A method for analyzing safety state of rock slope under dry-wet and freeze-thaw coupling action

Abstract

The application provides a kind of dry-wet-freeze coupling under rock slope safety state analysis method, it is related to geotechnical engineering safety monitoring technical field.The specific steps include: collecting rock mass microseism, strain temperature, surface deformation and environmental temperature and humidity and rainfall data;Identify microseismic events and locate the source, build fracture network topology structure;Calculate dry-wet and freeze-thaw cycle damage degree and its nonlinear superposition damage component, get equivalent structure damage degree;Update material parameters with the damage degree, establish water-heat-force-damage coupling control equation set;Build physical information neural network, train with equation residual as physical constraint, monitoring data as driving, output displacement field and damage field and calculate safety coefficient space-time distribution field;Based on safety coefficient space-time distribution field, safety evaluation and early warning are carried out.The application realizes the precise quantification of dry-wet-freeze coupling damage and the real-time dynamic early warning of slope safety state.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering safety monitoring technology, specifically a method for analyzing the safety status of rock slopes under the coupled effects of dry-wet and freeze-thaw cycles. Background Technology

[0002] Currently, in the safety status analysis of rock slopes under the coupled effects of wet-dry and freeze-thaw cycles, the integration and utilization of multi-source monitoring data still suffers from significant fragmentation. Traditional methods typically process microseismic signals, strain-temperature data, and surface deformation information separately, lacking a systematic framework that unifies fracture network topology identification with the thermo-mechanical-damage multi-field coupled control equations. This limits the characterization of fracture development, moisture migration, and damage evolution within the slope to a single physical field level, making it difficult to reflect the true mechanism of rock mass strength degradation under the combined effects of wet-dry alternation and freeze-thaw cycles.

[0003] Existing studies mostly employ independent linear summation models, neglecting the nonlinear superposition effect resulting from the synergistic interaction of the two factors in time and space. When drastic changes in water content and temperature crossing the freezing point occur simultaneously, simply calculating the damage degree of each cycle separately and adding them together will severely underestimate the rock mass fracture propagation rate and strength decay rate, leading to a biased assessment of slope safety status. Furthermore, the lack of pre-calibrated nonlinear superposition components through indoor coupled experiments also makes damage quantification lack reliable parameter basis.

[0004] At the level of safety status early warning, existing technologies often use fixed early warning thresholds, which cannot be adaptively adjusted based on historical early warning performance and the confidence level of environmental forecasts. The combination of physical-driven models and data-driven models is often superficial, failing to construct a digital twin of the slope that can both satisfy the constraints of physical equations and respond in real time to changes in multi-source heterogeneous data. This results in untimely updates to reliability indicators, and the safety factor prediction trajectory is difficult to reflect the risk of sudden instability under complex environmental conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the safety status of rock slopes under the coupled effects of wet-dry and freeze-thaw cycles, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for analyzing the safety status of rock slopes under wet-dry and freeze-thaw coupling effects, comprising the following steps: S1: Collect slope monitoring data of the rock slope to be analyzed during the monitoring period. The slope monitoring data includes rock mass microseismic signals, internal rock mass strain data, internal rock mass temperature data, surface deformation data, environmental temperature and humidity data, and rainfall data. S2: Microseismic signals are used to identify microseismic events and locate seismic sources to determine the spatial distribution of microseismic events. Based on the spatial distribution of microseismic events, the fracture development area and fracture connectivity are determined, and the fracture network topology is constructed. S3: Determine wet-dry cycle events based on rainfall data and calculate wet-dry cycle damage degree; determine freeze-thaw cycle events based on temperature data and calculate freeze-thaw cycle damage degree; identify wet-dry cycle events and freeze-thaw cycle events that overlap in time as coupling events; calculate nonlinear superimposed damage components based on coupling events; determine the equivalent wet-dry-freeze-thaw coupling structural damage degree based on wet-dry cycle damage degree, freeze-thaw cycle damage degree and nonlinear superimposed damage components. S4: The structural damage degree is used as a damage variable to update the material parameters of the rock mass of the rock slope to be analyzed, and the updated material parameters are obtained. Based on the fracture network topology, the updated material parameters, and strain and temperature data, a set of control equations for water-thermal-mechanical-damage coupling is established. S5: Construct a physical information neural network, and use the residuals of the partial differential equations corresponding to the control equations, the residuals of the initial conditions, and the residuals of the boundary conditions to form physical constraint loss terms. Use the surface deformation data and strain data to form data-driven loss terms. Train the physical information neural network to obtain the slope displacement field and damage field, and calculate the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field. S6: Based on the spatiotemporal distribution field of the slope safety factor, conduct a safety assessment of the rock slope to be analyzed and output the assessment results.

[0007] Furthermore, the specific logic for constructing the fracture network topology is as follows: The acquired microseismic signals are filtered and denoised to remove environmental noise interference signals and retain valid microseismic event signals. The sources of the valid microseismic events are located, and a time-difference positioning algorithm is used to calculate the coordinates of each microseismic event in the three-dimensional space of the slope. The spatial coordinates of all microseismic events are projected onto the slope monitoring profile to obtain a planar distribution map of the microseismic events. Based on the planar distribution map, a density clustering algorithm is used to identify densely populated areas of microseismic events, which are then identified as fracture development areas. The boundary contours of each fracture development area are extracted, and the spatial distance between adjacent fracture development areas is calculated. If the spatial distance between adjacent fracture development areas is less than a preset connectivity threshold, a fracture connectivity relationship is determined between them. A fracture network topology is constructed using each fracture development area as a node and the fracture connectivity relationship as an edge.

[0008] Furthermore, the specific method for determining wet-dry cycle events and calculating the wet-dry cycle damage degree based on rainfall data is as follows: According to rainfall data, the number of wet-dry cycles experienced by the slope rock mass within the monitoring period is counted. A complete wet-dry cycle is defined as the process of soil moisture content rising from a dry state to a saturated state and then falling back to a dry state. For each wet-dry cycle, the maximum and minimum moisture contents during the cycle are extracted, and the difference between the two is calculated as the moisture content change range of that cycle. Based on the moisture content change range, the corresponding single-cycle damage increment is retrieved from the preset wet-dry cycle fatigue curve. This wet-dry cycle fatigue curve is pre-calibrated through indoor rock sample wet-dry cycle tests. The single-cycle damage increments of all wet-dry cycles within the monitoring period are accumulated to obtain the cumulative wet-dry cycle damage degree, which is used as the wet-dry cycle damage degree.

[0009] Furthermore, the specific method for determining freeze-thaw cycle events and calculating freeze-thaw cycle damage based on temperature data is as follows: Based on temperature data, the number of freeze-thaw cycles experienced by the slope rock mass within the monitoring period is counted. A complete freeze-thaw cycle is defined as the process of the rock mass temperature dropping from above the freezing point to below the freezing point and then rising back above the freezing point. For each freeze-thaw cycle, the lowest and highest temperatures during the cycle are extracted, and the absolute value of the difference between the lowest temperature and the freezing point is calculated as the freezing depth index for that cycle. Based on the freezing depth index, the corresponding single freeze-thaw damage increment is retrieved from the preset freeze-thaw cycle damage curve. This freeze-thaw cycle damage curve is pre-calibrated through indoor rock sample freeze-thaw cycle tests. The single freeze-thaw damage increments of all freeze-thaw cycles within the monitoring period are accumulated to obtain the cumulative freeze-thaw cycle damage degree, which is used as the freeze-thaw cycle damage degree.

[0010] Furthermore, the specific method for calculating the nonlinear superimposed damage component based on the coupled events is as follows: identify wet-dry cycle and freeze-thaw cycle events that overlap in time; determine events in which drastic changes in water content and temperature crossing the freezing point occur simultaneously within the same time period as coupled events; for each coupled event, extract the water content change amplitude and freezing depth indices during the event; retrieve the corresponding single-cycle damage increment from the wet-dry cycle fatigue curve and the freeze-thaw cycle damage curve, respectively; calculate the product of the wet-dry cycle damage increment and the freeze-thaw cycle damage increment in the coupled event; multiply this product by a preset coupling strengthening coefficient as the nonlinear superimposed damage increment of the coupled event; this coupling strengthening coefficient is pre-calibrated through indoor wet-dry-freeze-thaw coupled cycle tests on rock samples; accumulate the nonlinear superimposed damage increments of all coupled events within the monitoring period to obtain the nonlinear superimposed damage component; and combine the wet-dry cycle damage degree, the freeze-thaw cycle damage degree, and the nonlinear superimposed damage component to obtain the equivalent wet-dry-freeze-thaw coupled structural damage degree.

[0011] Furthermore, the specific method for establishing the control equation set of water-thermal-mechanical-damage coupling is as follows: the equivalent dry-wet-freeze-thaw coupling structural damage degree is used as the damage variable, and the elastic modulus, cohesion and internal friction angle of the rock mass are reduced and corrected according to the damage variable to obtain the updated material parameters; based on the fracture network topology, the updated material parameters and the strain data and temperature data, the control equation set of water-thermal-mechanical-damage coupling is established. The control equation set includes a water migration equation describing the water transport law in the fracture-matrix dual medium, a heat conduction equation considering the influence of the latent heat of freeze-thaw phase change, a mechanical equilibrium equation coupling pore water pressure and rock mass deformation response, and a damage evolution equation reflecting the rock mass strength degradation law under cyclic loading.

[0012] Furthermore, the specific method for constructing the physical information neural network is as follows: A network input layer is constructed, which receives the slope spatial coordinates and environmental parameter vectors. The spatial coordinates contain three-dimensional spatial location information, and the environmental parameter vectors contain the current rainfall, ambient temperature, and soil moisture content. A physical constraint embedding layer is constructed, which transforms the water migration equation, heat conduction equation, mechanical equilibrium equation, and damage evolution equation established in S4 into corresponding partial differential equation residual terms, and transforms the initial conditions and boundary conditions into initial condition residual terms and boundary condition residual terms, respectively. These residual terms serve as physical constraint loss terms in network training. A data-driven supervision layer is constructed, which uses surface deformation data and rock mass strain data as supervision signals, compares them with the network prediction output, and generates data-driven loss terms. A network output layer is constructed, which outputs the predicted values ​​of the slope displacement field and damage field, and calculates the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field. The safety factor is determined according to the ratio of the slope's anti-sliding force to its sliding force.

[0013] Furthermore, the specific method for training the network using an adaptive loss function that dynamically adjusts weights based on the gradient statistical characteristics of each loss term is as follows: Calculate the gradient magnitudes of the physical constraint loss term, the data-driven loss term, and the boundary condition loss term in the current training round, respectively. Statistically calculate the relative proportions of the gradient magnitudes of each loss term. Identify the loss term with the largest gradient magnitude as the dominant loss term and the loss term with the smallest gradient magnitude as the weak loss term. Decrease the weight coefficient of the dominant loss term and increase the weight coefficient of the weak loss term to make the contribution of each loss term to the network parameter update more balanced. Multiply the adjusted weight coefficients of each loss term with the corresponding loss term and sum them to obtain the total loss function value for the current training round. Perform backpropagation based on the total loss function value to update the network parameters. Repeat the above gradient statistics and weight adjustment process until the network converges.

[0014] Furthermore, the specific method for conducting a safety assessment of the rock slope to be analyzed based on the spatiotemporal distribution field of the slope safety factor and outputting the assessment results is as follows: Based on the spatiotemporal distribution field of the slope safety factor, a digital twin of the slope is constructed by combining the slope displacement field and the damage field. The slope reliability index is corrected in real time using the Bayesian update method. The evolution trajectory of the safety factor within a preset time period is predicted using a long short-term memory network. The warning threshold is adaptively corrected based on the feedback of historical false alarm rate and the confidence of rainfall forecast. When the predicted safety factor is lower than the adaptively corrected warning threshold, a graded warning is triggered. The system analyzes past warning records across multiple warning periods, calculating the ratio of false alarms to total warnings as the historical false alarm rate. If the historical false alarm rate exceeds a preset upper threshold, the warning threshold is increased; if it falls below a preset lower threshold, the threshold is decreased. The system obtains the confidence level of future rainfall forecast data. If the confidence level is high, the warning threshold is significantly adjusted; if low, it is adjusted slightly. The historical false alarm rate correction and the rainfall forecast confidence level correction are combined to obtain the total warning threshold correction. An algebraic operation is performed between the base warning threshold and the total correction to obtain the adaptively adjusted warning threshold. Four warning threshold levels are set. The prediction safety factor is compared with each level. If the prediction safety factor is greater than the first warning threshold, no warning is triggered; if it is between the first and second thresholds, a blue warning is triggered; if between the second and third thresholds, a yellow warning is triggered; if between the third and fourth thresholds, an orange warning is triggered; and if less than the fourth threshold, a red warning is triggered.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention automatically identifies the fracture network topology using microseismic signals and establishes a fully coupled set of water-thermal-mechanical-damage control equations based on this. It incorporates water seepage, phase change heat conduction, skeletal mechanical response, and damage evolution within the fracture network into a unified solution framework, fundamentally overcoming the limitations of traditional multiphysics-based fragmented analysis. This method can accurately extract the connectivity relationships between different fracture development regions, quantitatively revealing the coupled driving mechanisms of water migration and temperature changes during wet-dry and freeze-thaw processes, providing strictly physical-consistent field inputs for subsequent damage calculations.

[0016] This invention explicitly proposes a method for calculating the damage degree of wet-dry cycle, the damage degree of freeze-thaw cycle, and the nonlinear superposition damage component of the two. By identifying coupled events and introducing a coupling strengthening coefficient calibrated by indoor experiments, the synergistic damage effect is accurately quantified. This approach overcomes the shortcomings of existing linear cumulative models, truly reflecting the accelerated damage phenomenon mutually induced by the change in water content and the freezing depth index in overlapping events. This allows the equivalent wet-dry-freeze-thaw coupled structural damage degree to more reliably reflect the actual process of rock mass strength degradation.

[0017] This invention constructs a physical information neural network and employs an adaptive loss function that dynamically adjusts weights based on gradient statistical properties. This ensures a balanced contribution of physical constraints and data-driven supervision during the training process, thereby accurately outputting the displacement and damage fields. Based on these fields, the spatiotemporal distribution of the slope safety factor is calculated. Furthermore, by combining Bayesian updates to correct reliability indices with long short-term memory network security factor prediction, and adaptively adjusting the early warning threshold using historical false alarm rates and rainfall forecast confidence, a complete closed loop is formed, from physical modeling and digital twin construction to tiered early warning. This significantly improves the real-time performance of slope safety status assessment and the accuracy of early warning. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 A bar chart comparing the damage components of the dry-wet-freeze-thaw coupled cycle provided in an embodiment of the present invention; Figure 3 The PINN adaptive weight convergence curve is provided for an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] Example: Please see Figures 1 to 3 The present invention provides a technical solution: A method for analyzing the safety status of rock slopes under wet-dry and freeze-thaw coupling effects, comprising the following steps: S1: Collect slope monitoring data of the rock slope to be analyzed during the monitoring period. The slope monitoring data includes rock mass microseismic signals, internal rock mass strain data, internal rock mass temperature data, surface deformation data, environmental temperature and humidity data, and rainfall data.

[0022] Under the coupled effects of wet-dry and freeze-thaw cycles, the internal damage evolution of rock slopes is a complex spatiotemporal process involving the coupling of multiple physical fields. Single-type monitoring data often only reflects the state information of a single aspect of the slope, making it difficult to comprehensively depict the overall damage development. Microseismic signals can capture the spatiotemporal distribution of micro-fracture events within the rock mass, serving as an effective means of identifying fracture initiation, propagation, and penetration; internal rock strain data directly reflects stress redistribution and structural deformation; temperature distribution data is a key characterization of the freeze-thaw phase transition process; surface deformation data provides macroscopic evidence of the overall slope deformation; and environmental temperature, humidity, and rainfall data serve as the external boundary conditions driving wet-dry and freeze-thaw cycles. These five types of data are interconnected in terms of physical mechanisms and complementary in terms of spatiotemporal scales, collectively constituting a multi-source heterogeneous data system describing the safety status of slopes.

[0023] In this embodiment, microseismic signals are acquired using an array of microseismic sensors deployed within the slope. The sensor density is determined based on the slope's rock mass integrity level, with a typical spacing of 10m to 30m. Strain and temperature distribution data within the rock mass are obtained from fiber optic grating sensor strings embedded in boreholes, with strain measurement accuracy no less than 1με and temperature measurement accuracy no less than 0.1℃. Surface deformation data is acquired jointly using GNSS displacement monitoring stations deployed on the slope surface and InSAR remote sensing technology. The GNSS monitoring frequency is no less than once per hour, and the InSAR image revisit period is no more than 12 days. Environmental temperature and humidity data are collected by automatic weather stations, and rainfall data is recorded by tipping bucket rain gauges, with a time resolution no less than 1 hour. All monitoring data are aggregated to a data center via a wireless transmission network, where time synchronization and quality control are performed before subsequent analysis.

[0024] Please refer to Table 1. This embodiment presents the test results of the basic physical and mechanical properties of three sets of rock samples taken from the slope engineering site. Standard cylindrical specimens (50 mm in diameter and 100 mm in height) were prepared and tested according to the "Standard for Test Methods of Engineering Rock Mass" (GB / T 50266).

[0025] Table 1: Test Data of Basic Physical and Mechanical Properties of Rock Samples As shown in Table 1, the average density of the sandstone group (YS-01 to YS-04) is 2651. The porosity is 8.5%, the uniaxial compressive strength is 85.4 MPa, the longitudinal wave velocity is 4199 m / s, and the mechanical properties are relatively homogeneous with a coefficient of variation of less than 2%. The average density of the mudstone group (YS-05 to YS-08) is 2380. The porosity is 15.2%, the uniaxial compressive strength is 45.3 MPa, the longitudinal wave velocity is 3100 m / s, and the cohesion (8.2 MPa) and internal friction angle (32°) are significantly lower than those of sandstone; the average density of the limestone group (YS-09 to YS-12) is 2710 N·m⁻². With a porosity of only 5.8%, a uniaxial compressive strength as high as 112.5 MPa, and a longitudinal wave velocity of 5200 m / s, mudstone represents dense hard rock. The three lithologies exhibit significant gradient differences in pore structure, water-bearing characteristics, and mechanical strength. Mudstone's porosity is approximately 1.8 times that of sandstone and 2.6 times that of limestone, while its uniaxial compressive strength is only 53% of that of sandstone and 40% of that of limestone. This indicates that mudstone is the most sensitive to water-thermal coupling, while limestone is the weakest. Subsequent damage calibration tests will be conducted separately for each of the three lithologies to cover the typical range of slope rock mass integrity levels.

[0026] S2: Microseismic signals are used to identify microseismic events and locate seismic sources to determine the spatial distribution of microseismic events. Based on the spatial distribution of microseismic events, the fracture development area and fracture connectivity are determined, and a fracture network topology is constructed.

[0027] Microseismic events are the acoustic manifestations of energy release within rock masses, and their spatiotemporal distribution contains rich information about fracture development. By analyzing the arrival time, amplitude, and waveform characteristics of microseismic signals, the source location and energy magnitude of microseismic events can be inverted, thereby tracing the initiation location, propagation path, and penetration trend of fractures. Transforming discretely distributed microseismic events into a continuous fracture network topology is a key step in achieving spatial characterization of damage within rock masses. Simultaneously, internal rock mass strain data reflects the deformation response caused by stress field adjustments, and temperature distribution data records the thermodynamic process of freeze-thaw phase transitions. These two factors, together with the fracture network, constitute the physical basis of the water-thermal-mechanical-damage coupling problem. This fracture network topology, internal rock mass strain data, and temperature distribution data will be used in subsequent steps to establish the coupled governing equations.

[0028] Furthermore, the specific logic for constructing the fracture network topology is as follows: The acquired microseismic signals are filtered and denoised to remove environmental noise interference signals and retain valid microseismic event signals. The sources of the valid microseismic events are located, and a time-difference positioning algorithm is used to calculate the coordinates of each microseismic event in the three-dimensional space of the slope. The spatial coordinates of all microseismic events are projected onto the slope monitoring profile to obtain a planar distribution map of the microseismic events. Based on the planar distribution map, a density clustering algorithm is used to identify densely populated areas of microseismic events, which are then identified as fracture development areas. The boundary contours of each fracture development area are extracted, and the spatial distance between adjacent fracture development areas is calculated. If the spatial distance between adjacent fracture development areas is less than a preset connectivity threshold, a fracture connectivity relationship is determined between them. A fracture network topology is constructed using each fracture development area as a node and the fracture connectivity relationship as an edge.

[0029] The acquired microseismic signals were filtered and denoised to remove environmental noise interference and retain valid microseismic event signals. A bandpass filter was used for filtering, with the passband frequency range determined based on the rock mass wave velocity characteristics, typically from 50Hz to 500Hz. Source location was performed on the valid microseismic event signals, and a time-difference positioning algorithm was used to calculate the coordinates of each microseismic event in the three-dimensional space of the slope.

[0030] The basic principle of the time difference positioning algorithm is as follows. Assume that the slope is equipped with... A micro-vibration sensor, sensor The coordinates are , For the first A microseismic event, with focal coordinates as follows: The time of the earthquake was Micro-seismic waves propagate from the seismic source to the sensor. The time is ,satisfy: in The longitudinal wave velocity of the rock mass is expressed in m / s. For any two sensors... and Its time difference is: The location of the earthquake source is determined by minimizing the objective function. in and The distance from the seismic source to the sensor is calculated based on the current estimated source coordinates. The Levenberg-Marquardt iterative algorithm is used to solve the above nonlinear least squares problem, with the iteration convergence threshold set to [value missing]. .

[0031] The spatial coordinates of all microseismic events are projected onto the slope monitoring profile to obtain a planar distribution map of the microseismic events. The projection direction is determined according to the main sliding direction of the slope, and generally a vertical profile parallel to the slope dip is selected as the projection plane.

[0032] Based on the planar distribution map of microseismic events, a density clustering algorithm is used to identify densely populated areas of microseismic events. This embodiment employs the DBSCAN density clustering algorithm, setting a neighborhood radius. For distances from 5m to 15m, the minimum number of points within the neighborhood. The value is 3 to 5. Areas with dense microseismic events are identified as fracture-developed regions, and the boundary contours of each fracture-developed region are extracted. Boundary contour extraction uses... - Shape algorithm, The value is determined based on the spatial distribution density of microseismic events, and is generally taken as the neighborhood radius. 0.5 to 1.0 times.

[0033] Calculate the spatial distance between adjacent fracture-developed regions. Let the fracture-developed regions be... The boundary contour point set is , fracture development region The boundary contour point set is The minimum spatial distance between the two regions is in This represents the Euclidean distance. If the spatial distance between adjacent fracture development regions is less than a preset connectivity threshold... If the condition is met, then a gap connectivity relationship is determined to exist between the two. Connectivity threshold. The value is determined based on the statistical characteristics of rock mass joint spacing, and is generally taken as 0.5 to 1.5 times the average joint spacing of the rock mass, with a typical range of 0.3m to 2.0m.

[0034] A fracture network topology is constructed, with each fracture development region as a node and fracture connectivity relationships as edges. The fracture network is represented as an undirected graph. ,in This is a set of nodes in a fracture development region. Let be a set of connected edges. This represents the number of regions with fracture development.

[0035] S3: Determine wet-dry cycle events based on rainfall data and calculate wet-dry cycle damage degree; determine freeze-thaw cycle events based on temperature data and calculate freeze-thaw cycle damage degree; identify wet-dry cycle events and freeze-thaw cycle events that overlap in time as coupling events; calculate nonlinear superimposed damage components based on coupling events; and determine the equivalent wet-dry-freeze-thaw coupling structural damage degree based on wet-dry cycle damage degree, freeze-thaw cycle damage degree, and nonlinear superimposed damage components.

[0036] Wet-dry cycles and freeze-thaw cycles are two major environmental processes driving the deterioration of rock slopes. Wet-dry cycles, through the periodic entry and exit of water into the rock mass, cause mineral expansion and contraction, cement dissolution, and changes in pore structure. Freeze-thaw cycles, through the frost heave force and thaw settlement caused by pore water phase change, directly lead to crack propagation and rock mass strength reduction. These two types of cycles may overlap in time and influence each other spatially; their damage effects are not simply additive but exhibit a significant synergistic enhancement effect. Therefore, quantifying the independent damage contributions of each type of cycle and identifying the additional damage increment generated by their coupling effect is crucial for accurately assessing the slope's safety status. The equivalent wet-dry / freeze-thaw coupled structural damage degree unifies and integrates the above three types of damage components, serving as a comprehensive indicator characterizing the overall deterioration degree of the rock mass under wet-dry / freeze-thaw coupled conditions.

[0037] Furthermore, the specific method for determining wet-dry cycle events and calculating the wet-dry cycle damage degree based on rainfall data is as follows: According to rainfall data, the number of wet-dry cycles experienced by the slope rock mass within the monitoring period is counted. A complete wet-dry cycle is defined as the process of soil moisture content rising from a dry state to a saturated state and then falling back to a dry state. For each wet-dry cycle, the maximum and minimum moisture contents during the cycle are extracted, and the difference between the two is calculated as the moisture content change range of that cycle. Based on the moisture content change range, the corresponding single-cycle damage increment is retrieved from the preset wet-dry cycle fatigue curve. This wet-dry cycle fatigue curve is pre-calibrated through indoor rock sample wet-dry cycle tests. The single-cycle damage increments of all wet-dry cycles within the monitoring period are accumulated to obtain the cumulative wet-dry cycle damage degree, which is used as the wet-dry cycle damage degree.

[0038] Based on rainfall data, the number of wet-dry cycles experienced by the slope rock mass during the monitoring period was counted. A complete wet-dry cycle was defined as the process of soil moisture content rising from a dry state to a saturated state and then falling back to a dry state. The criterion for determining the dry state was the soil moisture content. The criterion for determining saturation is soil moisture content. ,in This represents the saturated moisture content.

[0039] For each wet-dry cycle, extract the maximum moisture content during the cycle. With minimum moisture content The difference between the two values ​​is calculated as the magnitude of the moisture content change in this cycle. Based on the change in moisture content, the corresponding damage increment per cycle is retrieved from the preset wet-dry cycle fatigue curve. The wet-dry cycle fatigue curve was pre-calibrated using indoor rock sample wet-dry cycle tests. The calibration method is as follows: Several sets of standard rock samples with the same lithology as the slope rock mass were prepared. Wet-dry cycle tests with different moisture content variations were conducted in a temperature and humidity controlled environment chamber. After each cycle, the longitudinal wave velocity of the rock sample was measured. With uniaxial compressive strength With wave speed ratio or strength ratio The attenuation rate is used as a damage metric to establish a curve relating the change in water content to the damage increment per cycle. The curve is typically fitted using a power function. in and For fitting parameters, The typical range of values ​​is to , The typical value range is from 1.0 to 2.5.

[0040] All during the monitoring period The damage increments from each wet-dry cycle are accumulated to obtain the cumulative damage degree of the wet-dry cycle. As the degree of damage from the dry and wet cycle.

[0041] Furthermore, the specific method for determining freeze-thaw cycle events and calculating freeze-thaw cycle damage based on temperature data is as follows: Based on temperature data, the number of freeze-thaw cycles experienced by the slope rock mass within the monitoring period is counted. A complete freeze-thaw cycle is defined as the process of the rock mass temperature dropping from above the freezing point to below the freezing point and then rising back above the freezing point. For each freeze-thaw cycle, the lowest and highest temperatures during the cycle are extracted, and the absolute value of the difference between the lowest temperature and the freezing point is calculated as the freezing depth index for that cycle. Based on the freezing depth index, the corresponding single freeze-thaw damage increment is retrieved from the preset freeze-thaw cycle damage curve. This freeze-thaw cycle damage curve is pre-calibrated through indoor rock sample freeze-thaw cycle tests. The single freeze-thaw damage increments of all freeze-thaw cycles within the monitoring period are accumulated to obtain the cumulative freeze-thaw cycle damage degree, which is used as the freeze-thaw cycle damage degree.

[0042] Based on temperature data, the number of freeze-thaw cycles experienced by the slope rock mass within the monitoring period was counted. A complete freeze-thaw cycle was defined as the process in which the rock mass temperature dropped from above freezing point to below freezing point and then rose back above freezing point. Specifically, the criterion was that the temperature... Descending to It rose again to ,in This is the freezing point temperature, with a value of 273.15K. The temperature threshold, ranging from 1K to 3K, is used to eliminate false freeze-thaw cycle counts caused by temperature measurement noise.

[0043] For each freeze-thaw cycle, the lowest temperature during the cycle is extracted. With the highest temperature The absolute value of the difference between the lowest temperature and the freezing point is calculated as the freezing depth index for that cycle. The freezing depth index reflects the degree of sub-zero temperature experienced by the rock mass during a single freeze-thaw cycle; the lower the sub-zero temperature and the longer the duration, the more severe the frost heave damage. Based on the freezing depth index, the corresponding single freeze-thaw damage increment is retrieved from the preset freeze-thaw cycle damage curve. The freeze-thaw cycle damage curve was also pre-calibrated using indoor rock sample freeze-thaw cycle tests. The calibration method was similar to that for the wet-dry cycle fatigue curve. A correlation was established between the freezing depth index and the damage increment in a single freeze-thaw cycle, and the curve was fitted using an exponential function. in and For fitting parameters, The typical range of values ​​is to , The typical value range is 0.05 to 0.2K. - ¹.

[0044] All during the monitoring period The incremental damage from each freeze-thaw cycle is accumulated to obtain the cumulative damage degree of the freeze-thaw cycle. The degree of damage from the freeze-thaw cycle is referred to as the degree of damage.

[0045] Furthermore, the specific method for calculating the nonlinear superimposed damage component based on the coupled events is as follows: identify wet-dry cycle and freeze-thaw cycle events that overlap in time; determine events in which drastic changes in water content and temperature crossing the freezing point occur simultaneously within the same time period as coupled events; for each coupled event, extract the water content change amplitude and freezing depth indices during the event; retrieve the corresponding single-cycle damage increment from the wet-dry cycle fatigue curve and the freeze-thaw cycle damage curve, respectively; calculate the product of the wet-dry cycle damage increment and the freeze-thaw cycle damage increment in the coupled event; multiply this product by a preset coupling strengthening coefficient as the nonlinear superimposed damage increment of the coupled event; this coupling strengthening coefficient is pre-calibrated through indoor wet-dry-freeze-thaw coupled cycle tests on rock samples; accumulate the nonlinear superimposed damage increments of all coupled events within the monitoring period to obtain the nonlinear superimposed damage component; and combine the wet-dry cycle damage degree, the freeze-thaw cycle damage degree, and the nonlinear superimposed damage component to obtain the equivalent wet-dry-freeze-thaw coupled structural damage degree.

[0046] Identify overlapping wet-dry cycles and freeze-thaw cycles in time. Events involving simultaneous drastic changes in moisture content and temperature crossing the freezing point within the same time period are classified as coupled events. Specifically, the criterion is that for the first... The second wet-dry cycle and the first In a freeze-thaw cycle, if the time intervals of the two cycles intersect, and both conditions are met simultaneously within that intersecting time period... and If so, it is determined to be a coupling event.

[0047] For each coupled event, extract the magnitude of the water content change during that event. With freeze depth index The corresponding single-cycle damage increment was retrieved from the wet-dry cycle fatigue curve and the freeze-thaw cycle damage curve, respectively. and Calculate the product of the damage increment from the wet-dry cycle and the damage increment from the freeze-thaw cycle in this coupled event, and then multiply this product by a preset coupling enhancement coefficient. The product of these is used as the nonlinear superposition damage increment of the coupled event. Coupling strengthening coefficient Pre-calibration was performed using indoor wet-dry / freeze-thaw coupled cyclic tests on rock samples. The calibration method involved preparing standard rock samples with the same lithology as the slope rock mass. Coupled tests of moisture content change and temperature cycling were conducted simultaneously in a controlled environment chamber. Damage evolution curves of the rock samples under coupled conditions were recorded and compared with damage curves under individual wet-dry and freeze-thaw cycles. The damage acceleration effect was then determined based on these results. . The typical value ranges from 5 to 20, with the specific value depending on the mineral composition and pore structure characteristics of the rock mass. For soft rocks containing a large amount of clay minerals, The value is too large; for dense hard rock, The value is too small.

[0048] Please refer to Table 2. This embodiment compares the differences in damage evolution of three types of lithology under single-cycle linear superposition and coupled-cycle conditions.

[0049] Table 2: Data from Dry-Wet / Freeze-Thaw Coupled Cyclic Damage Calibration Tests Table 2 shows that, in the sandstone group (YS-C-01 to YS-C-04), the linear superposition damage of YS-C-01 after 20 individual wet-dry and freeze-thaw cycles is as follows: The total damage measured in the coupled test under the same conditions reached Exceeding the linear superposition value , calculated in reverse YS-C-02 has a larger variation in moisture content ( ), Increased to 15.6. Ten short-cycle coupling tests (YS-C-03, YS-C-04) The values ​​were 14.2 and 13.9 respectively, with an average of 14.1 for the four sandstone groups. The mudstone groups (YS-C-05 and YS-C-06) exhibited a more significant coupled strengthening effect due to their high porosity (15.2%) and high water content (18.6%). YS-C-05 showed a higher value. The damage amplification factor of YS-C-06 after 10 cycles was 16.5, higher than that of the sandstone group, confirming the pattern that soft rocks containing clay minerals tend to have a larger coupled damage amplification factor. The limestone group (YS-C-07), due to its dense and low-porosity (5.8%) formation, had relatively small individual cycle damage, resulting in a larger total damage in the coupled test. Only slightly higher than the linear superposition value , The value was the lowest among the three lithologies, verifying the weak coupling strengthening effect of dense hard rocks. If a linear cumulative model is uniformly adopted, sandstone will underestimate the damage by 34% to 42%, mudstone by 38% to 48%, and limestone by 20%, resulting in a significantly biased safety assessment of mudstone and sandstone slopes towards danger.

[0050] Please see Figure 2 This embodiment shows a comparison of the damage components of four groups of sandstone samples under single-cycle and coupled-cycle conditions. From left to right, each group represents: cumulative damage under single wet-dry cycle conditions. Cumulative damage from individual freeze-thaw cycles Linear superposition value Measured total damage degree from coupling test Taking YS-C-01 as an example, , The linear superposition value is The measured coupling value is as high as Nonlinear superposition of damage components Corresponding coupling strengthening coefficient YS-C-02 has a larger variation in moisture content ( ), Increase to , Ten short-period coupling experiments (YS-C-03, YS-C-04) The scores were 14.2 and 13.9 respectively, with a mean of 14.1 for all four groups. Figure 2 The height difference between the red column and the diagonally filled column visually demonstrates the existence of nonlinear superimposed damage components, verifying the damage acceleration effect under the coupling of wet-dry and freeze-thaw cycles. If a traditional linear accumulation model is used, the actual damage will be underestimated by approximately 34% to 42%, leading to a slope safety assessment that is biased towards danger.

[0051] All during the monitoring period The nonlinear superposition damage increments of each coupled event are accumulated to obtain the nonlinear superposition damage component. in This is the set of indices for all coupled events.

[0052] Combining the above three types of damage components, the equivalent dry-wet-freeze-thaw coupled structural damage degree Defined as The equivalent damage value ranges from 0 to 1. This indicates that the rock mass is undamaged. This indicates that the rock mass has completely lost its bearing capacity; the degree of structural damage will be used as a damage variable input to the next step to update the rock mass material parameters and establish a set of water-thermal-mechanical-damage coupled control equations.

[0053] S4: The structural damage degree is used as a damage variable to update the material parameters of the rock mass of the rock slope to be analyzed. The updated material parameters are obtained. Based on the fracture network topology, the updated material parameters, and strain and temperature data, a set of control equations for water-thermal-mechanical-damage coupling is established.

[0054] The obtained equivalent dry-wet-freeze-thaw coupling structural damage degree As a damage variable, the elastic modulus reduction formula is used. , cohesion reduction formula and the formula for correcting the internal friction angle Update the rock mass elastic modulus, cohesion, and internal friction angle, among which... , , The initial material parameters of the rock samples are shown in Table 1. The updated material parameters are fed back into the rock mass mechanical response calculation in real time to reflect the rock mass stiffness degradation and strength reduction caused by structural damage.

[0055] Based on the fracture network topology constructed in the preceding steps, the updated material parameters, and the collected strain and temperature data, a set of water-thermal-mechanical-damage coupled control equations was established. This set of control equations includes a water migration equation describing the water transport law in the fracture-matrix dual-medium system, a heat conduction equation considering the latent heat of freeze-thaw phase change, a mechanical equilibrium equation coupling pore water pressure and rock mass deformation response, and a damage evolution equation reflecting the rock mass strength degradation law under cyclic loading.

[0056] A moisture migration equation was established. This equation employs the governing equations describing seepage in an unsaturated fracture-matrix dual-medium medium. In the fracture network, moisture flow follows the cubic law, and the fracture... seepage velocity satisfy: in For cracks The equivalent hydraulic opening, in meters; The dynamic viscosity of water is expressed in Pa·s. For cracks The pore water pressure in the fracture is expressed in Pa. The equivalent hydraulic aperture of the fracture is... With fracture mechanical aperture The relationship is: in The effective normal stress on the fracture surface is expressed in Pa. The reference stress is set to a value of [value to be filled in]. Pa.

[0057] In the matrix rock mass, water diffusion is described using a capillary permeation model, and the matrix water content is... The evolution satisfies: in is the hydraulic diffusion coefficient of the matrix, in m² / s; is the unsaturated hydraulic conductivity of the matrix, in m / s; The coordinates are vertically upwards. and All are described using the van Genuchten model: in is the saturated hydraulic conductivity, in m / s; This represents the saturated moisture content. Residual moisture content; It is the reciprocal of the intake air value, in meters (m). - ¹; , This is the aperture distribution index.

[0058] Moisture exchange between fractures and the matrix is ​​achieved through source-sink coupling, with each node in the fracture network... Water exchange capacity for: in To the fracture node Adjacent matrix unit sets; The fracture-matrix exchange coefficient is expressed in m / (Pa·s). The exchange area is expressed in m². matrix unit The pore water pressure is expressed in Pa.

[0059] A heat conduction equation is established. This equation, based on the classical heat conduction equation, incorporates the equivalent heat capacity method to handle the latent heat of freeze-thaw phase transition. Rock mass temperature field. The governing equations are: in This represents the density of the rock mass, expressed in kg / m³. This is the equivalent specific heat capacity, expressed in J / (kg·K). Equivalent thermal conductivity, in units of W / (m·K); The latent heat of phase change of water is taken as a value. J / kg; This is the density of water, expressed in kg / m³. This represents the volumetric water content of ice in the rock mass. This refers to heat source items, including external heat inputs such as solar radiation and geothermal energy.

[0060] The equivalent heat capacity method converts the latent heat of phase change into a change in equivalent heat capacity, namely equivalent specific heat capacity. Based on the current temperature and freezing point temperature The relative relationships are determined segment by segment: in Specific heat capacity of the rock skeleton, expressed in J / (kg·K); The specific heat capacity of water is taken as 4186 J / (kg·K); The specific heat capacity of ice is 2108 J / (kg·K); This refers to the volumetric water content of liquid water. This refers to the volumetric water content of ice. The half-width of the phase transition temperature range, typically taken as 0.5K to 2.0K. Equivalent thermal conductivity. Similarly, a piecewise function is used to describe it: in The thermal conductivity of the rock skeleton is expressed in W / (m·K). The thermal conductivity of water is taken as 0.6 W / (m·K); The thermal conductivity of ice is 2.2 W / (m·K); The porosity is the density of the rock mass.

[0061] A mechanical equilibrium equation is established. This equation employs the consolidation theory coupled with pore water pressure to express the total stress in the rock mass. Decomposed into effective stress With pore water pressure Two parts: in Using Kronecker notation. Effective stress causes elastic and plastic deformation of the rock mass; the elastic constitutive relation adopts the generalized Hooke's law: in It is the elastic stiffness tensor; This represents the elastic strain tensor. Plastic deformation is assessed using the Drucker-Prager yield criterion. in It is the second invariant of stress deviator; It is the first invariant of stress; and The relationship between the Drucker-Prager parameters and the Mohr-Coulomb intensity parameters is as follows: in Cohesion, measured in Pa; The internal friction angle is expressed in degrees.

[0062] Pore ​​water pressure affects rock mass stability through seepage force via fracture network; seepage force is a volume force. In the crack The components in are: in The acceleration due to gravity is taken as 9.8 m / s². For cracks The water head in the figure is measured in meters (m).

[0063] A damage evolution equation is established. This equation uses statistical distributions to describe the rock mass strength degradation process, taking the Weibull probability distribution of the rock mass element strength as the basis for the evolution of damage variables. Damage variables Defined as: in For equivalent strain; The scaling parameter of the Weibull distribution; Let be the shape parameter of the Weibull distribution. The growth rate of the damage variable is positively correlated with the equivalent stress level and the number of cyclic loading cycles. The damage evolution rate equation is: in This is the equivalent stress, in Pa. This represents the uniaxial compressive strength of the rock mass, expressed in Pa. This represents the number of times the loop will load. Damage rate coefficient, in seconds. - ¹; It is a stress sensitivity index; The damage deceleration index; The cyclic damage index is used. All the above parameters were calibrated through indoor rock sample mechanical tests. The typical range of values ​​is to s- ¹, The typical value range is 2 to 5. The typical value range is from 0.5 to 2.0. The typical value range is from 0.3 to 1.0.

[0064] The coupled control equations established based on the updated material parameters are embedded as physical constraints in the physical information neural network of the next step.

[0065] S5: Construct a physical information neural network, using the residuals of the partial differential equations corresponding to the control equations, the residuals of the initial conditions, and the residuals of the boundary conditions as physical constraint loss terms, and the surface deformation data and strain data as data-driven loss terms. Train the physical information neural network to obtain the slope displacement field and damage field, and calculate the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field.

[0066] The Physics-Informed Neural Network (PINN) embeds the physical constraints of the control partial differential equations into the loss function of the neural network, enabling the network's predictions to not only fit the observed data but also satisfy the underlying physical laws. Compared to traditional purely data-driven neural networks, PINN exhibits stronger generalization ability and physical consistency in scenarios with sparse or noisy monitoring data. For problems involving complex multi-physics coupling, such as rock slopes, PINN can utilize known physical laws (moisture migration, heat conduction, mechanical equilibrium, damage evolution) to constrain the solution space, preventing the neural network from producing predictions that violate physical common sense. Simultaneously, multi-source heterogeneous monitoring data is used as a supervisory signal to ensure that the network predictions are consistent with actual observations. By dynamically balancing the weights of physical constraints and data fitting through an adaptive loss function, the contribution of each loss term tends to be balanced during network training, ultimately outputting the slope displacement field and damage field, and calculating the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field.

[0067] Furthermore, the specific method for constructing the physical information neural network is as follows: A network input layer is constructed, which receives the slope spatial coordinates and environmental parameter vectors. The spatial coordinates contain three-dimensional spatial location information, and the environmental parameter vectors contain the current rainfall, ambient temperature, and soil moisture content. A physical constraint embedding layer is constructed, which transforms the water migration equation, heat conduction equation, mechanical equilibrium equation, and damage evolution equation established in S4 into corresponding partial differential equation residual terms, and transforms the initial conditions and boundary conditions into initial condition residual terms and boundary condition residual terms, respectively. These residual terms serve as physical constraint loss terms in network training. A data-driven supervision layer is constructed, which uses surface deformation data and rock mass strain data as supervision signals, compares them with the network prediction output, and generates data-driven loss terms. A network output layer is constructed, which outputs the predicted values ​​of the slope displacement field and damage field, and calculates the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field. The safety factor is determined according to the ratio of the slope's anti-sliding force to its sliding force.

[0068] Construct the network input layer. This input layer receives the slope's spatial coordinates and environmental parameter vectors. The spatial coordinates contain three-dimensional spatial location information. ,in The horizontal coordinates are along the slope direction. The horizontal coordinates are along the slope's dip. The coordinates are vertically upwards, in meters (m). Environmental parameter vector. Including rainfall at the current moment Ambient temperature and soil moisture content ,Right now The total dimension of the network input layer is 6, that is... .

[0069] This embedding layer transforms the moisture migration equation, heat conduction equation, mechanical equilibrium equation, and damage evolution equation established in the previous step into corresponding partial differential equation residual terms. For the moisture migration equation, the residual is defined as follows: for For the heat conduction equation, the residual is defined. for For the equations of mechanical equilibrium, the residual is defined as follows: for in This is the total stress tensor; This is the vector of gravitational acceleration; This is the penetration force vector.

[0070] For the damage evolution equation, the residual is defined. for The initial conditions and boundary conditions are transformed into initial condition residual terms and boundary condition residual terms, respectively. Initial condition residual Defined as the deviation between the network's predicted value and the measured value at the initial time. in The vector of state variables predicted by the network includes displacement, temperature, water content, and damage variables; These are the observations at the initial time.

[0071] Boundary condition residuals These boundaries include four types: displacement boundaries, stress boundaries, temperature boundaries, and seepage boundaries. Let's take displacement boundaries as an example. in Spatial coordinates on the boundary; Let be the given boundary displacement function.

[0072] The aforementioned residual terms are used as physical constraint loss terms in network training, and the physical constraint loss... Defined as in , , , These are the weighting coefficients for the residuals of each physical equation; This is the calculation domain for the slope.

[0073] This monitoring layer uses surface deformation data and rock mass strain data as monitoring signals, compares them with the network prediction output, and generates a data-driven loss term. : in , These represent the number of monitoring points for strain and surface deformation, respectively. , These are the weighting coefficients for the corresponding data items.

[0074] Construct the network output layer. This output layer outputs the predicted values ​​of the slope displacement field. With damage field prediction value The spatiotemporal distribution field of the slope safety factor is calculated based on the displacement field and damage field. The safety factor is determined based on the ratio of the slope's anti-sliding force to its sliding force, and the calculation formula is as follows: in This is a potential slip surface; For effective cohesion, For the effective internal friction angle, and These are the material parameters updated based on structural damage in the previous step; The effective normal stress on the slip surface; This refers to the downward shear stress.

[0075] The network architecture employs a fully connected deep neural network with 8 to 12 hidden layers and 128 to 512 neurons per layer. The Swish function is used as the activation function. The network depth and width are determined based on the complexity of the slope computational domain and the amount of monitoring data. For slopes with complex crack development and a large amount of data, the network depth and width are appropriately increased.

[0076] Furthermore, the specific method for training the network using an adaptive loss function that dynamically adjusts weights based on the gradient statistical characteristics of each loss term is as follows: Calculate the gradient magnitudes of the physical constraint loss term, the data-driven loss term, and the boundary condition loss term in the current training round, respectively. Statistically calculate the relative proportions of the gradient magnitudes of each loss term. Identify the loss term with the largest gradient magnitude as the dominant loss term and the loss term with the smallest gradient magnitude as the weak loss term. Decrease the weight coefficient of the dominant loss term and increase the weight coefficient of the weak loss term to make the contribution of each loss term to the network parameter update more balanced. Multiply the adjusted weight coefficients of each loss term with the corresponding loss term and sum them to obtain the total loss function value for the current training round. Perform backpropagation based on the total loss function value to update the network parameters. Repeat the above gradient statistics and weight adjustment process until the network converges.

[0077] Calculate the physical constraint loss term separately Data-driven loss items and boundary condition loss term The gradient magnitude in the current training epoch. Let the network parameters be... Then the gradient of each loss term with respect to the network parameters is: Gradient magnitude is quantized using the L2 norm. Calculate the relative proportions of the gradient magnitudes of each loss term. Let the gradient magnitudes of the three loss terms in the current training epoch be... , , Calculate their relative proportions The loss term with the largest gradient magnitude is identified as the dominant loss term, and the loss term with the smallest gradient magnitude is identified as the weak loss term. Let... , The corresponding dominant loss term weight is The weight of the weak loss item is .

[0078] The weighting coefficients of the dominant loss term are reduced, while those of the weaker loss terms are increased, to balance the contribution of each loss term to the network parameter updates. The weight adjustment strategy employs an adaptive rule based on the inverse relationship between gradient magnitude and weight. in This represents the average gradient magnitude. The adjusted weights are then normalized. The total loss function value for the current training epoch is obtained by multiplying the adjusted weight coefficients of each loss term by their corresponding loss terms and then summing the results. Backpropagation is performed based on the total loss function value to update the network parameters. The Adam optimizer is used, and the initial learning rate is set to [value missing]. to The learning rate decay strategy uses cosine annealing, with a minimum learning rate of no less than [missing value]. .

[0079] Please refer to Table 3. This embodiment records the dynamic adjustment and convergence process of the adaptive loss function during the training of the physical information neural network.

[0080] Table 3: Convergence Data of Physical Information Neural Network Training Please see Figure 3 This embodiment shows the weight coefficient change curves corresponding to Table 3.

[0081] As shown in Table 3, in the initial rounds, The gradient magnitude is significantly higher than and As the dominant loss term, the system adjusts the weights based on gradient statistics. Prioritize increasing the contribution of data-driven items. At round 100, the losses of all three items reach the same order of magnitude. The weights were adjusted to (0.320, 0.380, 0.300); at round 500, the weights further converged to (0.350, 0.330, 0.320), and the total loss decreased to The validation set RMSE was simultaneously reduced to After round 1000, all loss items will be entered into... The level and weight fluctuated slightly around 0.33; by round 2000, all three losses had decreased. At the specified levels, gradient magnitude differences are less than 5%, weights are stable at (0.333, 0.334, 0.333), and the total loss is... After round 3000, the total loss and RMSE no longer decreased significantly, and the decrease was less than [a certain percentage] for 500 consecutive rounds. The network was determined to be converged, and the final validation set RMSE was [value missing]. This indicates that the adaptive mechanism has successfully achieved a balance between the contributions of physical constraints and data-driven supervision, and the network has good physical consistency and generalization ability.

[0082] Figure 3 The convergence process described above is visually illustrated: the physical constraint weight coefficient monotonically increases from 0.280 to 0.333, the data-driven weight coefficient monotonically decreases from 0.520 to 0.333, and the boundary condition weight coefficient monotonically increases from 0.200 to 0.333, ultimately converging to equilibrium. If the relative difference in gradient magnitude is less than 5%, the network is considered converged. Table 3 and Figure 3 Together, they verified that the adaptive loss function successfully achieved a balance between the contributions of physical constraints and data-driven supervision.

[0083] Repeat the gradient statistics and weight adjustment process described above until the network converges. The convergence criterion is that the decrease in the total loss function value over 500 consecutive training iterations is less than [a certain value]. Or the prediction error on the validation set no longer decreases.

[0084] S6: Based on the spatiotemporal distribution field of the slope safety factor, conduct a safety assessment of the rock slope to be analyzed and output the assessment results.

[0085] A digital twin is a real-time mapping and dynamic simulation model of a slope's physical entity in digital space. It integrates multi-source monitoring data, physical mechanism models, and artificial intelligence algorithms to achieve comprehensive perception, accurate diagnosis, and early warning of slope safety status. The spatiotemporal distribution field of the obtained slope safety factor, combined with the slope displacement and damage fields, serves as the core state variables of the digital twin, constructing a three-dimensional visualized digital mirror of the slope. Based on this, a Bayesian update method is used to incorporate the latest monitoring data into a priori reliability model, enabling real-time correction and uncertainty quantification of slope reliability indicators. Long Short-Term Memory (LSTM) networks, as time-series prediction models, can capture long-term dependencies in the safety factor time series, enabling prediction of the safety factor evolution trajectory within a preset future time period. The setting of the early warning threshold directly affects the sensitivity and reliability of the early warning system. Fixed thresholds are difficult to adapt to dynamic changes in slope status and uncertainties in the external environment. Therefore, two adaptive correction factors—historical false alarm rate feedback and rainfall forecast confidence—are introduced to dynamically adjust the early warning threshold, ensuring timely warnings while reducing the false alarm rate.

[0086] Furthermore, the specific method for conducting a safety assessment of the rock slope to be analyzed based on the spatiotemporal distribution field of the slope safety factor and outputting the assessment results is as follows: Based on the spatiotemporal distribution field of the slope safety factor, a digital twin of the slope is constructed by combining the slope displacement field and the damage field. The slope reliability index is corrected in real time using the Bayesian update method. The evolution trajectory of the safety factor within a preset time period is predicted using a long short-term memory network. The warning threshold is adaptively corrected based on the feedback of historical false alarm rate and the confidence of rainfall forecast. When the predicted safety factor is lower than the adaptively corrected warning threshold, a graded warning is triggered. The system analyzes past warning records across multiple warning periods, calculating the ratio of false alarms to total warnings as the historical false alarm rate. If the historical false alarm rate exceeds a preset upper threshold, the warning threshold is increased; if it falls below a preset lower threshold, the threshold is decreased. The system obtains the confidence level of future rainfall forecast data. If the confidence level is high, the warning threshold is significantly adjusted; if low, it is adjusted slightly. The historical false alarm rate correction and the rainfall forecast confidence level correction are combined to obtain the total warning threshold correction. An algebraic operation is performed between the base warning threshold and the total correction to obtain the adaptively adjusted warning threshold. Four warning threshold levels are set. The prediction safety factor is compared with each level. If the prediction safety factor is greater than the first warning threshold, no warning is triggered; if it is between the first and second thresholds, a blue warning is triggered; if between the second and third thresholds, a yellow warning is triggered; if between the third and fourth thresholds, an orange warning is triggered; and if less than the fourth threshold, a red warning is triggered.

[0087] Statistics of the past Calculate the number of false alarms from the warning records within each warning period. Total number of warnings The ratio of the two values ​​is used as the historical false alarm rate. Preset false alarm upper limit threshold With the false alarm lower limit threshold If the historical false alarm rate exceeds the preset false alarm upper limit threshold, i.e. If the historical false alarm rate is lower than the preset false alarm lower limit, then the warning threshold will be raised; if the historical false alarm rate is lower than the preset false alarm lower limit, then... If so, the warning threshold will be lowered. The historical false alarm rate correction amount for the warning threshold. for in This is the baseline correction range, typically ranging from 0.05 to 0.15. The typical value ranges from 0.3 to 0.5; The typical value ranges from 0.05 to 0.15.

[0088] Obtain the confidence level of future rainfall forecast data. Rainfall forecast confidence levels are provided by meteorological departments and are typically divided into three levels: high confidence, medium confidence, and low confidence. High confidence corresponds to a predicted probability of precipitation. medium confidence level corresponds to Low confidence level corresponds to The confidence correction for rainfall forecasts based on the warning threshold. for in , , The correction range corresponding to each confidence level satisfies... High-confidence rainfall forecasts imply a significantly increased risk of slope instability; therefore, the warning threshold should be lowered substantially to improve warning sensitivity. Low-confidence rainfall forecasts have greater uncertainty; therefore, the warning threshold should be lowered only slightly to avoid over-warning. Typical value ranges are... to , to , to .

[0089] The total correction to the warning threshold is obtained by superimposing the historical false alarm rate correction and the rainfall forecast confidence correction. Basic warning threshold By performing algebraic operations on the total correction amount of the warning threshold, the adaptively corrected warning threshold is obtained. Basic warning threshold The value is determined based on the slope design safety factor and the engineering safety level, and is generally taken as 0.8 to 0.9 times the design safety factor.

[0090] Set four warning thresholds , , , ,satisfy ,and The specific value of the Level IV warning threshold is determined based on the slope engineering grade and risk tolerance level, with a typical value being [value missing]. , , , .

[0091] The security factor predicted by the LSTM network within a preset future time period Compare with the Level 4 warning threshold. If the predicted safety factor... If, then no warning will be triggered; if If so, a blue alert will be triggered; if If so, a yellow alert will be triggered; if If so, an orange alert will be triggered; if If this occurs, a red alert will be triggered.

[0092] The response measures for each level of warning are as follows: Blue warning indicates that the slope is in a normal state and routine monitoring continues; Yellow warning indicates that the slope has a slight anomaly, monitoring frequency is increased to once every 2 hours, and on-site management personnel are notified; Orange warning indicates that the slope has obvious signs of instability, monitoring frequency is increased to once every 30 minutes, emergency plans are activated, and personnel in the slope toe area are evacuated; Red warning indicates that the slope is about to or has already become unstable, emergency response is immediately activated, all personnel in the affected area are evacuated, and roads and facilities are closed.

[0093] Please refer to Table 4. This embodiment shows the evolution of the safety factor and the entire process of early warning triggering of a rock slope during the heavy rainfall-cooling coupling process from day 1 to day 4.

[0094] Table 4: Verification Data Table for Slope Safety Factor Prediction and Graded Early Warning As shown in Table 4, the measured safety factor The temperature index (QI) dropped continuously from 1.38 to 0.98, a decrease of 29.0%. The main driving factor was the continuous 36-hour rainfall (cumulative rainfall of 142 mm), which increased the rock mass water content from 8.5% to 18.6%, coupled with the cumulative freeze-thaw damage caused by sub-zero nighttime temperatures (-8.5℃ to -15.5℃). The predicted value output by the physical information neural network... The results showed good agreement with the measured values. The relative error at each time point increased slightly from 1.45% to 2.04%, remaining within 2.5%, verifying PINN's accurate characterization of slope mechanical response under complex coupled conditions. The prediction error of the Long Short-Term Memory Network (LSTM) for the safety factor in the next 24 hours increased from 3.62% to 5.10%. Although this increased with the prediction duration, it still met the time and accuracy requirements for early warning. The historical false alarm rate for this period was [not specified]. Higher than the preset upper limit threshold Furthermore, the meteorological department issued a high-confidence rainfall forecast. Based on the adaptive correction rule, the historical false alarm rate correction amount... Rainfall forecast confidence correction Total correction amount Adaptive early warning threshold Day 2, 14:00: The predicted safety factor of 1.16 is below the first warning threshold for the first time. At that time, the system triggered a blue alert, and the monitoring frequency remained normal; the predicted value of 1.10 dropped to 02:00 on day 3. and A yellow alert was triggered, the monitoring frequency was increased to once every 2 hours, and on-site management personnel were notified; the predicted value at 14:00 on day 3 was 1.06, lower than... An orange alert was triggered, monitoring frequency was increased to once every 30 minutes, and emergency response plans were activated, including evacuating people from the foot of the slope area; the predicted value at 02:00 on day 4 was 1.00, lower than... A red alert was triggered, and an emergency response was immediately activated, including the complete evacuation of people from the affected area and road closures. The measured safety factor dropped to 0.98 at 08:00 on day 4, indicating a localized landslide on the slope, which confirmed the timeliness and accuracy of the early warning system and achieved a complete closed loop from physical modeling and digital twin construction to tiered early warning response.

[0095] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0096] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0097] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0098] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects, characterized in that, Specifically, it includes: S1: Collect slope monitoring data of the rock slope to be analyzed during the monitoring period. The slope monitoring data includes rock mass microseismic signals, internal rock mass strain data, internal rock mass temperature data, surface deformation data, environmental temperature and humidity data, and rainfall data. S2: Microseismic signals are used to identify microseismic events and locate seismic sources to determine the spatial distribution of microseismic events. Based on the spatial distribution of microseismic events, the fracture development area and fracture connectivity are determined, and the fracture network topology is constructed. S3: Determine wet-dry cycle events based on rainfall data and calculate wet-dry cycle damage degree; determine freeze-thaw cycle events based on temperature data and calculate freeze-thaw cycle damage degree; identify wet-dry cycle events and freeze-thaw cycle events that overlap in time as coupling events; calculate nonlinear superimposed damage components based on coupling events; determine the equivalent wet-dry-freeze-thaw coupling structural damage degree based on wet-dry cycle damage degree, freeze-thaw cycle damage degree and nonlinear superimposed damage components. S4: The structural damage degree is used as a damage variable to update the material parameters of the rock mass of the rock slope to be analyzed, and the updated material parameters are obtained. Based on the fracture network topology, the updated material parameters, and strain and temperature data, a set of control equations for water-thermal-mechanical-damage coupling is established. S5: Construct a physical information neural network, and use the residuals of the partial differential equations corresponding to the control equations, the residuals of the initial conditions, and the residuals of the boundary conditions to form physical constraint loss terms. Use the surface deformation data and strain data to form data-driven loss terms. Train the physical information neural network to obtain the slope displacement field and damage field, and calculate the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field. S6: Based on the spatiotemporal distribution field of the slope safety factor, conduct a safety assessment of the rock slope to be analyzed and output the assessment results.

2. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 1, characterized in that, The specific logic for constructing the fracture network topology is as follows: The acquired microseismic signals are filtered and denoised to remove environmental noise interference signals and retain valid microseismic event signals. The sources of the valid microseismic events are located, and a time-difference positioning algorithm is used to calculate the coordinates of each microseismic event in the three-dimensional space of the slope. The spatial coordinates of all microseismic events are projected onto the slope monitoring profile to obtain a planar distribution map of the microseismic events. Based on this planar distribution map, a density clustering algorithm is used to identify densely populated areas of microseismic events, which are then identified as fracture development areas. The boundary contours of each fracture development area are extracted, and the spatial distance between adjacent fracture development areas is calculated. If the spatial distance between adjacent fracture development areas is less than a preset connectivity threshold, a fracture connectivity relationship is determined between them. The fracture network topology is constructed using each fracture development area as a node and the fracture connectivity relationship as an edge.

3. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 2, characterized in that, The specific method for determining wet-dry cycle events and calculating the wet-dry cycle damage degree based on rainfall data is as follows: According to rainfall data, the number of wet-dry cycles experienced by the slope rock mass within the monitoring period is counted. A complete wet-dry cycle is defined as the process of soil moisture content rising from a dry state to a saturated state and then falling back to a dry state. For each wet-dry cycle, the maximum and minimum moisture contents during the cycle are extracted, and the difference between the two is calculated as the moisture content change range of that cycle. Based on the moisture content change range, the corresponding single-cycle damage increment is retrieved from the preset wet-dry cycle fatigue curve. This wet-dry cycle fatigue curve is pre-calibrated through indoor rock sample wet-dry cycle tests. The single-cycle damage increments of all wet-dry cycles within the monitoring period are accumulated to obtain the cumulative wet-dry cycle damage degree, which is used as the wet-dry cycle damage degree.

4. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 3, characterized in that, The specific method for determining freeze-thaw cycle events and calculating freeze-thaw cycle damage based on temperature data is as follows: Based on temperature data, the number of freeze-thaw cycles experienced by the slope rock mass within the monitoring period is counted. A complete freeze-thaw cycle is defined as the process in which the rock mass temperature drops from above the freezing point to below the freezing point and then rises back above the freezing point. For each freeze-thaw cycle, the lowest and highest temperatures during the cycle are extracted, and the absolute value of the difference between the lowest temperature and the freezing point is calculated as the freezing depth index for that cycle. Based on the freezing depth index, the corresponding single freeze-thaw damage increment is retrieved from the preset freeze-thaw cycle damage curve. This freeze-thaw cycle damage curve is pre-calibrated through indoor rock sample freeze-thaw cycle tests. The single freeze-thaw damage increments of all freeze-thaw cycles within the monitoring period are accumulated to obtain the cumulative freeze-thaw cycle damage degree, which is used as the freeze-thaw cycle damage degree.

5. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 4, characterized in that, The specific method for calculating the nonlinear superimposed damage component based on coupled events is as follows: identify wet-dry cycle and freeze-thaw cycle events that overlap in time; determine coupled events as events where drastic changes in water content and temperature crossing the freezing point occur simultaneously within the same time period; for each coupled event, extract the water content change amplitude and freezing depth index during the event; retrieve the corresponding single-cycle damage increment from the wet-dry cycle fatigue curve and the freeze-thaw cycle damage curve respectively; calculate the product of the wet-dry cycle damage increment and the freeze-thaw cycle damage increment in the coupled event; multiply the product of this product and the preset coupling strengthening coefficient as the nonlinear superimposed damage increment of the coupled event; the coupling strengthening coefficient is pre-calibrated through indoor wet-dry-freeze-thaw coupled cycle test of rock samples; and accumulate the nonlinear superimposed damage increments of all coupled events within the monitoring period to obtain the nonlinear superimposed damage component. The equivalent dry-wet cycle damage degree, freeze-thaw cycle damage degree, and nonlinear superimposed damage component are combined to obtain the structural damage degree of dry-wet-freeze-thaw coupling.

6. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 5, characterized in that, The specific method for establishing the control equation set of water-thermal-mechanical-damage coupling is as follows: the equivalent dry-wet-freeze-thaw coupling structural damage degree is used as the damage variable, and the elastic modulus, cohesion and internal friction angle of the rock mass are reduced and corrected according to the damage variable to obtain the updated material parameters; based on the fracture network topology, the updated material parameters and the strain data and temperature data, the control equation set of water-thermal-mechanical-damage coupling is established. The control equation set includes a water migration equation describing the water transport law in the fracture-matrix dual medium, a heat conduction equation considering the influence of the latent heat of freeze-thaw phase change, a mechanical equilibrium equation coupling pore water pressure and rock mass deformation response, and a damage evolution equation reflecting the rock mass strength degradation law under cyclic loading.

7. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 6, characterized in that, The specific method for constructing the physical information neural network is as follows: An input layer is constructed, which receives the slope's spatial coordinates and environmental parameter vectors. The spatial coordinates contain three-dimensional spatial location information, and the environmental parameter vectors contain the current rainfall, ambient temperature, and soil moisture content. A physical constraint embedding layer is constructed, which transforms the water migration equation, heat conduction equation, mechanical equilibrium equation, and damage evolution equation established by S4 into corresponding partial differential equation residuals, and transforms the initial conditions and boundary conditions into initial condition residuals and boundary condition residuals, respectively. These residuals serve as physical constraint loss terms in network training. A data-driven supervision layer is constructed, which uses surface deformation data and rock mass strain data as supervision signals, compares them with the network's predicted output, and generates data-driven loss terms. A network output layer is constructed, which outputs predicted values ​​for the slope displacement field and damage field, and calculates the spatiotemporal distribution field of the slope safety factor based on the displacement field and damage field. The safety factor is determined based on the ratio of the slope's anti-sliding force to its sliding force.

8. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 7, characterized in that, The specific method for training the network using an adaptive loss function that dynamically adjusts weights based on the gradient statistical characteristics of each loss term is as follows: Calculate the gradient magnitudes of the physical constraint loss term, data-driven loss term, and boundary condition loss term in the current training epoch. Statistically calculate the relative proportions of the gradient magnitudes of each loss term. Identify the loss term with the largest gradient magnitude as the dominant loss term and the loss term with the smallest gradient magnitude as the weak loss term. Decrease the weight coefficient of the dominant loss term and increase the weight coefficient of the weak loss term to balance the contribution of each loss term to the network parameter update. Multiply the adjusted weight coefficients of each loss term by their corresponding loss terms and sum them to obtain the total loss function value for the current training epoch. Perform backpropagation based on the total loss function value to update the network parameters. Repeat the above gradient statistics and weight adjustment process until the network converges.

9. The method for analyzing the safety status of rock slopes under wet-dry / freeze-thaw coupling effects according to claim 8, characterized in that, The specific method for assessing the safety of the rock slope under analysis based on the spatiotemporal distribution field of the slope safety factor and outputting the assessment results is as follows: Based on the spatiotemporal distribution field of the slope safety factor, a digital twin of the slope is constructed by combining the slope displacement field and the damage field. The slope reliability index is corrected in real time using the Bayesian update method. The evolution trajectory of the safety factor within a preset time period is predicted using a long short-term memory network. The warning threshold is adaptively corrected based on the feedback of historical false alarm rate and the confidence of rainfall forecast. When the predicted safety factor is lower than the adaptively corrected warning threshold, a graded warning is triggered. The system analyzes past warning records over multiple warning periods and calculates the ratio of false alarms to total warnings as the historical false alarm rate. If the historical false alarm rate is higher than a preset upper limit threshold, the warning threshold is increased; if the historical false alarm rate is lower than a preset lower limit threshold, the warning threshold is decreased. The system obtains the confidence level of future rainfall forecast data. If the confidence level is high, the warning threshold is significantly adjusted; if the confidence level is low, the warning threshold is slightly adjusted. The total adjustment of the warning threshold is obtained by adding the historical false alarm rate adjustment and the rainfall forecast confidence level adjustment. The basic warning threshold and the total warning threshold adjustment are then algebraically calculated to obtain the adaptively adjusted warning threshold. A four-level warning threshold is set, and the predicted safety factor is compared with the four-level warning threshold. If the predicted safety factor is greater than the first warning threshold, the warning is not triggered. If the value falls between the first and second warning thresholds, a blue warning is triggered; if it falls between the second and third warning thresholds, a yellow warning is triggered; if it falls between the third and fourth warning thresholds, an orange warning is triggered. If the value is less than the fourth warning threshold, a red warning will be triggered.

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