A slope stability prediction method based on deep learning

Abstract

The present invention belongs to the technical field of measurement and data processing, and particularly relates to a slope stability prediction method based on deep learning. The method includes: Step 1: Periodically scan the surface of the target slope with a high-precision lidar to obtain point cloud data; Step 2: Calculate the expansion potential energy of the slope area corresponding to each rock mass unit during the water absorption process according to the geological data and hydro-meteorological data of the slope area corresponding to each rock mass unit; Step 3: Take the mean output as the input quantity and input it into a pre-trained deep learning autoencoder, combine the variance output, and output the latent variable; calculate the difference between the latent variable and the mean output, and perform a ratio calculation on the difference and a preset basic threshold to obtain the instability probability of the slope area corresponding to each rock mass unit. This method can dynamically respond to environmental changes, provide stability evaluation results in real time, and has high prediction accuracy, real-time performance and adaptability.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement and data processing, and particularly relates to a method for predicting slope stability based on deep learning. Background Art

[0002] With the development of society and the increasing human activities, the problem of slope instability has gradually become an important safety hazard in fields such as mountainous areas, mining areas, and highway construction. Especially for expansive rock slopes, due to their unique physical and chemical properties, they are prone to deformation and instability under the action of natural and human factors, posing a great threat to engineering construction and the safety of people's lives and property. Therefore, how to accurately predict the stability of expansive rock slopes has become a technical problem faced by the current geotechnical engineering field. The stability of expansive rock slopes is affected by various factors, mainly including geological characteristics, hydro-meteorological conditions, geotechnical engineering properties, and human activities. As a kind of rock containing expansive minerals such as montmorillonite, during the water absorption and swelling process of expansive rock, the volume of the rock mass changes significantly, resulting in a decrease in the strength of the rock mass and deformation. In this process, factors such as the water infiltration rate, precipitation intensity, mineral composition of the rock mass, and geometric shape of the slope all have an important impact on the stability of the expansive rock. Therefore, traditional methods for predicting slope stability usually only rely on experience or simple physical models, and often cannot fully consider the comprehensive influence of these complex factors.

[0003] At present, the research on the prediction of the stability of swelling rock slopes mainly focuses on traditional mechanical models and empirical data analysis methods. Common slope stability analysis methods include limit equilibrium method, finite element method, numerical simulation method, etc. The limit equilibrium method analyzes the stability of the slope by assuming a sliding surface, which is suitable for situations where the calculation is simplified and the slope conditions are relatively simple. However, this method often ignores the nonlinear and heterogeneous properties of swelling rock, and cannot effectively deal with complex hydrological and meteorological factors, and has poor accuracy and adaptability. The finite element method and numerical simulation method can better consider the deformation characteristics of swelling rock and perform numerical calculations by establishing a three-dimensional model of the slope. These methods have advantages in dealing with the geometric morphology of the slope and the anisotropy of the rock mass, and can more accurately simulate the deformation of swelling rock under external loads and hydrological environment. However, the finite element method and numerical simulation method require a lot of computing resources and have high requirements for input parameters. Especially under complex hydrological and meteorological conditions, how to accurately model the penetration and distribution of water is still a technical problem. In addition, the calculation results of these methods often rely on expert experience and require detailed field survey data support, which increases the complexity of calculation and the difficulty of data collection. In addition, some slope stability prediction models based on statistical methods and machine learning have also received widespread attention in recent years. Statistical methods establish empirical models by analyzing historical data, and combine regression analysis, cluster analysis and other techniques to mine the potential laws of slope instability from the data. This type of method has good data adaptability and can avoid the assumption bias in traditional mechanical models to a certain extent. However, statistical methods rely on a large amount of historical data and are often limited in dealing with nonlinear relationships. Especially for complex geotechnical media such as expansive rock, the prediction accuracy of statistical methods is low, and it is difficult to capture the dynamic changes under the coupling of multiple factors. Summary of the invention

[0004] In view of this, the main purpose of the present invention is to provide a slope stability prediction method based on deep learning, which can dynamically respond to environmental changes and provide stability assessment results in real time. It has high prediction accuracy, real-time and adaptability, overcomes the limitations of traditional methods in dealing with nonlinearity, multi-factor coupling and data scarcity, and provides a scientific basis for slope monitoring and disaster warning.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A slope stability prediction method based on deep learning, the method comprising:

[0007] Step 1: Periodically scan the surface of the target slope with a high-precision lidar to obtain point cloud data; perform point cloud segmentation on the point cloud data to obtain multiple rock mass units; perform the following operations in the slope area corresponding to each rock mass unit: obtain the geological data of this slope area through geological surveys, and obtain the hydro-meteorological data of this slope area at multiple consecutive times through meteorological station records;

[0008] Step 2: According to the geological data and hydro-meteorological data of the slope area corresponding to each rock mass unit, calculate the swelling potential energy of the slope area corresponding to each rock mass unit during the water absorption process at each time; according to the swelling potential energy, calculate the volume strain of the slope area corresponding to each rock mass unit at each time and the principal strain under isotropic conditions, and according to the volume strain and principal strain, calculate the effective stress of the slope area corresponding to each rock mass unit at each time, then calculate the mean value of the effective stress at all times to obtain the mean value output; further calculate the variance of the effective stress at all times to obtain the variance output;

[0009] Step 3: Take the mean value output as the input quantity and input it into the pre-trained deep learning autoencoder, and combine the variance output to output the latent variable; calculate the difference between the latent variable and the mean value output, and perform a ratio calculation on the difference and the preset basic threshold to obtain the instability probability of the slope area corresponding to each rock mass unit.

[0010] Furthermore, the geological data of the slope area corresponding to each rock mass unit obtained in Step 1 includes: dry density of the rock mass, average particle size of the rock and soil, water content, swelling pressure, unit weight of water, hydration heat of rock and soil minerals, elastic modulus of the rock mass, Poisson's ratio, cohesion, internal friction angle, montmorillonite content, and quartz content; the elastic modulus of the rock mass is determined by collecting rock mass samples of each rock mass unit and performing uniaxial compression tests on the rock mass samples; the cohesion and internal friction angle are determined by collecting rock mass samples of each rock mass unit and performing direct shear tests on the rock mass samples; the Poisson's ratio represents the lateral deformation ratio in the other direction when the rock mass sample is stretched or compressed in one direction.

[0011] Furthermore, the hydro-meteorological data of the slope area corresponding to each rock mass unit obtained in Step 1 includes: infiltration rate, rainfall, and temperature.

[0012] Furthermore, the method of periodically scanning the surface of the target slope with a high-precision lidar to obtain point cloud data and performing point cloud segmentation on the point cloud data to obtain multiple rock mass units in Step 1 includes: through the following formula, perform adaptive filtering on the th point in the point cloud data:

[0013] ;

[0014] where, is the point The point cloud density at is the number of points within the search sphere; is the radius of the search sphere; is the point to the distance to the nearest neighbor point; is the standard deviation of the Gaussian distribution; is the point at the normal vector; is the lidar line-of-sight direction vector; and then through the following formula, determine the neighboring point of whether it belongs to a rock mass unit:

[0015] ;

[0016] wherein, is the determination value. If , then it is determined that the point and its neighboring point are in a rock mass unit; is the Euclidean distance between the point and its neighboring point ; is the normal vector at the neighboring point of the point ; is the point cloud density at the point ; is the set angle threshold; is the set distance threshold; is the set density threshold.

[0017] Furthermore, in step 2, through the following formula, according to the geological data and hydro-meteorological data of each rock mass unit, calculate the swelling potential energy of each rock mass unit during the water absorption process at each time:

[0018] ;

[0019] wherein, is the swelling potential energy of the th rock mass unit during the water absorption process at time; is the dry density of the rock mass in the slope area corresponding to the th rock mass unit; is the average particle size of the rock and soil in the slope area corresponding to the th rock mass unit; is the water content of the slope area corresponding to the th rock mass unit; is the swelling pressure of the slope area corresponding to the th rock mass unit; is the The unit weight of water in the slope area corresponding to a rock mass unit; is the hydration heat of rock and soil minerals in the slope area corresponding to the th rock mass unit; is the average height of the slope area corresponding to the th rock mass unit; is the elastic modulus of the rock mass in the slope area corresponding to the th rock mass unit; is the Poisson's ratio of the slope area corresponding to the th rock mass unit; is the gas constant; is the absolute temperature; is the temperature at time is the rainfall at time is the infiltration rate at time

[0020] Furthermore, in step 2, according to the swelling potential energy, the volumetric strain of the slope area corresponding to each rock mass unit at each time and the principal strain under isotropic conditions are calculated through the following formula:

[0021] ;

[0022] where is the volume of the th rock mass unit;

[0023] ;

[0024] where , and are the principal strains.

[0025] Furthermore, in step 2, the effective stress of the slope area corresponding to each rock mass unit at each time is calculated through the following formula:

[0026] ;

[0027] Among them, is the effective stress of the slope area corresponding to the th rock mass unit at time.

[0028] Furthermore, in step 3, the process of inputting the mean output as the input quantity into the pre-trained deep learning autoencoder and outputting the latent variable specifically includes: Let the mean output be ; Encode the mean output through the following formula:

[0029] ;

[0030] Among them, is the encoding result; is the mean distribution function; is the logarithmic variance distribution function; ; Among them, is the number of past feature inflation times, and its value is equal to the number of landslides occurring within a circular area centered on the target slope with a set value as the radius; ; The variance of the effective stress at all times is ; represents a normal distribution with a mean of 0 and a variance of 1; Then input the encoding result into a single-layer deep learning network to output the latent variable ; is the variance output; is the Hadamard product.

[0031] Furthermore, in step 3, the latent variable is calculated through the following formula:

[0032] ;

[0033] Among them, represents calculating the maximum value; represents the activation function.

[0034] Adopting the above technical solutions, the present invention has the following beneficial effects:

[0035] By integrating physical modeling and deep learning techniques, the present invention successfully overcomes the limitations of traditional methods. Traditional slope stability prediction methods, such as the limit equilibrium method and the finite element method, usually rely on simplified assumptions and cannot comprehensively consider the nonlinear and spatio-temporal variation characteristics of expansive rock under complex hydro-meteorological conditions. These methods often struggle to meet the high-precision requirements in practical applications, especially when dealing with dynamic changes, complex geotechnical media, and the coupling of multiple factors. In contrast, the present invention combines physical quantities such as expansion potential energy, volume strain, and effective stress with a deep learning model to achieve a more comprehensive and dynamic stability prediction. The deep learning model can automatically extract key features in the expansive rock slope through an autoencoder, without relying too much on artificially set assumptions, making the prediction model more flexible, accurate, and adaptable.

[0036] By introducing dynamic hydro-meteorological data and historical landslide information, the present invention significantly improves the model's adaptability to complex environments. The stability of expansive rock slopes is affected by multiple factors. In particular, hydro-meteorological conditions such as precipitation, temperature, and infiltration rate have a direct impact on the water absorption and swelling characteristics of expansive rock. However, existing methods usually cannot effectively process multi-dimensional hydro-meteorological data and ignore the long-term impact of historical landslide events on the current slope stability. By introducing deep learning-based encoding and latent variable modeling, the present invention can fuse multi-source hydro-meteorological data and the number of historical landslides in real time, thereby improving the comprehensive assessment ability of slope stability. For example, by encoding the effective stress and the number of historical landslides of each rock mass unit, the model can capture the potential impact of historical landslide events on the current slope stability and dynamically adjust the prediction results. This comprehensive modeling based on historical events and dynamic hydro-conditions makes the prediction results more in line with the changing laws of actual slope stability and has stronger accuracy and reliability.

[0037] The deep learning autoencoder of the present invention improves the accuracy and efficiency of feature expression through the efficient compression and abstraction of the stability characteristics of expansive rock slopes. By compressing the input data through the autoencoder, the present invention can transform multi-dimensional and complex data into a low-dimensional latent space representation and extract the most important feature information. This process not only reduces the complexity of data processing but also improves the computational efficiency of the model when facing high-dimensional data. The deep learning model can adaptively adjust the weights of the model according to the characteristics of the input data, thereby achieving precise and personalized prediction of the stability of expansive rock slopes. This way of feature compression and abstraction enables the model to quickly learn in complex environments and make customized predictions for different types of slopes and different hydro-meteorological conditions. Brief Description of the Drawings

[0038] Figure 1Schematic diagram of the method flow of a slope stability prediction method based on deep learning provided by an embodiment of the present invention. Detailed implementation manners

[0039] All features disclosed in this specification, or steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any manner.

[0040] Any feature disclosed in this specification (including any additional claims, abstract) can be replaced by other equivalent or similar-purpose alternative features unless specifically stated. That is, unless specifically stated, each feature is only an example of a series of equivalent or similar features.

[0041] Example 1: Refer to Figure 1 , a slope stability prediction method based on deep learning, the method includes:

[0042] Step 1: Periodically scan the surface of the target slope with a high-precision lidar to obtain point cloud data; perform point cloud segmentation on the point cloud data to obtain multiple rock mass units; perform the following operations in the slope area corresponding to each rock mass unit: obtain the geological data of this slope area through geological surveys, and obtain the hydro-meteorological data of this slope area at multiple consecutive times through meteorological station records;

[0043] Traditional manual measurement methods usually cannot meet the requirements of slope monitoring for accuracy and efficiency, while lidar can achieve high-density coverage scanning of the entire slope area in a short time, and its spatial accuracy can usually reach centimeter level or even millimeter level, which is especially suitable for capturing the microscopic deformation characteristics of swelling rock during the water absorption process. Secondly, lidar uses non-contact measurement, which not only ensures the safety of data collection, but also avoids disturbing the slope surface, thus maintaining the authenticity and reliability of the data. After obtaining the point cloud data, it must be segmented and processed to extract the rock mass units that reflect the characteristics of specific areas of the slope. Point cloud segmentation is to divide a large amount of original point cloud data into several subsets with geometric consistency or specific attributes according to certain rules. In the present invention, this process is usually realized by algorithms based on geometric features, such as region growing method, density clustering algorithm (such as DBSCAN), etc. These algorithms can classify points with similar characteristics into one category according to the characteristics of points such as distance and normal vector, so as to form sub-regions representing specific rock mass units. The division of rock mass units provides a structured basis for subsequent data analysis, enabling complex point cloud data to be gradually simplified into discrete calculation units.

[0044] Once the point cloud segmentation is completed, geological survey and meteorological monitoring data can be combined to endow each rock mass unit with rich physical meanings. Geological survey data usually includes information such as the type of rock, the distribution of fractures, and mineral composition. These parameters directly affect the water absorption and swelling characteristics of the rock mass. For example, different mineral compositions may lead to significant differences in the swelling rate of the rock after water absorption, while the distribution of fractures affects the diffusion path of water within the rock mass. In addition, the continuous-time hydro-meteorological data provided by weather stations (such as rainfall, temperature, and humidity) supports the dynamic monitoring of changes in the environmental conditions of expansive rocks. Combining these data can establish a complete characteristic description for each rock mass unit. The significance of Step 1 is to organically integrate multi-source data and dynamically update it at different time points, providing high-quality input for the entire model. In traditional slope stability analysis, there are often problems such as discontinuous data acquisition, insufficient accuracy, or limited coverage in data acquisition, resulting in large errors in the description of rock mass behavior. With high-precision lidar and point cloud segmentation technology, the present invention can achieve fine capture of the geometric shape and structural characteristics of the slope surface. At the same time, through the auxiliary supplement of geological and meteorological data, the dynamic environmental conditions are incorporated into the characteristic modeling of rock mass units. In this way, each rock mass unit not only represents its geometric attributes but also carries multi-dimensional physical and environmental information, enabling the subsequent calculation of expansion potential energy and stress state to accurately reflect its real behavior.

[0045] Step 2: Calculate the expansion potential energy during the water absorption process of the slope area corresponding to each rock mass unit at each time according to the geological data and hydro-meteorological data of the slope area corresponding to each rock mass unit; calculate the volumetric strain and the principal strain under isotropic conditions of the slope area corresponding to each rock mass unit at each time according to the expansion potential energy, and calculate the effective stress of the slope area corresponding to each rock mass unit at each time according to the volumetric strain and the principal strain. Then calculate the mean value of the effective stress at all times to obtain the mean value output; and then calculate the variance of the effective stress at all times to obtain the variance output.

[0046] The swelling characteristics of expansive rock mainly stem from hydrophilic minerals such as montmorillonite in its internal mineral structure. When water molecules enter the lattice interlayers of these minerals, it causes lattice swelling and potential energy changes. This swelling potential energy is the fundamental cause driving the volume change and deformation of rock mass units. In the present invention, the calculation of swelling potential energy fully considers the mineral composition, water absorption capacity, fracture structure of the rock mass, as well as the dynamic changes in meteorological conditions. By introducing multi-time-step hydro-meteorological data, the non-linear behavior during the process of water entering the rock mass can be accurately simulated. This high-timeliness and high-resolution calculation provides an accurate basis for subsequent stress state analysis. Based on the calculation of swelling potential energy, the volume strain and principal strain of the rock mass unit are further derived. These parameters are important physical quantities describing the deformation characteristics of the rock mass. The volume strain reflects the overall volume change of the rock mass during water absorption, which is directly related to the swelling potential energy, while the principal strain further describes the deformation components of the rock mass in different directions through the isotropic assumption. After the expansive rock absorbs water, the volume change and directional deformation have significant impacts on the slope stability. This kind of deformation not only changes the geometric shape of the rock mass but also affects the redistribution of internal stress. By combining actual geological data, the present invention refines the calculation of volume strain and principal strain to enable it to truly reflect the behavior characteristics of expansive rock.

[0047] After calculating the volume strain and principal strain, the present invention directly links the deformation characteristics of expansive rock with its stability state through the calculation of effective stress. Effective stress is a key parameter in the stability analysis of rock mass, which reflects the actual stress state of the rock mass under the combined action of external loads and internal pore water pressure. During the water absorption process of expansive rock, due to the gradual increase of water in the pores, the effective stress will be significantly reduced, thus increasing the risk of slope instability. The calculation of effective stress in the present invention fully considers the dynamic changes in pore water pressure and obtains the effective stress distribution of the rock mass unit at different times through multi-time-step calculation. Such dynamic calculation results not only improve the understanding of the variation law of the stability of expansive rock slopes but also provide a scientific basis for the quantitative analysis of the instability probability. After completing the calculation of effective stress at all times, the present invention further extracts the mean and variance of the effective stress as characteristic outputs. The mean of the effective stress can reflect the average stress state of the rock mass within the entire time range, while the variance reveals the degree of fluctuation of the effective stress. The combination of these two parameters can comprehensively reflect the stability state of the expansive rock slope. Because when the mean is low, the slope is more likely to enter an unstable state, and a larger variance may indicate a higher instability of the rock mass stress and a potential failure risk. This way of extracting the mean and variance not only reveals the dynamic behavior of expansive rock from a physical level but also provides high-quality input features for deep learning models.

[0048] Step 3: Input the mean output as the input quantity into the pre-trained deep learning autoencoder, combine the variance output, and output the latent variable; calculate the difference between the latent variable and the mean output, and perform a ratio calculation between the difference and the preset basic threshold to obtain the instability probability of the slope area corresponding to each rock mass unit.

[0049] An autoencoder is a neural network model for unsupervised learning. Its basic principle is to compress high-dimensional data into a low-dimensional latent space through an encoder and then reconstruct it into the original data through a decoder. This structure can effectively extract the core features of the data and show strong modeling capabilities when there are high-dimensional non-linear relationships in the data. In the present invention, the autoencoder is used to process the mean and variance of the effective stress of the expansive rock slope. These two characteristic quantities contain the stability information of the rock mass unit under dynamic loading at multiple time steps. The mean of the effective stress reflects the overall stress level of the rock mass unit, while the variance reveals the magnitude of its stress fluctuation, which may be caused by changes in meteorological conditions, differences in rock mass properties, or external loads. By inputting into the autoencoder, this information is further compressed and mapped into the latent space to generate latent variables that can reflect complex characteristic relationships. The generation process of the latent variables reflects the powerful ability of deep learning in dealing with non-linear problems. In traditional methods, feature engineering often relies on artificially set rules and assumptions and is difficult to capture the potential high-order relationships between data. The autoencoder automatically learns the implicit relationships between features through the neural network, not only can retain the physical meaning of the mean and variance of the effective stress, but also can dig out the non-linear patterns hidden behind these characteristic quantities. For example, in an expansive rock slope, the rainfall intensity may affect the stress distribution of the rock mass through complex water infiltration paths, and these complex coupling effects cannot be directly described by a linear model. The autoencoder extracts and retains these non-linear relationships through the representation of the latent space, providing a comprehensive feature description for the subsequent calculation of the instability probability.

[0050] The generation of latent variables does not directly reflect the stability of the slope. Instead, it is necessary to further compare with the mean value of effective stress to reveal the instability risk of the expansive rock slope. In the present invention, the difference between the latent variable and the mean value output is calculated and normalized to a ratio related to a preset threshold, thereby quantifying the instability probability of each rock mass unit. This difference can be regarded as a deviation amount, reflecting the difference between the stress state of the current rock mass unit and the latent mode. If this difference is significant, it indicates that the stress state of the rock mass unit is abnormal and may be in a critical state of instability. Through normalization, this difference is further converted into a probability value, thus realizing the quantitative characterization of the instability risk. It should be noted that the preset basic threshold plays a crucial role in the whole process. The setting of the threshold is usually based on empirical data or engineering standards, reflecting the critical conditions for the transformation of the rock mass unit from a stable state to an unstable state. In an expansive rock slope, instability may be caused by local stress concentration or sudden changes in environmental conditions. Therefore, the selection of the threshold needs to comprehensively consider the physical properties of the expansive rock and the actual geological environment. In practical applications, the threshold can be adjusted to adapt to different slope environments and engineering requirements, thereby improving the adaptability and robustness of the model.

[0051] Embodiment 2: The geological data of the slope area corresponding to each rock mass unit obtained in Step 1 includes: dry density of the rock mass, average particle size of the rock and soil, water content, swelling pressure, unit weight of water, hydration heat of the rock and soil minerals, elastic modulus of the rock mass, Poisson's ratio, cohesion, internal friction angle, montmorillonite content, and quartz content; the elastic modulus of the rock mass is determined by collecting rock mass samples of each rock mass unit and conducting uniaxial compression tests on the rock mass samples; the cohesion and internal friction angle are determined by collecting rock mass samples of each rock mass unit and conducting direct shear tests on the rock mass samples; Poisson's ratio represents the lateral deformation ratio in the other direction when the rock mass sample is subjected to tensile or compressive stress in one direction.

[0052] Specifically, the dry density of the rock mass is an important index reflecting the compactness of the rock mass, which is defined as the mass of the rock mass per unit volume in the dry state. The dry density is closely related to the porosity of the rock mass and directly affects the penetration rate and water absorption capacity of water inside the rock mass. In an expansive rock slope, a higher dry density usually means a lower porosity and water absorption capacity, which may delay the swelling process but may also cause local stress concentration, thereby increasing the instability risk. The present invention provides basic parameters for subsequent calculation of swelling potential energy by accurately measuring the dry density of the rock mass unit. The average particle size of the rock and soil describes the geometric characteristics of the rock and soil particles and is an important parameter affecting water diffusion and swelling rate. The size of the particle size determines the permeability of the rock mass and the distribution form of the hydraulic gradient inside. In an expansive rock slope, a smaller particle size may cause water to rapidly diffuse inside the rock mass, inducing faster swelling behavior. By obtaining the average particle size of the rock and soil, the present invention can more accurately simulate the dynamic change of water distribution during the water absorption process.

[0053] The water content is a basic index for describing the water content in rock masses, which directly determines the water absorption capacity and swelling degree of expansive rocks. In the present invention, by real-time monitoring and recording the water content of each rock mass unit, the water absorption behavior of the rock mass can be dynamically tracked, and input can be provided for the calculation of swelling potential energy and volume strain. The change of this parameter can also reflect the influence of environmental conditions on the slope stability. For example, a rapid increase in water content caused by rainfall may be a precursor to slope instability. The swelling pressure is an important index for describing the mechanical response of expansive rocks during the water absorption process due to volume expansion. The swelling pressure is not only related to the physical properties of the rock mass but also restricted by external boundary conditions. In the present invention, the acquisition of the swelling pressure provides a direct basis for subsequent stress calculation and can also be used to evaluate the instability risk of rock mass units in the water-absorbed state. The unit weight of water is an important parameter affecting the pore water pressure in expansive rocks, which is defined as the weight of water per unit volume. In an expansive rock slope, the pore water pressure is the main factor causing the decrease of effective stress, and the effective stress is the core index for stability analysis. In the present invention, by considering the unit weight of water, its effect is incorporated into the swelling potential energy and stress calculation models, so as to more accurately reflect the true mechanical state of the rock mass. The hydration heat of geotechnical minerals refers to the heat released or absorbed when minerals in the rock mass undergo hydration reactions during the water absorption process. This parameter directly affects the water absorption rate and swelling potential energy of expansive rocks. Rock masses with a relatively high content of hydrophilic minerals such as montmorillonite usually have greater hydration heat, resulting in more intense swelling behavior during the water absorption process. In the present invention, by measuring the hydration heat, a thermodynamic basis is provided for the calculation of swelling potential energy. The elastic modulus of the rock mass is an important parameter for describing the deformation resistance of the rock mass in the elastic deformation stage, which is determined by uniaxial compression tests. The uniaxial compression test places the rock mass sample in a stressed state, measures the relationship between its deformation and stress, and determines the elastic modulus. In an expansive rock slope, the elastic modulus determines the response speed and deformation degree of the rock mass to the swelling pressure. In the present invention, by accurately measuring each rock mass unit, the deformation characteristics of the rock mass during the swelling process can be better simulated. The Poisson's ratio describes the ratio of the lateral deformation to the longitudinal deformation of the rock mass when it is stressed in one direction. This parameter is obtained through uniaxial compression tests and is an important basis for the isotropic assumption of the rock mass. In the present invention, the Poisson's ratio is used to calculate the volume strain and principal strain and is an important bridge for converting the swelling potential energy into a strain state. The cohesion and internal friction angle are two basic parameters reflecting the shear strength of the rock mass, which are determined by direct shear tests. The cohesion describes the internal cohesion between rock mass particles, while the internal friction angle reflects the frictional resistance between rock mass particles. In an expansive rock slope, the water absorption process may reduce the cohesion and internal friction angle, thus weakening the shear strength of the rock mass. In the present invention, by accurately measuring these parameters, a direct basis is provided for predicting the instability probability. The contents of montmorillonite and quartz are key mineralogical parameters affecting the water absorption behavior of expansive rocks.Montmorillonite has strong water absorption and swelling characteristics. The higher its content, the greater the swelling potential of the rock mass. Quartz, on the other hand, has relatively high rigidity and plays a certain inhibitory role in the swelling behavior. In the present invention, by measuring the contents of these two minerals, the swelling behavior of the rock mass during water absorption and its impact on slope stability can be predicted more accurately.

[0054] Example 3: The hydro-meteorological data of the slope area corresponding to each rock mass unit obtained in Step 1 include: infiltration rate, rainfall, and temperature.

[0055] Specifically, the infiltration rate describes the rate at which water enters the interior of the rock mass from the ground surface and is a direct factor affecting the water absorption behavior of expansive rock and the change of pore water pressure. The water absorption and swelling characteristics of expansive rock are highly sensitive to the infiltration rate. When the infiltration rate is high, a large amount of water quickly penetrates into the interior of the rock mass, resulting in a rapid increase in pore water pressure and further reduction of effective stress, which may accelerate the occurrence of slope instability. The magnitude of the infiltration rate depends on factors such as the permeability of the rock mass, fracture distribution, and rainfall intensity. In expansive rock, the degree of fracture development often makes the spatial distribution of the infiltration rate highly heterogeneous. By dynamically monitoring and recording the infiltration rate of each rock mass unit in the present invention, the real-time process of water entering the interior of the rock mass can be reflected more accurately, providing basic input for the calculation of swelling potential energy. Rainfall is one of the most direct meteorological parameters in the stability analysis of expansive rock slopes, and its influencing mechanism is mainly reflected in two aspects. On the one hand, rainfall directly determines the total amount of water supply, affecting the saturated state of the rock mass and the change of pore water pressure; on the other hand, heavy rainfall events may trigger high-intensity infiltration in a short period of time, thereby inducing stress concentration and instability in local rock mass units. The change of rainfall not only has dynamic characteristics in time but also shows differences in regional distribution. For example, the change of local rainfall intensity may lead to significant differences in the water absorption rate and swelling degree of different rock mass units. By obtaining the rainfall data of the slope area corresponding to each rock mass unit in real time and combining geological and hydrogeological conditions in the present invention, an accurate model of the swelling effect caused by rainfall is established, thereby improving the prediction ability of slope instability risk. Temperature is an indirect factor affecting the water absorption and swelling process of expansive rock, and it mainly plays a role by changing the physical and chemical properties of water and the water absorption behavior of the rock mass. Higher temperature usually reduces the viscosity of water and increases the infiltration rate, thus accelerating the process of water entering the rock mass; at the same time, temperature may also affect the hydration reaction rate of rock mass minerals. For example, the water absorption and swelling behavior of expansive minerals such as montmorillonite may be more intense in a high-temperature environment. In addition, the diurnal change of temperature causes the thermal expansion and contraction effect of the rock mass, which, combined with water absorption and swelling, may lead to stress concentration and crack expansion in local areas of the slope. By recording the temperature data of each rock mass unit in the present invention and incorporating it into the dynamic analysis of swelling potential energy and stress state, the influence of environmental conditions on slope stability can be captured more comprehensively.

[0056] Example 4: In step 1, the target slope surface is periodically scanned by a high-precision lidar to obtain point cloud data; the method for segmenting the point cloud data to obtain multiple rock mass units includes: Through the following formula, adaptive filtering is performed on the th point in the point cloud data:

[0057] ;

[0058] where, is the point cloud density at point ; is the number of points within the search sphere; is the radius of the search sphere; is the distance from point to its nearest neighbor; is the standard deviation of the Gaussian distribution; is the normal vector at point ; is the lidar line-of-sight direction vector; Then, through the following formula, it is determined whether the neighbor of point belongs to a rock mass unit:

[0059] ;

[0060] where, is the determination value. If , then it is determined that point and its neighbor are in a rock mass unit; is the Euclidean distance between point and its neighbor ; is the normal vector at the neighbor of point ; is the point cloud density at point ; is the set angle threshold; is the set distance threshold; is the set density threshold.

[0061] Specifically, the core of the point cloud data adaptive filtering lies in calculating the local density of each point. This density value not only reflects the degree of density of point in space, but also takes into account its geometric characteristics and the relative relationship with the lidar line-of-sight direction. The first part of the density calculation formula determines the basic density through the number of points within the search sphere and the sphere volume . This part directly captures the point The distribution characteristics of the surrounding local space. However, this density calculation may have limitations on complex slope surfaces because the geometric shape of expansive rock is usually highly irregular, and simply relying on the point cloud density of geometric distribution may not fully reflect the local characteristics of points. Therefore, the formula further introduces a Gaussian distribution factor , and adjusts the density value through the distance of the nearest neighbor points . Points with closer distances contribute more to the density, while the influence of points with farther distances is significantly attenuated. This design not only improves the accuracy of point cloud density calculation but also enhances the sensitivity to local geometric details. At the same time, the third part in the formula further adjusts the point cloud density through the inner product of the normal vector and the lidar line-of-sight direction vector . The physical basis of this design is that during the lidar measurement process, the angle between the normal vector direction and the line-of-sight direction affects the intensity and accuracy of laser reflection. When the normal vector is close to parallel to the line-of-sight direction, the correction value of the density is higher, thus emphasizing the importance of these points in slope structure analysis more. This density correction based on geometry and observation angle enables the formula to adaptively adjust and has higher resolution ability for complex areas (such as steep edges or convex parts) on the slope surface.

[0062] After calculating the point cloud density, the formula further introduces a neighboring point determination criterion to determine whether there is spatial, density, and geometric continuity in the point cloud. Due to factors such as water absorption and swelling and crack development, the slope surface of expansive rock often has a complex internal structure, and this structural characteristic requires that point cloud segmentation can meet multiple constraint conditions at the same time. The first term of the neighboring point determination formula, through the comparison of the inner product of the normal vector with the threshold , ensures that the point clouds judged to be the same rock mass unit have similar local surface geometric characteristics. Excessive directional differences in the normal vector mean that there may be cracks or changes in material properties, so allocating these points to different units can better reflect the actual slope characteristics. In addition, the spatial distance and density difference of neighboring points are the other two important criteria. Point cloud segmentation requires that the Euclidean distance between point and is less than the set threshold , and this condition ensures the spatial continuity of the segmentation result. And the density difference threshold It is used to further restrict the physical consistency of points. Points with overly large density differences usually reflect significant changes in material properties and may not belong to the same rock mass unit. This comprehensive constraint of multiple conditions enables the point cloud segmentation results to fully reflect the physical and geometric characteristics of the rock mass units, providing accurate unit division for subsequent calculation of swelling potential energy and stress analysis. The design of the formula fully considers the characteristics of swelling rock slopes and the observation characteristics of lidar scanning. Due to its water absorption and swelling characteristics, swelling rock causes the slope surface to have high irregularity at the microscale, and the changes in point cloud density, normal vector, and observation angle during lidar scanning further increase the complexity of data processing. By introducing a combined formula of adaptive filtering and multi-condition determination, the present invention can effectively address these challenges, thereby ensuring accurate division of rock mass units under different environmental conditions. The innovation of this point cloud segmentation method is not only reflected in the accuracy of its algorithm but also in its seamless connection with subsequent deep learning models. The segmented rock mass unit data has clear physical and geometric characteristics and can be directly used as the basic input for calculating swelling potential energy and effective stress. The deep learning model further realizes the dynamic prediction of slope instability probability by learning the feature distribution in the segmentation results. Compared with traditional methods, this point cloud segmentation scheme based on the combination of formula and deep learning not only improves the accuracy of slope stability prediction but also significantly enhances the adaptability to complex environments.

[0063] Example 5: In step 2, according to the following formula, based on the geological data and hydro-meteorological data of each rock mass unit, calculate the swelling potential energy of each rock mass unit during the water absorption process at each time:

[0064] ;

[0065] Where, is the swelling potential energy of the th rock mass unit during the water absorption process at time; is the dry density of the rock mass in the slope area corresponding to the th rock mass unit; is the average particle size of the rock and soil in the slope area corresponding to the th rock mass unit; is the water content in the slope area corresponding to the th rock mass unit; is the swelling pressure in the slope area corresponding to the th rock mass unit; is the unit weight of water in the slope area corresponding to the th rock mass unit; is the hydration heat of the rock and soil minerals in the slope area corresponding to the th rock mass unit; is the The average height of the slope area corresponding to a rock mass unit; is the elastic modulus of the rock mass in the slope area corresponding to the th rock mass unit; is the Poisson's ratio of the slope area corresponding to the th rock mass unit; is the cohesion of the slope area corresponding to the th rock mass unit; is the internal friction angle of the slope area corresponding to the th rock mass unit; is the montmorillonite content of the slope area corresponding to the th rock mass unit; is the quartz content of the slope area corresponding to the th rock mass unit; is the universal gas constant; is the temperature at time is the rainfall at time is the infiltration rate at time

[0066] Specifically, through the basic volume and dry density of the rock and soil, the mass distribution of the rock mass unit is calculated. Here, the average particle size of the rock and soil is a core geometric parameter in the expansive rock slope, which directly determines the porosity and moisture diffusion path of the rock mass unit. The larger the particle size, the lower the porosity of the rock mass unit is usually, and the water absorption capacity may be limited, but the distribution of the swelling pressure inside the rock mass is more uniform. And the dry density indicates the mass distribution of the rock mass unit, and together with the particle size, determines the physical behavior of the rock mass during the water absorption process. By combining the geometric characteristics with the density characteristics, the formula can accurately describe the basic physical characteristics of the rock mass unit, which is the core basis for the calculation of the swelling potential energy. The swelling pressure and water content are important dynamic variables reflecting the rock mass unit during the water absorption process. The swelling pressure comes from the unique water absorption and swelling phenomenon of the expansive rock, that is, when water enters the pores or mineral lattices of the rock mass, it causes the volume increase effect inside the rock mass. The water content is a direct index to measure the water content inside the rock mass. In the formula, through The combined relationship dynamically correlates the change in swelling pressure with the water content. The higher the water content, the stronger the total effect of the swelling pressure. This dynamic model can well capture the swelling behavior of rock mass units at different water absorption stages. Especially under conditions of heavy rainfall or continuous infiltration, when the water content rises rapidly, the swelling pressure will increase significantly, leading to a rapid accumulation of swelling potential. In addition, the formula further considers the dynamic influence of hydro-meteorological parameters on the swelling potential, specifically through to represent. This term combines the infiltration rate , rainfall , the unit weight of water , and the average height of the rock mass unit. The infiltration rate and rainfall directly determine the amount of water entering the rock mass per unit time, while the unit weight of water reflects the gravitational effect of water on the interior of the rock mass. The average height is related to the slope structure and the water infiltration path, determining the distribution law of water under the action of gravity. The combination of these parameters enables the formula to simulate the driving effect of hydro-meteorological conditions on the swelling potential at a macroscopic scale. For example, in a heavy rainfall event, a high infiltration rate and high rainfall will significantly increase the water supply of the rock mass unit, further enhancing the swelling pressure and water content, thus triggering a rapid increase in swelling potential. This dynamic relationship is particularly crucial in the instability process of swelling rock slopes and can accurately capture the instantaneous effects caused by hydro-meteorological conditions.

[0067] The formula introduces a thermodynamic term , and the core of this part is to describe the influence of the hydration reaction of rock minerals on the swelling potential. During the water absorption process of geotechnical minerals (such as montmorillonite), water molecules enter the interlayer of the mineral lattice and undergo a hydration reaction. This reaction is usually accompanied by the release or absorption of heat, and its degree is determined by the mineral hydration heat . The formula uses a thermodynamic model to depict the dynamic regulation effect of the hydration reaction on the swelling potential through the relationship between and the absolute temperature . When the temperature is relatively high, the rate and degree of the hydration reaction may increase significantly, thus accelerating the accumulation of swelling potential; while a lower temperature will inhibit this process. The introduction of this thermodynamic term enables the formula to adapt to the characteristics of swelling rocks under different climate and temperature conditions. Especially in regions with significant diurnal temperature differences or drastic seasonal changes, the influence of temperature fluctuations on the swelling behavior can be accurately captured. The formula further quantifies the deformation response of the rock mass unit under the action of swelling pressure through the combined term of the elastic modulus and the Poisson's ratio . The elastic modulus represents the ability of the rock mass to resist deformation within the elastic range, while the Poisson's ratio ​It reflects the deformation ratio in the other direction when the rock mass is compressed or stretched in one direction. The exponential decay term of Poisson's ratio indicates that the greater the Poisson's ratio, the lower the contribution of the lateral deformation of the rock mass to the swelling potential energy. This part of the formula closely combines the swelling pressure with the material properties of the rock mass, and can describe in detail the swelling characteristics of the rock mass in different directions. This refinement of the mechanical response provides basic data for the subsequent calculation of volumetric strain and principal strain, enabling the formula to more comprehensively reflect the swelling behavior of the rock mass unit. Finally, the last part of the formula uses the friction angle , cohesion , montmorillonite content and quartz content and other parameters to reveal the regulation effect of the mineral composition inside the rock mass on the swelling potential energy. The friction angle and cohesion are key indicators of the shear strength of the rock mass. They not only affect the conversion efficiency of the swelling potential energy, but also are directly related to the stability of the rock mass. The formula uses the correction term to describe the weakening effect of cohesion on the swelling pressure distribution. This relationship is particularly applicable to areas where there are obvious changes in cohesion inside the swelling rock. In addition, the ratio of the montmorillonite content and quartz content further reflects the influence of the mineral composition on the swelling behavior. Montmorillonite is the main swelling mineral in the swelling rock. The higher its content, the greater the swelling potential of the rock mass; while quartz is a rigid mineral that can inhibit the swelling behavior to a certain extent. The formula dynamically balances the influence of these two minerals on the swelling potential energy through the ratio , so as to more accurately describe the regulation effect of the mineralogical characteristics of the rock mass unit on the swelling process. This modeling of the mineral composition is particularly important for the prediction of swelling rock slopes, because the regional differences in the mineral composition may lead to significant changes in the swelling behavior, and this difference is difficult to capture by traditional prediction models.

[0068] Example 6: In step 2, according to the following formula, calculate the volumetric strain at each time of the slope area corresponding to each rock mass unit and the principal strain under isotropic conditions based on the swelling potential energy:

[0069] ;

[0070] where is the volume of the th rock mass unit; is the volumetric strain; under isotropic conditions, the three principal strains are equal, and the calculation formula is:

[0071] ;

[0072] where , and are the principal strains.

[0073] Specifically, the calculation formula of volumetric strain takes the swelling potential energy as the core, directly reflecting how the energy accumulation during the water absorption process of the rock mass unit is converted into volumetric deformation. The core of this energy conversion relationship lies in that the swelling potential energy is caused by the increase in internal energy triggered by the entry of water into the pores or mineral lattices of the rock mass. The higher the swelling potential energy, the greater the swelling pressure on the rock mass, and the more significant its volumetric deformation. The formula, through the coupling of the elastic modulus and Poisson's ratio , clarifies the constraint effect of the material properties of the rock mass during the swelling process. The elastic modulus describes the anti-deformation ability of the rock mass unit against the swelling pressure. The higher its value, the smaller the volumetric strain, indicating that the rock mass exhibits higher stiffness during the swelling process. And Poisson's ratio, through the correction coefficient , depicts the influence of lateral deformation on volumetric strain. For rock mass units with a higher Poisson's ratio, their lateral swelling effect is more significant, thus reducing the accumulation of overall volumetric strain. The volume in the formula It is an important scale parameter for the expansion potential energy to be distributed into the interior of rock mass units. The introduction of volume can adjust the contribution rate of the expansion potential energy to the volume strain, enabling the formula to adapt to the deformation characteristics of rock mass units of different scales. For example, for rock mass units with a smaller volume, the same expansion potential energy may trigger more significant volume strain, while for rock mass units with a larger volume, the expansion potential energy will be more evenly distributed, resulting in a weakened strain effect. This volume-based dynamic adjustment can truly reflect the deformation differences in different regions of the expansive rock slope, providing a more refined description for slope stability analysis. Based on the volume strain, the formula further utilizes the isotropic assumption to evenly divide the volume strain into three principal strains, defining the deformation components of the rock mass unit in each direction. This assumption indicates that during the water absorption and expansion process, the deformation of the rock mass unit is evenly distributed, without obvious directional stress concentration. The calculation results of the principal strains not only reflect the overall deformation trend within the rock mass but also can reveal the stability state of local areas. For example, when the principal strain value of a certain rock mass unit is significantly greater than that of the surrounding units, it may indicate that there is abnormal expansion pressure concentration or insufficient material strength in this area, which may become a potential risk point for slope instability. Through the distribution calculation of the principal strains, the present invention further links the expansion potential energy with the deformation characteristics of the rock mass, providing key inputs for subsequent effective stress calculation and instability probability prediction. The magnitude of the principal strain directly affects the stress distribution within the rock mass unit. When the principal strain is larger, the stress concentration degree of the rock mass unit is also higher, which may lead to risks such as crack propagation, material failure, and even overall instability. The uniformity of the principal strain reflects the coordination within the rock mass. A uniform principal strain distribution usually means that the rock mass unit has better stability. This quantitative description of the deformation characteristics not only improves the accuracy of slope stability analysis but also provides richer feature data for deep learning models.

[0074] Example 7: In step 2, through the following formula, calculate the effective stress of the slope area corresponding to each rock mass unit at each time:

[0075] ;

[0076] where, is the effective stress of the slope area corresponding to the th rock mass unit at time.

[0077] Specifically, the first part of the formula focuses on the internal mechanical response of the expansive rock material, reflecting the stress distribution of the rock mass in the elastic deformation stage. The elastic modulus and Poisson's ratio It is the core parameter of this part, describing the resistance ability and deformation characteristics of rock mass materials to external forces. The higher the elastic modulus, the greater the stiffness of the rock mass, the smaller its deformation response, and the greater the internal stress generated at the same time; the Poisson's ratio, through its composite form and , correlates the volumetric strain with the three-dimensional stress distribution, reflecting the regulating effect of lateral deformation on the total stress of the rock mass. In expansive rock, the role of Poisson's ratio is particularly important because a rock mass with significant lateral expansion may weaken stress concentration in some directions while enhancing the non-uniformity of stress distribution in other directions. This complex mechanical response is fully reflected in the formula, ensuring an accurate modeling of the true stress state of the rock mass material. The volumetric strain is the key variable driving the generation of internal stress, and its value depends on the relationship between the swelling potential and the characteristics of the rock mass material. In expansive rock, water absorption and swelling directly cause changes in the volume of the rock mass, and the volumetric strain is a quantitative index of this change. When the swelling potential is high, the swelling pressure of the rock mass increases significantly, resulting in a rapid rise in the volumetric strain and an increase in the internal stress accordingly. This dynamic relationship not only reflects the deformation mechanism of expansive rock but also embodies the direct influence of environmental conditions on the mechanical behavior of the rock mass. For example, under heavy rainfall conditions, the concentration and growth of internal swelling stress. The formula, through the coupling of the volumetric strain with the elastic modulus and Poisson's ratio, accurately maps the energy conversion during the water absorption and swelling process of expansive rock into the generation process of internal stress. This mapping not only covers the elastic properties of the rock mass material but also can capture the non-linear changes under dynamic environmental conditions, enabling the model to adapt to complex hydro-meteorological conditions. The second part of the formula focuses on the weakening effect of hydro-meteorological conditions on the effective stress of the rock mass unit, specifically manifested through the pore water pressure term . Here, the unit weight of water describes the weight of water per unit volume, and its value reflects the basic contribution of water to the pore pressure; the height of the rock mass unit further defines the pressure effect of the water column. The greater the height, the higher the pore water pressure inside the rock mass; and the water content is a dynamic variable that directly determines the change range of the moisture content inside the rock mass. When the water content increases, such as under heavy rainfall or continuous infiltration conditions, the pore water pressure increases significantly, thereby greatly weakening the effective stress of the rock mass. The introduction of pore water pressure is of particular significance in the stability analysis of expansive rock slopes. Due to its high water absorption and significant volume expansion characteristics, expansive rock often exhibits a high pore water pressure. This pressure not only reduces the ability of the rock mass to bear external loads but also may trigger the expansion of cracks inside the rock mass and the weakening of material strength, ultimately leading to slope instability. By introducing this term, the formula can accurately capture the influence of moisture dynamic changes on the stress distribution of the rock mass, providing a reliable basis for slope stability prediction under complex hydrogeological conditions.

[0078] Example 8: In step 3, the process of taking the mean output as the input quantity and inputting it into the pre-trained deep learning autoencoder to output the latent variable specifically includes: Let the mean output be ; Encode the mean output through the following formula:

[0079] ;

[0080] where, is the encoding result; is the mean distribution function; is the log variance distribution function; ; where, is the number of past feature inflation times, and its value is equal to the number of landslides that occurred within a circular area centered on the target slope with a set value as the radius; ; The variance of the effective stress at all times is ; represents a normal distribution with a mean of 0 and a variance of 1; Then input the encoding result into a single-layer deep learning network to output the latent variable ; is the variance output; is the Hadamard product.

[0081] Specifically, the formula first converts the effective stress mean into a probability distribution. The core idea of this step is to describe the dynamic behavior and its uncertainty of the mean output through random mapping. Specifically, the encoding result follows a normal distribution, and its mean is determined by the distribution function , and the variance is determined by the log variance distribution function . The advantage of this probability modeling is that it can not only reflect the central tendency of the effective stress mean but also quantify its volatility. Especially in areas where environmental conditions change drastically or historical landslides on the slope are frequent, it can more comprehensively characterize the dynamic characteristics of rock mass units. The mean distribution function introduces a Poisson distribution weight in its definition to combine the number of landslides and the regional landslide influence radius . The Poisson distribution term is an important tool for describing the spatio-temporal distribution of historical landslide events. determines the spatial scale of the landslide event, while reflects the landslide frequency within the target slope area. Through this design, the mean distribution function not only describes the current state of the effective stress mean but also dynamically couples the historical landslide characteristics with the current environmental state. For areas with a high number of landslides, In larger areas, the weight of the Poisson distribution is higher, indicating that in regions with frequent landslides, the cumulative effect of historical disasters has a stronger impact on the current slope stability. Conversely, when is lower or is smaller, the influence of the Poisson weight weakens, and the mean distribution function depends more on the current mean of the effective stress . The logarithmic variance distribution function further characterizes the degree of fluctuation of the mean effective stress and its complex relationship with the landslide history. By introducing the term and the exponential factor , the variance distribution function explicitly quantifies the regulatory effect of the number of historical landslides and the regional landslide influence radius on the effective stress fluctuation. The higher the number of landslides , the larger the dynamic range of the variance, indicating that the frequent occurrence of historical landslide events leads to an increase in the uncertainty of the current effective stress. And reflects the spatial scale of the landslide influence range by affecting the amplitude of . The normalization factor of the variance ensures that the effective stress fluctuations at different time points and spatial scales can be reasonably compared, avoiding the characteristic expression deviation caused by regional characteristic differences.

[0082] After defining the mean and variance distributions, the formula further generates potential coding results through random variables. Specifically, the formula introduces Gaussian noise , and couples the noise with the variance distribution in the form of to generate random samples that conform to the normal distribution. This design is based on the idea of the variational autoencoder (VAE), expressing the coding result as a joint distribution of the mean and volatility. The generated coding result not only retains the temporal dynamic trend of the effective stress but also introduces randomness through noise, enhancing the generalization ability of the features. The final latent variable It is the result of further non - linear transformation of the encoding result through a single - layer deep - learning network. Through this transformation, the latent variable can not only capture the core features of the input data but also extract hidden patterns that are difficult to directly observe in the deep - learning model. The formula models the mean distribution and variance distribution, dynamically combines historical landslide information and current effective stress, enabling the latent variable to simultaneously reflect the static stability and dynamic evolution trend of the slope. This method can capture the long - term impact of historical events in the slope area. For example, in areas with a high number of landslides, the distribution of the latent variable may have greater volatility, indicating a higher risk of instability. At the same time, for areas with relatively stable current environmental conditions, the distribution of the latent variable may be more concentrated, reflecting a lower risk of instability. This method of describing dynamic characteristics through probability distribution provides highly robust and sensitive inputs for subsequent slope stability prediction based on deep learning. Compared with traditional methods that only rely on mean - value feature extraction, the present invention jointly models the mean and variance distributions of effective stress, introduces historical landslide events and regional environmental factors, greatly enhancing the complexity and accuracy of feature expression. The latent variable generated through this dynamic encoding method can not only improve the prediction accuracy of the model for slope instability risk but also capture the stability differences between different time points and regions, thus providing a scientific basis for slope monitoring and disaster warning.

[0083] Example 9: In step 3, the latent variable is calculated by the following formula:

[0084] ;

[0085] where, represents calculating the maximum value of; represents the activation function.

[0086] Specifically, the core operation in the formula is to extract the maximum value from the encoding result . The stability of expansive rock slopes is the result of the dynamic influence of multiple factors. There are complex interactions among the stress state of the slope, historical events (such as landslides), and environmental changes (such as rainfall, temperature, etc.). As a key indicator, the effective stress shows obvious fluctuations in the time series, and the amplitude of these fluctuations may be closely related to the occurrence of actual instability events. Therefore, the extraction of the maximum value can focus on the important features in the encoding result, that is, those that reflect the most extreme changes experienced by rock mass units or slope areas at a specific moment. This extraction of the maximum value not only improves the sensitivity of the model to outliers but also ensures that the latent variable can capture the most representative state, which is particularly important for predicting slope instability risk. Then, the formula normalizes the maximum value, using Convert it into a value within the stable range in a certain form. The role of normalization is to adjust the range of eigenvalues, enabling the features of different input data to be compared and processed on the same scale. The normalized values are further transformed through activation functions, and the activation functions play a crucial role in this process. The activation function compresses or expands the input values into the latent space through non-linear transformation, ensuring that the latent variables can more accurately represent the high-order features in the input data. The stability of expansive rock slopes is affected by various factors, such as changes in environmental conditions, rock mass properties, and external loads. A simple linear model cannot comprehensively capture the complex interactions between these factors. Through the non-linear transformation of the activation function, the model can automatically learn these complex interaction relationships, thereby achieving higher accuracy and robustness in predicting slope stability.

[0087] The introduction of the activation function not only enhances the model's ability to capture the dynamic behavior of slopes but also provides stronger expressive power for feature learning in subsequent deep learning models. Predicting the stability of expansive rock slopes requires not only identifying the stress state of the rock mass in the current environment but also capturing the risk signals hidden in historical data, especially in slope areas where extreme events such as landslides occur. The activation function enables the output of the latent variables to better conform to these complex, non-linear relationships, making the model's prediction ability more accurate. For example, the extreme effective stress change at a certain time point may be a precursor to a landslide, and this change may be highlighted through maximum value extraction during the encoding process, thus affecting the calculation result of the latent variable. The activation function amplifies this change non-linearly, enabling the model to better reflect the warning effect of these abnormal data on slope instability. Throughout the process, the latent variable is not just a simple transformation of the input features. It is the result of the autoencoder's efficient compression and deep abstraction of the input data. By performing maximum value extraction, normalization, and activation function transformation on , the latent variable can capture the most important features in the input data and map these features into a low-dimensional latent space, so that the deep learning model can utilize these refined features for subsequent instability probability prediction. The design and calculation method of the latent variable enable the model to handle the complex environmental dynamics of expansive rock slopes and improve the accuracy and reliability of slope instability risk prediction.

[0088] Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that these specific embodiments are merely illustrative. Without departing from the principles and essence of the present invention, those skilled in the art can make various omissions, substitutions, and changes to the details of the above methods and systems. For example, combining the above method steps so as to perform substantially the same function in a substantially the same way to achieve substantially the same result falls within the scope of the present invention. Therefore, the scope of the present invention is only defined by the appended claims.

Claims

1. A slope stability prediction method based on deep learning, characterized in that: The method comprises: Step 1: Periodically scan the target slope surface with a high-precision laser radar to obtain point cloud data; segment the point cloud data to obtain multiple rock mass units; perform the following operations in the slope area corresponding to each rock mass unit: obtain the geological data of the slope area through geological surveys, and obtain the hydrological and meteorological data of the slope area at multiple continuous times through meteorological station records; Step 2: According to the geological data and hydro-meteorological data of the slope area corresponding to each rock mass unit, the expansion potential energy of the slope area corresponding to each rock mass unit at each time during the water absorption process is calculated; according to the expansion potential energy, the volume strain and the principal strain under isotropic conditions of the slope area corresponding to each rock mass unit at each time are calculated, and according to the volume strain and the principal strain, the effective stress of the slope area corresponding to each rock mass unit at each time is calculated, and then the mean of the effective stress at all times is calculated to obtain the mean output; then the variance of the effective stress at all times is calculated to obtain the variance output; Step 3: Input the mean output as input into the pre-trained deep learning autoencoder, combine it with the variance output, and output the latent variable; calculate the difference between the latent variable and the mean output, and compare the difference with the preset basic threshold to obtain the instability probability of the slope area corresponding to each rock mass unit; In step 1, the surface of the target slope is periodically scanned by a high-precision laser radar to obtain point cloud data; the method of segmenting the point cloud data to obtain multiple rock mass units includes: using the following formula, Adaptive filtering is performed on each point: ； in, For point Point cloud density at ; To search for points inside the sphere; is the radius of the search sphere; For point The distance to the nearest neighbor; is the standard deviation of the Gaussian distribution; For point The normal vector at ; is the laser radar line of sight direction vector; then use the following formula to determine the point Neighbors Belongs to a rock mass unit: ； in, is the judgment value, if , then the judgment point Its neighboring points in a rock mass unit; For point Its neighboring points The Euclidean distance of For point Neighbors The normal vector at ; For point Point cloud density at ; is the set angle threshold; is the set distance threshold; is the set density threshold.

2. The slope stability prediction method based on deep learning according to claim 1, characterized in that: The geological data of the slope area corresponding to each rock unit obtained in step 1 include: rock dry density, rock and soil average particle size, water content, expansion pressure, water density, rock and soil mineral hydration heat, rock elastic modulus, Poisson's ratio, cohesion, internal friction angle, montmorillonite content and quartz content; the rock elastic modulus is measured by collecting rock samples from each rock unit and performing a uniaxial compression test on the rock samples; the cohesion and internal friction angle are measured by collecting rock samples from each rock unit and performing a direct shear test on the rock samples; the Poisson's ratio represents the lateral deformation ratio in another direction when the rock sample is stretched or compressed in one direction.

3. The slope stability prediction method based on deep learning according to claim 2, characterized in that: The hydrological and meteorological data of the slope area corresponding to each rock mass unit obtained in step 1 include: infiltration rate, rainfall and temperature.

4. The slope stability prediction method based on deep learning according to claim 1, characterized in that: In step 2, the expansion potential energy of each rock unit during water absorption at each time is calculated according to the geological data and hydrological and meteorological data of each rock unit by the following formula: ； in, For the The rock mass unit The expansion potential energy during the water absorption process over time; For the The dry density of rock mass in the slope area corresponding to each rock mass unit; For the The average particle size of rock and soil in the slope area corresponding to each rock mass unit; For the The water content of the slope area corresponding to each rock mass unit; For the The expansion pressure of the slope area corresponding to each rock mass unit; For the The bulk density of water in the slope area corresponding to each rock mass unit; For the The hydration heat of rock and soil minerals in the slope area corresponding to each rock mass unit; For the The average height of the slope area corresponding to each rock mass unit; For the The rock mass elastic modulus of the slope area corresponding to each rock mass unit; For the Poisson's ratio of the slope area corresponding to each rock mass unit; For the The cohesion of the slope area corresponding to each rock mass unit; For the The internal friction angle of the slope area corresponding to each rock mass unit; For the The montmorillonite content of the slope area corresponding to each rock mass unit; For the Quartz content of the slope area corresponding to each rock mass unit; is the gas constant; is the absolute temperature; for The temperature of time; for rainfall over time; for The penetration rate over time.

5. The slope stability prediction method based on deep learning according to claim 4, characterized in that: In step 2, the volume strain of the slope area corresponding to each rock mass unit at each time and the principal strain under isotropic conditions are calculated according to the expansion potential energy using the following formula: ； in, For the The volume of a rock mass unit; is the volume strain; under the isotropic conditions, the three principal strains are equal, and the calculation formula is: ； in, , and Take the initiative to respond.

6. The slope stability prediction method based on deep learning according to claim 5, characterized in that: In step 2, the effective stress of the slope area corresponding to each rock mass unit at each time is calculated by the following formula: ； in, For the The slope area corresponding to the rock mass unit is Effective stress of time.

7. The slope stability prediction method based on deep learning according to claim 6, characterized in that: In step 3, the mean output is input as the input to the pre-trained deep learning autoencoder. The process of outputting the latent variable specifically includes: assuming that the mean output is ; The mean output is encoded using the following formula: ； in, is the encoding result; is the mean distribution function; is the logarithmic variance distribution function; ;in, is the number of characteristic expansions in the past, and its value is equal to the target slope as the center, with the setting The value is the radius, the number of landslides that occurred in the circular area; ; The variance of the effective stress at all times is ; represents a normal distribution with a mean of 0 and a variance of 1; the encoded result is then input into a single-layer deep learning network to output the latent variable ; is the variance output; It is Hadamard.

8. The slope stability prediction method based on deep learning according to claim 7, characterized in that: In step 3, the latent variables are calculated using the following formula: ； in, Representation calculation The maximum value of Represents the activation function.

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