A method for predicting displacement of reservoir bank hydrodynamic landslides based on seepage-stress coupled physical information neural networks

Abstract

This invention discloses a method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network. First, time-series monitoring data of reservoir water level, rainfall, and displacement in the landslide area are collected and preprocessed. Then, a physical model is constructed, incorporating infiltration line calculation, stress calculation, and displacement calculation, using the Boussinesq equation, Terzaghi effective stress principle, and power-law creep model to characterize the relevant processes, respectively. Subsequently, a physical information neural network is constructed, using the monitoring data as input and embedding a loss function into the physical model's control equations as physical constraints to establish a hybrid loss function. Finally, the network is trained to obtain a prediction model, which is used for predicting future landslide displacement and evaluating its accuracy. This invention integrates physical mechanisms and deep learning, improving prediction accuracy and interpretability, and is applicable to deformation analysis and early warning of reservoir water level fluctuations and rainfall-induced infiltration landslides.

Description

Technical Field

[0001] This invention relates to the field of geological disaster prediction, specifically to a method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network. Background Technology

[0002] Reservoir bank landslides are among the most common and destructive geological hazards during reservoir operation. Due to the combined effects of periodic rises and falls in reservoir water levels, rainfall infiltration, and groundwater activity, the pore water pressure and effective stress within the reservoir bank soil constantly change, easily triggering long-term creep deformation and even overall instability of the landslide mass. Rapid drops in water levels or continuous heavy rainfall can lead to a redistribution of the seepage field within the landslide mass, causing the phreatic line to rise or fall rapidly, thereby altering the shear strength and safety factor of the slip zone and forming a typical reservoir bank hydrodynamic landslide. This type of landslide exhibits significant time-varying and hysteretic characteristics; its deformation evolution is influenced by the coupling effects of multiple factors, including seepage, seepage pressure, stress, and soil constitutive relationships, making it one of the most complex types of landslides to predict.

[0003] Existing landslide prediction research mainly follows two approaches: one is based on physical models, which establish governing equations such as seepage equations, stress balance equations, and constitutive relations to reflect the mechanical mechanism of landslide deformation. However, these models have many parameters, require a large amount of computation, and are difficult to update in real time. The other approach is based on data-driven models, such as backpropagation neural networks (BPNN) and long short-term memory networks (LSTM), which achieve trend prediction by learning from historical monitoring data. However, machine learning models are black-box models, heavily reliant on the availability and quality of data, and do not respect the physical mechanisms of the process they are modeling. Their generalization ability is also limited.

[0004] The emergence of Physics-Informed Neural Networks (PINN) offers a revolutionary approach to solving the aforementioned problems. This is a new paradigm that embeds physical knowledge (usually in the form of governing equations, boundary conditions, or known physical laws) into deep learning models. By introducing physical constraints into the loss function, it forces the neural network to adhere to predefined physical laws while learning data features.

[0005] Therefore, existing technologies lack a displacement prediction method that can simultaneously consider the universality of physical mechanisms, the high accuracy of data-driven approaches, and the essential characterization of the temporal evolution of landslides. Against this backdrop, this invention proposes a displacement prediction method for reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network, aiming to overcome the shortcomings of existing technologies. Summary of the Invention

[0006] This invention provides a method for predicting reservoir bank hydrodynamic landslide displacement based on a seepage-stress coupled physical information neural network, addressing the problems of disconnect between physical models and data-driven models, and the lack of physical consistency and extrapolation ability in prediction results in existing technologies. The core idea of ​​this invention is to construct a loss function that deeply integrates physical mechanisms, embedding the physical evolution model describing the landslide displacement accumulation process as a strong constraint into the regularization term of the neural network. This guides the neural network to adhere to fundamental physical laws while learning from monitoring data.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network, the method comprising the following steps: S1. Data Acquisition and Preprocessing: Collect historical time-series monitoring data of the target landslide area, including reservoir water level elevation, rainfall and landslide monitoring point displacement data, and perform noise reduction and smoothing on the data; S2. Construct a physical model for landslide displacement prediction, which includes three sub-models: seepage line calculation, stress calculation, and displacement calculation. The calculation of the phreatic line is based on the Boussinesq equation of the unsteady seepage theory to calculate the phreatic line of the landslide, and includes the following steps: Under the combined effects of reservoir water level fluctuations and rainfall, the governing differential equation for one-dimensional unsteady seepage along the Boussinesq phreatic line can be established as follows: ; in, H Indicates water head. h Indicates the thickness of the aquifer. K Indicates the aquifer permeability coefficient. x This indicates the horizontal distance from the calculation point to the origin. m Indicates the gravity runoff coefficient. W Indicates rainfall intensity. t Indicates time.

[0008] In reality, although the aquifer thickness h Some changes will occur, but these changes are relatively small and negligible on a spatiotemporal scale. Therefore, for analytical purposes, the aquifer thickness is... h Treating it as a constant parameter, the average thickness of the unsteady flow at the beginning and end times of the time interval is used. h m replace: ; ; ,x The temporal evolution of the groundwater level along the reservoir landslide is as follows: ; in H(x,0) yes x The initial water level at the location is a fixed value that can be determined through on-site monitoring. u(x, t) for t time x The change in the height of the wetting line at that location.

[0009] when t=0 hour: ; when x=0 hour: ; Among them, by function The change in reservoir water level is measurable and can be considered a known quantity.

[0010] Therefore, the unsteady flow of groundwater can be described by the following equation: ; in, u(∞,t)=βt This represents time at an infinite distance from the origin. t The change in groundwater level. Assume that the fluctuation of the reservoir water level has no effect on the groundwater level at an infinite distance, and that the groundwater level is only affected by rainfall infiltration, while the rainfall intensity can be obtained through on-site monitoring.

[0011] To solve for the initial water level under steady-state conditions, this study employs the Dupuy assumption. The flow rates at initial cross-sections 1 and 2 are set as follows: q 1. Set the flow rate from 1 to x to [value]. q 2.

[0012] ; According to the principle of water balance, that is q 1= q 2. It can be deduced that x Water head at cross-section: ; Unsteady flow of groundwater can be solved using the Laplace integral transform. Both sides of the model equation are multiplied by... e -st The equation after the integral transformation is as follows: ; Assumption The general solution of the second-order nonhomogeneous differential equation is: ; Further simplification by taking the inverse Laplace transform yields: ; ; ; ; in, erfc(λ) λ is the residual error function, which can be obtained by consulting the error function table. λ is the groundwater influence factor. K , h m It is a constant, λ is x (distance from the origin) and t A function of (duration). λ and x Positive correlation with t Negative correlation. R(λ) The groundwater influence coefficient is obtained using a polynomial fitting method: ; u(x,t) and H(x,t) This can be further expressed as: ; ; The formula for calculating the groundwater phreatic line can be expressed as: ; in, H(x,t) Indicates the elevation of the wetting line. H 0 represents the initial elevation of the seepage line, function The change in reservoir water level is indicated. a 1. a 2 、a 3 and a 4. Fit coefficient.

[0013] The stress calculation includes the following steps: The stress distribution within a landslide is controlled by a combination of factors, including the height of the phreatic line, soil weight, and the slope angle of the sliding surface. As reservoir water levels and rainfall conditions change, the spatial position of the phreatic line within the landslide changes over time, causing periodic fluctuations in pore water pressure and total stress within the landslide. To accurately calculate the stress state within the slip zone, this invention comprehensively considers the layered unit weight characteristics of the landslide body and the influence of seepage pressure, establishing a stress calculation model.

[0014] Shear stress of the sliding body along the sliding direction τ(x,t) This can be expressed as the component of the sliding body's own weight on the slope surface: ; in, It is the elevation of the landslide surface. It is the elevation of the slip surface. It is a natural heavy sliding body. It is the saturated specific gravity of the sliding body. It is the slope angle.

[0015] Pore ​​water pressure is given by the product of water head and unit weight: ; In the formula, h(x,t) The difference in elevation between the wetting line and the slip surface. c w The density of water, Pore ​​water pressure; According to Terzaghi's effective stress principle, the effective stress at any point in a landslide mass can be expressed as: ; σ′(x,t) For effective stress, σ(x,t) This represents the total stress.

[0016] For a certain depth Z in the landslide profile, the corresponding total stress is: ; in, c s Weighting is applied to the soil.

[0017] ; Its shear strength t f This can be expressed by the Mohr-Coulomb criterion: ; in, For cohesion, Let be the internal friction angle. Substituting this into the effective stress formula, we get: ; In the formula, For shear strength, Z(x) The depth of the landslide. h(x,t) This represents the height difference between the wetting line and the slip surface.

[0018] The displacement calculation includes the following steps: Based on the power-law creep model proposed by Singh & Mitchell, the stress-displacement dynamic equation is constructed, and the creep rate can be expressed as: ; in, It is the creep rate, and A is the material creep constant. n This is the stress index.

[0019] when When <1, the creep rate is extremely slow; when As the velocity approaches 1, the rate increases sharply, exhibiting a step deformation. The physical model predicts the cumulative displacement. It can be represented as: ; in, yes you Displacement at any moment yes ti-1 Displacement at any moment For the time span.

[0020] S3. Design and construct a Physical Information Neural Network (PINN), take the monitoring data as input, embed the control equation of the physical model into the loss function as a physical constraint term, and establish a hybrid loss function that includes data fitting loss and physical constraint loss; The framework of the physical information neural network is as follows: PINN employs a backpropagation neural network structure, taking rainfall, water level, and historical displacement as inputs, and outputting the predicted displacement. It uses three hidden layers, each with 50 neurons. The activation function is tanh, and the optimizer is adam.

[0021] Furthermore, the S3 physical constraints and loss function are as follows; ; in; It is the physical loss of the PDE at the wetting line; It is the physical loss in the stress-displacement dynamic equation; It is a data loss; , and These are the weighting parameters for each loss.

[0022] The PDE loss of the wetting line is constructed from the residuals based on the Boussinesq equation, and the corresponding loss can be expressed as: ; Physical losses based on the stress-displacement dynamic equation: ; The loss of monitored displacement data is: ; in, yes t Predicted value at time, This is the actual value.

[0023] S4. Train the physical information neural network using monitoring data, ensuring the network parameters converge under the condition of minimizing the mixed loss function, to obtain a landslide displacement prediction model that conforms to physical laws. Use the trained PINN model to predict the monitored displacement of the landslide. Compare the predicted results with the measured displacement to evaluate the model's prediction accuracy.

[0024] Compared with the prior art, the beneficial effects of the present invention include: (1) This invention is the first to organically integrate the landslide seepage-stress-displacement evolution mechanism with deep learning algorithms, and proposes a landslide displacement prediction method based on Physical Information Neural Network (PINN). Compared with existing pure data models, this invention not only improves the accuracy of landslide deformation prediction, but also gives the model clear physical meaning and interpretability, providing a new technical approach for risk assessment and early warning of landslide disasters.

[0025] (2) This invention uses the one-dimensional unsteady Boussinesq seepage equation to calculate the spatiotemporal variation of the phreatic line under the influence of reservoir water level fluctuations and rainfall infiltration. A segmented equivalent unit weight model controlled by the phreatic line is introduced into the stress calculation, while considering the unit weight difference between the unsaturated and saturated zones, effectively improving the estimation accuracy of total stress and pore water pressure, and enhancing the accuracy of stress and shear strength calculations. Finally, a power-law creep model is used to describe the landslide deformation rate, achieving a unified modeling of the landslide seepage, stress, and deformation evolution processes under the influence of reservoir water level fluctuations and rainfall infiltration.

[0026] (3) The physical information neural network constructed in this invention introduces physical equation constraints in the loss function and uses physical loss and data loss to jointly construct the loss function, so that the network can automatically follow physical laws while learning historical monitoring data, thereby realizing the dual constraints of data and mechanism. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] Figure 1 This is an overall flowchart of the method of the present invention.

[0029] Figure 2 This is a schematic diagram of the calculation model for the infiltration line of a landslide under the combined effect of rainfall and reservoir water level fluctuations, as described in this invention.

[0030] Figure 3 This is a schematic diagram of the Physical Information Neural Network (PINN) structure of the method of the present invention.

[0031] Figure 4 This is a comparison chart of the prediction results and errors of the PINN model using the method of this invention and the existing BPNN model. Detailed Implementation

[0032] The following example of the Baishuihe landslide further illustrates the proposed displacement prediction method for reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network. This embodiment uses the Baishuihe landslide as the research object. This landslide is located on the bank slope of the Three Gorges Reservoir area and is a typical reservoir bank hydrodynamic landslide, exhibiting significant hysteresis deformation characteristics due to the combined influence of reservoir water level fluctuations and rainfall infiltration. Multiple monitoring points are set at the leading edge of the landslide, among which the displacement monitoring data at point ZG118 is the most complete and representative. This embodiment uses monitoring point ZG118 as the core of the research, utilizing the method described in this invention to predict the physical constraints of landslide displacement. The overall process is as follows: Figure 1 As shown. Specifically, it includes the following: S1. Long-term monitoring of the landslide area was conducted to acquire multi-source time-series data, including reservoir water level, rainfall, and landslide surface displacement. The data spanned from 2006 to 2018, with sampling occurring monthly. The monitoring data originated from the Three Gorges Reservoir Area Geological Disaster Automated Monitoring System. After missing data completion, noise reduction, and smoothing, the raw data was used to establish a time-consistent sequence. In terms of sample division, all data were divided into training and test sets according to time sequence, with the training set comprising 80% and the test set comprising 20%, used for later verification of prediction accuracy.

[0033] S2. To reflect the deformation evolution mechanism of landslides under changing hydrological conditions, a physical model of landslide seepage-stress-displacement coupling is established. A schematic diagram of the calculation model is shown below. Figure 2 As shown in the figure. The model consists of three parts: wetting line calculation, stress calculation, and displacement calculation.

[0034] Calculation of the infiltration line: The dynamic changes of the groundwater level within the landslide body are controlled by unsteady seepage. Based on the geological structure of the Baishuihe landslide, the landslide body is considered as a one-dimensional unsteady seepage medium. The Boussinesq equation, based on unsteady seepage theory, is used to describe the groundwater movement under the combined effects of reservoir water level fluctuations and rainfall infiltration. The equation can be written as: ; in, H Indicates water head; h m This represents the thickness of the aquifer, taken as 30m. K The aquifer permeability coefficient is taken as 1.17 × 10⁻⁶. - 2 cm / s; Taking the intersection of the reservoir water level (elevation 145m) and the landslide as the origin, the horizontal coordinates of monitoring point ZG118 are taken. x= 225m; m This represents the gravity runoff coefficient, taken as 0.082; W Indicates rainfall intensity; T Indicates time.

[0035] ; R(λ) is obtained using a polynomial fitting method: ; ; Stress calculation: Shear stress of the sliding body along the sliding direction τ(x,t) It can be expressed as the component of the sliding body's own weight on the slope surface. ; Among them, the landslide surface elevation The elevation of the slip surface is 193.2m. The length is 158.6m, and the natural weight of the sliding body is... Take 20 kN·m -3 Saturated density of sliding body Take 21 kN·m -3 slope angle Take 17°.

[0036] According to Terzaghi's effective stress principle and the Mohr-Coulomb criterion, the shear strength is: ; Among them, cohesion Take 27.5 kPa, internal friction angle Take 17.8°, the specific gravity of water. It is 9.81 kN·m -3 .

[0037] The ratio of slip zone shear stress to shear strength determines the deformation rate of the landslide. The Singh-Mitchell power-law creep model is used to describe the nonlinear deformation relationship of the landslide. The creep rate expression is: ; Among them, the material creep constant A Take 0.07 mm / month, stress index n Take 3. Its corresponding cumulative displacement is: ; S3. Based on the above physical mechanism model, the physical constraint equations of landslides are embedded into a neural network framework to construct a PINN-based reservoir bank landslide displacement prediction model. The PINN structure is as follows: Figure 3As shown. This model integrates monitoring data with physical equation constraints, achieving a unification of data-driven and mechanism-constrained approaches through joint optimization. The neural network employs a multi-layer feedforward structure. The input layer takes rainfall R, reservoir water level W, and current month's displacement D as inputs, and outputs the next month's displacement. Three hidden layers are used, each containing 50 neurons. The activation function is tanh, and the optimization algorithm is Adam gradient descent. The total loss function is defined as: ; It is the physical loss of the PDE at the wetting line; It is the physical loss of the stress-displacement dynamic equation, representing the sum of squared residuals between the time derivative of the predicted displacement and the calculation rate of the power-law creep model; It is the data loss, representing the mean square error between the network-predicted displacement and the measured displacement; , and These are the weighting parameters for each loss, set to 0.1, 0.2, and 0.7 respectively, to balance data fitting and physical consistency.

[0038] During training, the network continuously adjusts its parameters through backpropagation to minimize the total loss function. At this point, the network not only learns the statistical patterns of the monitoring data but also automatically captures the implicit physical equations. Once training converges, the PINN model can be used to predict reservoir bank landslide displacement under arbitrary hydrological conditions.

[0039] S4. Input the training set into the PINN model for training. In each iteration, the network simultaneously calculates the data error and physical residual, updating the weight parameters through gradient descent. After approximately 2000 training iterations, the loss function converges and stabilizes, and the total loss decreases to 10. -4 The magnitude indicates that the network has achieved a coordinated fit between physics and data.

[0040] After training, the test data from the ZG118 monitoring point of the Baishuihe landslide were input into the trained PINN model to obtain the predicted displacement for the corresponding time period. Comparison of the predicted and measured displacements shows that the PINN model of this invention can accurately capture the temporal variation characteristics of landslide deformation. Especially during periods of rapid reservoir water level decline and heavy rainfall, the predicted curve significantly reflects the accelerating displacement trend and shows good agreement with the measured results.

[0041] To verify the effectiveness of this method, a traditional backpropagation neural network (BPNN) model is used as a control, such as... Figure 4 As shown, training and prediction are performed under the same dataset and input conditions. The BPNN model relies solely on data-driven learning and does not include physical constraint terms. The prediction error metrics (correlation coefficient R) of the two models are compared. 2 The mean square error (MSE) and mean absolute error (MAE) are as follows:

[0042] Table 1 Therefore, the PINN model significantly outperforms the traditional BPNN in both prediction accuracy and physical consistency. The PINN model reduces the RMSE by approximately 11.4% and the MAE by approximately 9.4% compared to BPNN, while increasing the correlation coefficient to 0.914, indicating that the PINN model has a higher degree of fit between its predictions and the measured displacements, and thus better prediction performance.

Claims

1. A method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network, characterized in that, Includes the following steps: S1. Data Acquisition and Preprocessing: Collect historical time-series monitoring data of the target landslide area, including reservoir water level elevation, rainfall and landslide monitoring point displacement data, and perform noise reduction and smoothing on the data; S2. Construct a physical model for landslide displacement prediction, which includes three sub-models: seepage line calculation, stress calculation, and displacement calculation. S3. Design and construct a Physical Information Neural Network (PINN), take the monitoring data as input, embed the control equation of the physical model into the loss function as a physical constraint term, and establish a hybrid loss function that includes data fitting loss and physical constraint loss; S4. Train the physical information neural network using the monitoring data, so that the network parameters converge under the condition of minimizing the mixed loss function, and obtain a landslide displacement prediction model that conforms to physical laws. Use the trained PINN model to predict the monitored displacement of the landslide, compare the prediction results with the measured displacement, and evaluate the prediction accuracy of the model.

2. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, The infiltration line calculation in step S2 uses the Boussinesq equation based on the unsteady seepage theory to describe the seepage motion under the combined effects of reservoir water level fluctuations and rainfall infiltration. Its governing equation and analytical expression are as follows: ； ； in, , , H(x,t) Indicates the elevation of the wetting line. H 0 represents the initial elevation of the wetting line, function The change in reservoir water level is indicated. h m Indicates the average thickness of the aquifer. K Indicates the aquifer permeability coefficient. x This indicates the horizontal distance from the calculation point to the origin. μ Indicates the gravity runoff coefficient. W Indicates rainfall intensity. t Indicates time, a 1. a 2 、a 3 and a 4. Fit coefficient.

3. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, The stress calculation in step S2 is based on the Terzaghi effective stress principle. Considering the location of the wetting line and the saturation characteristics of the sliding body, the shear stress and shear strength are calculated as follows: ； ； in, It is shear stress and It is shear strength. It is the elevation of the landslide surface. It is the elevation of the slip surface. It is a natural heavy sliding body. It is the saturated specific gravity of the sliding body. It is the density of water. For the slope angle, For cohesion, It is the internal friction angle.

4. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, The displacement calculation in step S2 uses a power-law creep model to construct the stress-displacement dynamic equation, and the relationship between strain rate and stress ratio is as follows: ； in, It is the creep rate, and A is the material creep constant. n Stress index; The cumulative displacement is: ； in, yes ti Displacement at any moment yes ti-1 Displacement at any moment For the time span.

5. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, The physical information neural network in step S3 includes an input layer, a hidden layer, and an output layer. The input layer receives time, rainfall, water level, and monthly displacement. The hidden layers consist of three layers, with 50 neurons in each layer; The output layer outputs the next month's displacement; The activation function is tanh, and the Adam optimization algorithm is used. The gradient of the loss function is calculated by automatic differentiation to achieve joint optimization of physical constraints and data fitting until the loss converges.

6. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, The hybrid loss function in step S4 includes data loss and physical loss: ； in, It is the physical loss of the PDE in the wetting line. It is the physical loss in the stress-displacement dynamic equation. It's data loss. , and These are the weighting parameters for each loss; The PDE loss of the wetting line is constructed from the residuals based on the Boussinesq equation, and the corresponding loss can be expressed as: ； Physical losses based on the stress-displacement dynamic equation: ； The loss of monitored displacement data is: ； in, yes t Predicted value at time, This is the actual value.

7. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, In the displacement calculation of step S2, the stress ratio SL of the power-law creep model is... The deformation characteristics of landslides are dynamically characterized by the real-time coupling calculation of shear stress and shear strength. When SL < 1, the landslide exhibits slow creep deformation, while when SL approaches 1, it exhibits step-accelerated deformation.

8. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, In the stress calculation of step S2, the total stress calculation takes into account the soil weighting corresponding to the depth of the landslide profile. Combined with the saturated and unsaturated zones divided by the seepage line, the saturated unit weight and natural unit weight of the landslide body are used for segmented calculation. Then, the shear strength is solved by coupling the Terzaghi effective stress principle and the Mohr-Coulomb criterion.

9. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, In the model training process of step S4, the training set and test set are divided in chronological order, with the training set accounting for 80% of the total data and the test set accounting for 20%. Through multiple iterations, the hybrid loss function converges to 10. -4 The magnitude ensures that the model fully learns the temporal deformation characteristics of landslides.

10. The method for predicting displacement of reservoir bank hydrodynamic landslides based on a seepage-stress coupled physical information neural network according to claim 1, characterized in that, In the evaluation of the prediction accuracy of the model in step S4, the correlation coefficient R is used. 2 A multi-index system including mean square error and mean absolute error was used to verify the model's prediction accuracy and consistency with physical conditions by comparing it with measured displacement and with the error index of traditional backpropagation neural networks.

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