values ​​of multiple random field samples at the same spatial grid location is calculated, as well as the absolute cumulative value of the input feature deviation from the baseline value at that spatial grid location. Extract the first The multi-channel soil parameter random field sample is in the _ ... The absolute value of the deviation of the input feature from the baseline value at each spatial grid location is denoted as . ; The formula for calculating the Normalized Global Sensitivity Index (NGSI) is as follows: In the formula, The total number of random field samples used for global interpretation; To prevent numerical stability constants with a denominator of zero; The normalized global sensitivity index (NGSI) is used to decouple the inherent sensitivity of the model from the amplitude of input fluctuations, and the high-sensitivity region of the parameters is extracted based on the spatial numerical distribution of NGSI.

8. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The specific algorithm and physical conversion formula for searching the potential sliding surface of the output single-channel maximum shear strain increment field grayscale image in step 8 include: Mapping pixel values ​​from a single-channel maximum shear strain increment field image to physical space, and denoteing spatial grid cells. The normalized maximum shear strain increment at is ,in Construct a nonlinear spatial cost function based on the exponential decay of the maximum shear strain increment. Its formula is: In the formula, For sensitivity parameters; Traverse the geometric boundary nodes of the slope numerical model, identify and extract the local maxima of the maximum shear strain increment field, and select the two maxima with the greatest spatial distance as the start and end anchor points of the potential sliding surface. In the spatial cost field, A is used The heuristic search algorithm uses the start and end anchor points as the starting and ending points to solve for the minimum cumulative cost path, thereby forcing the search path to converge to the trajectory of the maximum shear strain increment and extracting the discrete sliding surface path. The discrete sliding surface path is subjected to curve fitting and geometric smoothing using a cubic B-spline interpolation algorithm, resulting in a potential sliding surface with geometric continuity.

9. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, The spatial coupling criteria for determining the key reinforcement area and the preferred layout area in step 9 are as follows: Construct a spatial coordinate system to map the areas with high sensitivity to soil parameters and high-frequency sliding areas into the same spatial coordinate system; The geometric intersection of the high-sensitivity region and the high-frequency sliding region in spatial location is calculated, and this overlapping region is defined as the key reinforcement region of the slope. Using this key reinforcement area as the preferred location for the lateral layout of anti-slide piles or anti-slide retaining walls, the vertical main body of the support structure penetrates the highly sensitive area of ​​the parameters and cuts off the high-frequency sliding area, so as to achieve spatial coupling reinforcement of local shear strength enhancement and macroscopic sliding surface blockage.

10. The method for slope reliability analysis and reinforcement area identification considering the spatial variability of soil as described in claim 1, characterized in that, Step 9 involves using a numerical regression surrogate model to predict the safety factor and calculating reliability indicators and failure probabilities before and after reinforcement for verification. Specifically, this includes: Using the same random field samples, numerical simulation software was used to calculate results including both reinforced and unreinforced samples, and these results were combined into a dataset. A numerical regression surrogate model was then trained, and predictions were made based on Monte Carlo simulation. The safety factor of the sub-random samples is used to form a data pool, and limit state conditions are applied. As a criterion for determining instability, failure probability Directly calculate as the number of instabilities in the Monte Carlo data pool With data pool size The ratio: Based on the calculated failure probability Slope reliability index The following can be calculated: In the formula, This represents the inverse cumulative distribution function of the standard normal distribution.

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