Slope displacement multi-model collaborative prediction method and system considering rainfall-intensity degradation dynamic coupling

Abstract

This invention discloses a multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation, relating to the field of slope stability analysis. The method includes: establishing at least two slope stability analysis models; constructing a damage degradation model based on the strength parameters of the slip zone soil; constructing a rainfall-coupled dynamic displacement rate prediction model, obtaining predicted displacement rates and converting them into predicted cumulative displacement values; weighted fusion of the predicted values ​​from each model; constructing a likelihood function and calculating its value; and dynamically updating the model weights based on a recursive probability estimation scheme for cumulative displacement fusion in the next time step. This invention fully considers the control mechanism of slope displacement evolution by the coupling effect of dynamic rainfall infiltration and slip zone soil intensity degradation, accurately describing the nonlinear displacement response of slopes under the combined action of rainfall and creep during long-term service. It provides a theoretical basis for slope stability prediction and safety early warning in projects such as deep mineral resource mining, high dam reservoir operation, and major transportation infrastructure construction.

Description

Technical Field

[0001] This invention relates to the field of slope stability analysis technology in geotechnical engineering, specifically to a multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation. Background Technology

[0002] Slope instability is one of the major geological hazards faced in the construction and operation of infrastructure in high mountains and canyons. It is characterized by its suddenness and destructiveness, posing a serious threat to people's lives and property and the safety of major projects. With the deepening of the Western Development Strategy, numerous water conservancy and hydropower projects and transportation infrastructure are being constructed and operated under complex geological conditions, while also facing the impact of heavy rainfall brought about by extreme weather events, making the long-term stability of slopes increasingly prominent. Accurate prediction of slope deformation is a core requirement for geological hazard prevention and engineering safety management.

[0003] Currently, slope deformation prediction and stability analysis mainly employ the following two types of methods:

[0004] One approach is the single-physical-model analysis method, such as the limit equilibrium method, which is the most widely used method in engineering practice. It assesses slope stability by calculating the ratio of resisting force to sliding force using the slice method, offering advantages such as simple calculation and clear physical meaning. However, the limit equilibrium method relies on rigid body assumptions and simplified inter-slice force assumptions, failing to accurately characterize the complex stress distribution and deformation coordination relationships within the slope, especially when the slope approaches its limit state, where its predictions often deviate significantly from reality. Furthermore, traditional limit equilibrium analysis typically uses constant strength parameters, failing to fully consider the time-dependent characteristics of the shear strength of the slip zone soil gradually decreasing from peak to residual strength during shearing. The finite element method (FEM), based on continuum mechanics, can simulate the stress-strain response and progressive failure process of slopes, exhibiting better adaptability to complex geological and boundary conditions than the limit equilibrium method. However, the FEM involves large computational loads, is sensitive to model parameters, and even a single FEM model can suffer from deviations due to model selection, boundary condition settings, and parameter values.

[0005] Second, there are multi-model combined prediction methods, but existing methods generally have the following technical gaps: First, some methods use fixed weights or static weighting based on expert experience, which cannot reflect the dynamic waxing and waning of the predictive capabilities of different models at different deformation stages of the slope. When the model prediction accuracy changes with the slope evolution stage, the fixed weight combination cannot automatically adjust to select the optimal model or optimal weight allocation for the current stage, failing to incorporate the dynamic effects of rainfall into the multi-model fusion framework. Second, rainfall is a key external factor inducing accelerated slope deformation, and existing methods mostly treat rainfall as an independent influencing factor for ex-post correction, failing to establish a dynamic coupling relationship between rainfall intensity and displacement rate within the multi-model fusion framework. Especially when rainfall exhibits seasonal fluctuations or extreme rainstorm events occur, prediction models lacking rainfall coupling mechanisms often produce significant hysteresis errors. Third, the time-varying characteristics of slip zone soil strength degradation are not considered simultaneously: numerous engineering practices and experimental studies have shown that during shearing, due to irreversible structural damage, the shear strength parameter of slip zone soil gradually decreases from its peak value to residual strength as cumulative displacement increases. This strength degradation process has a significant impact on the long-term deformation evolution of slopes. However, existing combined prediction methods often treat the strength parameters of soil and rock as invariant constants, neglecting the coupling effect between strength degradation over time and deformation. Fourth, a unified and collaborative prediction framework for rainfall-strength degradation-displacement response has not yet been established: In existing technologies, the dynamic effects of rainfall and the time-varying degradation of strength are often treated separately, lacking a collaborative prediction method that can incorporate "dynamic rainfall input—time-varying evolution of strength parameters—multi-model displacement prediction—dynamic self-correction of weights" into a unified mathematical framework. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a multi-model collaborative prediction method and system for slope displacement that considers the dynamic coupling of rainfall and intensity degradation, which can effectively solve the above problems.

[0007] The technical solution adopted in this invention is as follows:

[0008] In a first aspect, the present invention provides a multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation, comprising the following steps:

[0009] Step S1: Obtain engineering geological survey data of the target slope, including the physical and mechanical parameters of the sliding body and sliding zone soil, and the slope geometric parameters; and obtain the time step relative to the time step to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step;

[0010] Step S2: Establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions, denoted as slope stability analysis models. , , This indicates the number of types of slope stability analysis models;

[0011] Step S3: Construct a damage degradation model for the strength parameters of the slip zone soil. An exponential decay model is used to describe the degradation law of the slip zone soil strength parameters with cumulative displacement, based on time steps. Cumulative displacement fusion prediction value Update time step The strength parameters of the slip zone soil were determined and substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators;

[0012] Step S4: Construct stability analysis models for each type of slope. The corresponding rainfall-coupled dynamic displacement rate prediction model, based on each slope stability analysis model Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ;

[0013] Step S5, according to the time step Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value ;

[0014] Step S6: Obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value ;

[0015] Step S7, obtain the target slope at time step Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations The deviation is calculated for each slope stability analysis model. At time step The likelihood function value is obtained, and the slope stability analysis model is dynamically updated based on the recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ;

[0016] Step S8, set the time step Cumulative displacement observations Add to timing window, make Return to step S3.

[0017] Secondly, the present invention provides a multi-model collaborative prediction system for slope displacement considering the dynamic coupling of rainfall and intensity degradation, used to implement the aforementioned multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation, including:

[0018] The engineering geological survey data and monitoring data acquisition module is used to acquire engineering geological survey data of the target slope, including the physical and mechanical parameters of the sliding body and sliding zone soil and the slope geometric parameters; and to acquire the data relative to the time step to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step;

[0019] A slope stability analysis model is used to establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions. This is represented as a slope stability analysis model. , , This indicates the number of types of slope stability analysis models;

[0020] A damage degradation model for the strength parameters of slip zone soil is used to describe the degradation law of slip zone soil strength parameters with cumulative displacement in an exponential decay form, based on time steps. Cumulative displacement fusion prediction value Update time step The strength parameters of the slip zone soil were determined and substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators;

[0021] A rainfall-coupled dynamic displacement rate prediction model is used to predict slope stability based on each slope stability analysis model. Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ;

[0022] The cumulative displacement prediction module is used to predict displacement based on time steps. Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value ;

[0023] The cumulative displacement fusion prediction module is used to obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value ;

[0024] The model weight update module is used to obtain the target slope at time step. Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations The deviation is calculated for each slope stability analysis model. At time step The likelihood function value is obtained, and the slope stability analysis model is dynamically updated based on the recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ;

[0025] The model accuracy evaluation module is used to quantitatively evaluate and compare the prediction accuracy of each model by using normalized root mean square error, mean absolute error, and Nash efficiency coefficient.

[0026] The multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation provided by this invention has the following advantages:

[0027] This invention fully considers the control mechanism of slope displacement evolution by the synergistic coupling effect of dynamic rainfall infiltration and the strength deterioration of slip zone soil. It accurately describes the nonlinear displacement response of slopes under the combined action of rainfall and creep during long-term service, providing a theoretical basis for slope stability prediction and safety early warning in projects such as deep mineral resource mining, high dam reservoir operation and major transportation infrastructure construction. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 The flowchart shows the multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation provided by the present invention.

[0030] Figure 2 A time curve of the cumulative displacement observation value of a certain measuring point at different times, provided in an embodiment of the present invention;

[0031] Figure 3 This is a curve showing the displacement-rainfall time at the depth of the sliding surface at a certain measuring point at the end of each month, provided as an embodiment of the present invention. Detailed Implementation

[0032] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0033] This invention provides a multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation. It fully considers the control mechanism of the dynamic infiltration of rainfall and the intensity degradation of slip zone soil on the slope displacement evolution process, accurately describes the nonlinear displacement response of slope under the combined action of rainfall and creep during long-term service, and provides a theoretical basis for slope stability prediction and safety early warning in projects such as deep mineral resource mining, high dam reservoir operation and major transportation infrastructure construction.

[0034] Specifically, the inventors discovered through research that during the long-term service of slope engineering, the soil and rock mass not only bears constant overlying self-weight stress but also experiences periodic seepage field changes caused by seasonal rainfall infiltration and groundwater level fluctuations. Natural landslide deposits are essentially multi-layered composite geological bodies composed of the landslide body, slip zone soil, and bedrock. The slip zone soil, as a key layer controlling the overall stability of the slope, continuously deteriorates its physical and mechanical properties under the coupling effect of water and force. During rainfall infiltration, water seeps down along the pores of the landslide body to the slip zone. On the one hand, this weakens the effective stress of the slip zone soil by reducing matrix suction and increasing pore water pressure. On the other hand, after experiencing wet-dry cycles, the internal microstructure of the slip zone soil undergoes irreversible rearrangement and damage, macroscopically manifested as a gradual decrease in shear strength parameters (cohesion c and internal friction angle φ). However, existing slope stability analysis models typically treat the strength parameters of the slip zone soil as time-invariant deterministic constants, and only consider the impact of rainfall through a single reduction of the safety factor. This approach ignores the damage evolution of the slip zone soil during long-term shear displacement, from peak strength to residual strength, and also makes it difficult to accurately distinguish the different contributions of the hydraulic effect caused by rainfall infiltration and the mechanical damage induced by cumulative shear displacement to strength degradation. As a result, the gradual failure process of rainfall-induced landslides is oversimplified.

[0035] Meanwhile, the impact of rainfall on slope displacement rate is not a simple linear superposition. When rainwater infiltrates into the slip zone, the increased water content of the slip zone soil leads to a significant acceleration of the creep rate. The accumulation of creep displacement further exacerbates the deterioration of strength parameters, forming a multi-physics positive feedback loop of "rainfall infiltration → reduced matrix suction → accelerated creep → increased cumulative displacement → strength deterioration → decreased stability". Existing prediction models mostly treat rainfall as an independent external triggering factor for ex-post correction, or regard strength deterioration as a pure time function unrelated to rainfall, failing to establish a unified coupling framework of "dynamic rainfall input → time-varying evolution of slip zone strength → displacement rate response".

[0036] Therefore, this invention starts from the underlying mechanism of multi-physics synergy, proposing to use cumulative displacement as an embedded metric for slip zone soil strength damage, and constructing an exponential decay degradation model of strength parameters with displacement. Based on this, for two types of physical models—not limited to the limit equilibrium method and the finite element method—a rainfall-coupled dynamic displacement rate prediction submodule is established, introducing a creep scaling factor that dynamically changes with effective rainfall. Then, through a recursive probability estimation scheme, based on the likelihood function value of each model's prediction error, the weights of each model are automatically and in real-time updated, ultimately forming a complete technical chain of "dynamic rainfall input → time-varying evolution of slip zone strength → dual-model synergistic prediction → weight self-correction fusion." This method does not simply superimpose rainfall and strength degradation as two independent empirical correction terms, but rather allows rainfall to first influence displacement rate prediction through the dynamic creep scaling factor, and then drive the gradual degradation of slip zone strength parameters through real-time feedback of cumulative displacement, thus maintaining a clear division of labor and synergistic relationship among rainfall effects, strength degradation, and mechanical loading in the model expression.

[0037] Please see Figure 1 This invention provides a multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation, comprising the following steps:

[0038] Step S1: Obtain engineering geological survey data of the target slope, including the physical and mechanical parameters of the sliding body and sliding zone soil, and the slope geometric parameters; and obtain the time step relative to the time step to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step; the cumulative displacement observations at each time step can be the cumulative deep displacement observations obtained from the inclinometer, all referring to the cumulative displacement relative to the initial state; the initial state is... The state. In this invention, for each time step to be predicted... , constructed by up to the previous time step The historical cumulative displacement observation sequence, therefore, within a prediction period, as the time step... As the process progresses, new historical cumulative displacement observations are continuously received, and the number of elements in the time series window continues to increase. In other words, the length of the time series window is not a fixed value.

[0039] Step S2: Establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions, denoted as slope stability analysis models. , , This indicates the number of types of slope stability analysis models;

[0040] As one implementation method, the slope stability analysis model includes a limit equilibrium model and a finite element model. The slope stability analysis model outputs slope stability indices for each time step using Monte Carlo simulation or a surrogate model method. These indices include a safety factor or an average reliability index; for example, it outputs the safety factor probability distribution, failure probability, or reliability index for each time step. Specifically, the limit equilibrium model calculates the safety factor based on the slice method; the finite element model performs stress-strain analysis based on an elastoplastic constitutive model to obtain the average reliability index.

[0041] Step S3: Construct a damage degradation model for the strength parameters of the slip zone soil. Using cumulative displacement as the damage metric, an exponential decay model is employed to describe the degradation of the slip zone soil strength parameters with increasing cumulative displacement, based on time steps. Cumulative displacement fusion prediction update time step The strength parameters of the slip zone soil, including cohesion and internal friction angle, are substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators;

[0042] As one implementation method, the expression for the damage deterioration model of the slip zone soil strength parameters is:

[0043] (1)

[0044] (2)

[0045] in: and The strength parameters of the slip zone soil are as follows: time step, etc. The cohesive force and internal friction angle; and These are the residual strength parameters of cohesion and the residual strength parameters of internal friction angle, respectively. and These are the peak strength parameters of cohesion and the peak strength parameters of internal friction angle, respectively. and These are the cohesive degradation constant and the internal friction angle degradation constant, respectively, which control the rate of strength decline. For time step Cumulative displacement fusion prediction value.

[0046] Therefore, and As a time step The inputs are substituted into the slope stability analysis model respectively. In the middle, the stability analysis models for each slope were recalculated. At that time step The safety factor or average reliability index.

[0047] Step S4: Construct stability analysis models for each type of slope. The corresponding rainfall-coupled dynamic displacement rate prediction model, based on each slope stability analysis model Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ;

[0048] As one implementation method, time step Dynamic creep scaling factor The expression is:

[0049] (3)

[0050] in: The creep state memory coefficient, ; This is the time memory decay coefficient; The duration of each time step; For time step The dynamic creep scaling factor; This represents the maximum driving force of rainfall. This is the rainfall sensitivity coefficient; For time step The predicted effective rainfall; It is the basic creep scale factor, representing the basic creep rate under rainless conditions; This is a long-term inertia term, representing the degree to which the deviation of the dynamic creep scale factor from the baseline creep state in the previous time step is retained in the current time step. It is used to characterize the memory effect of the target slope on historical rainfall and existing creep state. As a short-term driving term, it reflects the immediate excitation effect of current rainfall and controls the short-term fluctuation range of creep rate. When rainfall suddenly increases, the short-term driving term responds quickly, while the long-term inertial term changes relatively slowly. The product of the two reflects the physical state of instantaneous disturbance based on historical state, which is more consistent with the response characteristics of creep rate to rainfall.

[0051] When slope stability analysis model For the limit equilibrium model, an exponential function relationship is established between the displacement rate and the average reliability index, and a dynamic creep scaling factor that varies with rainfall is introduced, which varies with time step. Predicted displacement rate The expression is:

[0052] (4)

[0053] in: The creep decay coefficient; For the limit equilibrium model at time step The average reliability index output; The exponential function relationship characterizing the displacement rate and the average reliability index;

[0054] When slope stability analysis model When using the finite element model, the relationship between stress and strain rate in creep theory is adopted, with the safety factor FS used as a measure of macroscopic stress level. The displacement rate is proportional to the reciprocal of the safety factor, and its value at time step... Predicted displacement rate The expression is:

[0055] (5)

[0056] in: For the finite element model at time step Output safety factor; The power-law exponent; The functional relationship between displacement rate and safety factor.

[0057] Step S5, using Euler's integral, according to the time step Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value The expression is:

[0058] (6)

[0059] in: The duration of each time step.

[0060] Step S6: Obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value The expression is:

[0061] (7)

[0062] By constructing a dynamic entropy exponential nonlinear power-mean fusion formula, the cumulative displacement prediction fusion result is automatically adjusted for nonlinearity based on the concentration of weights in each slope stability analysis model, reflecting the relative reliability differences among slope stability analysis models.

[0063] Step S7, obtain the target slope at time step Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations To account for the deviation, assuming the prediction error follows a zero-mean Gaussian normal distribution, we construct the likelihood function and calculate the probability for each slope stability analysis model. At time step likelihood function value The stability analysis model for each slope is dynamically updated based on a recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ;

[0064] In this step, the likelihood function value The expression is:

[0065] (8)

[0066] in: For slope stability analysis model The prediction error variance, based on the time-series window The fitting residuals are determined; For slope stability analysis model At time step The likelihood function value means: in the time window Given the given conditions, slope stability analysis model Time step The goodness of fit of the cumulative displacement prediction values For time step The cumulative displacement observations, and They have the same meaning.

[0067] The recursive probability estimation scheme dynamically updates each slope stability analysis model. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ,include:

[0068] Calculate the nonnormalized weights:

[0069] (9)

[0070] in: For slope stability analysis model At time step The posterior model weights; For slope stability analysis model At time step The non-normalized weights;

[0071] Calculate the nonnormalization constant:

[0072] (10)

[0073] in: For time step The nonnormalization constant; For slope stability analysis model At time step The likelihood function value; , This indicates the number of types of slope stability analysis models; For slope stability analysis model At time step The posterior model weights; For slope stability analysis model At time step The non-normalized weights;

[0074] Weight update expression:

[0075] (11)

[0076] in: For slope stability analysis model At time step The posterior model weights; initialization conditions, in When the initial model weights of all slope stability analysis models are equal (i.e., =1 and there is no prior information), the initial model weights are set to be equal. For example, when there are only two slope stability analysis models, the initial model weight for each slope stability analysis model is 0.5.

[0077] Step S8, set the time step Cumulative displacement observations Add to timing window, make Return to step S3.

[0078] In practical applications, step S9 is also included:

[0079] Step S9: Calculate the prediction performance indicators of the weighted fusion model and the single slope stability analysis model, including normalized root mean square error, mean absolute error and Nash efficiency coefficient, and quantitatively evaluate and compare the prediction accuracy of each model.

[0080] This invention also provides a multi-model collaborative prediction system for slope displacement considering the dynamic coupling of rainfall and intensity degradation, comprising:

[0081] The engineering geological survey data and monitoring data acquisition module is used to acquire engineering geological survey data of the target slope, including the physical and mechanical parameters of the sliding body and sliding zone soil and the slope geometric parameters; and to acquire the data relative to the time step to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step;

[0082] A slope stability analysis model is used to establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions. This is represented as a slope stability analysis model. , , This indicates the number of types of slope stability analysis models;

[0083] A damage degradation model for the strength parameters of slip zone soil is used to describe the degradation law of slip zone soil strength parameters with cumulative displacement in an exponential decay form, based on time steps. Cumulative displacement fusion prediction value Update time step The strength parameters of the slip zone soil were determined and substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators;

[0084] A rainfall-coupled dynamic displacement rate prediction model is used to predict slope stability based on each slope stability analysis model. Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ;

[0085] The cumulative displacement prediction module is used to predict displacement based on time steps. Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value ;

[0086] The cumulative displacement fusion prediction module is used to obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value ;

[0087] The model weight update module is used to obtain the target slope at time step. Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations The deviation is calculated for each slope stability analysis model. At time step The likelihood function value is obtained, and the slope stability analysis model is dynamically updated based on the recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ;

[0088] The model accuracy evaluation module is used to quantitatively evaluate and compare the prediction accuracy of each model by using normalized root mean square error, mean absolute error, and Nash efficiency coefficient.

[0089] The multi-model collaborative prediction method and system for slope displacement considering the dynamic coupling of rainfall and intensity degradation provided by this invention has the following advantages:

[0090] (1) By combining the intensity parameter exponential decay model and the rainfall dynamic creep scale factor, the prediction model can respond to both the long-term intensity deterioration trend and the short-term rainfall fluctuation, thus overcoming the technical defect of traditional methods that only focus on a single factor.

[0091] (2) Error self-correction multi-model collaboration is based on the automatic adjustment of model weights with the change of prediction error, without the need for manual intervention, which significantly improves the adaptability of the combined model to different deformation stages.

[0092] (3) This invention constructs an open probabilistic fusion framework. This framework is not only applicable to the fusion of two types of physical models, namely the limit equilibrium method and the finite element method, but can also be extended to more types of numerical models, such as the discrete element method and the matter point method.

[0093] Taking the downstream slope of a hydropower station as an example, a specific embodiment of the present invention is introduced during the model verification stage:

[0094] Step S1: Obtain engineering geological survey data of the target slope. In this embodiment, the research object is the downstream slope of a hydropower station in my country. Inclinometer data is selected as the analysis data. The cumulative deformation value of a certain measuring point is as follows: Figure 2As shown. The inclinometer monitoring data from 49 periods from February 2021 to February 2025 were processed, and the cumulative horizontal displacement at the sliding surface depth at the end of each month was extracted. The displacement-rainfall time curve is shown in the figure. Figure 3 As shown, a time series of observation data for the validation period is formed, with a time series length of 49. The initial state, February 2021, is defined as having a time shift of 0, and March 2021 is defined as the first time step. In this embodiment, the time step scale is monthly, and the duration of each time step is... It is the 30th.

[0095] Step S2: Establish slope stability analysis models. In this embodiment, two types of slope stability analysis models are established: limit equilibrium model M1 and finite element model M2. Each model has the same geometric dimensions and boundary conditions. The geometric dimensions of both models are 1416m in the X direction and 1218m in the Y direction. The boundary conditions are: normal constraints are applied on both sides, the bottom is fixed, and the slope surface is free.

[0096] Step S3: Construct a damage degradation model for the strength parameters of the slip zone soil. Using cumulative displacement as the damage metric, an exponential decay model is constructed to describe the degradation law of the strength parameters of the slip zone soil with cumulative displacement. At each time step t, the current strength parameters cohesion c and internal friction angle are... The model is updated using equations (1) and (2). The model parameters in equations (1) and (2) are obtained from experimental data. After determining the parameters, equations (1) and (2) are:

[0097] (1)

[0098] (2)

[0099] The updated intensity parameters mentioned above, i.e. and As input for the current time step, these values ​​are substituted into each slope stability analysis model to recalculate the safety factor or average reliability index of each model at that time step.

[0100] Step S4: Construct a rainfall-coupled dynamic displacement rate prediction model:

[0101] For the limit equilibrium model M1: establish an exponential function relationship between displacement rate and average reliability index, and introduce the dynamic creep scaling factor that varies with rainfall as shown in equation (3). For the finite element model M2: establish a functional relationship between displacement rate and safety factor, and introduce the dynamic creep scaling factor that varies with rainfall as shown in equation (3).

[0102] Using data from the first 10 months of 2021, from March to December 2021, as the parameter calibration window, the strength degradation parameters were determined using experimental results. Combined with cumulative displacement observations, monthly effective rainfall, and the output results of two types of slope stability analysis models, the dynamic creep scale factor, displacement rate relationship, and prediction error parameters were jointly calibrated. The main parameter values ​​used in this embodiment are shown in Table 1.

[0103] Table 1. Key parameter values ​​for the embodiments

[0104]

[0105] In this embodiment, the creep state memory coefficient is calculated according to... Calculation. When a standardized month is taken hour, =0.850、 =0.880. The verification phase uses... Figure 3 The monthly measured rainfall shown is used instead of the predicted effective rainfall. The value range is 0–106 mm. The prediction error variance is determined using the mean square value of the residuals from the previous 10 months, and is calculated as follows. =0.0210mm² =0.0980mm². In this embodiment, the relevant parameters of the limit equilibrium model M1 are identified by the subscript 1; the relevant parameters of the finite element model M2 are identified by the subscript 2.

[0106] Therefore, equations (4) and (5) are obtained as follows:

[0107] (4)

[0108] (5)

[0109] Initialization conditions: =1.2×10 -4 , =8.0×10 -5 Initial state of effective rainfall =0mm; When making the prediction at the first time step t=1, the initial prior weights of both models are set to 0.5.

[0110] in: , The limit equilibrium model M1 and the finite element model M2 are respectively at time step The predicted displacement rate; and The two models are at time steps respectively. Dynamic creep scaling factor; average reliability index and safety factor These are all dynamic output values ​​recalculated by the corresponding slope stability analysis model at each time step, and are not assigned as fixed parameters.

[0111] Step S5: Based on the established rainfall-coupled dynamic displacement rate prediction model, the cumulative displacement prediction value is calculated using equation (6). The monitoring and prediction time step is one month. To ensure that the dimensions of the displacement rate and the time step are consistent, the numerical calculation in this embodiment uses Δt=30d, and the calculated cumulative displacement is uniformly converted to mm. For different calendar months, the actual number of days in the month can also be used as Δt.

[0112] Step S6, during the process The predicted value at the first time step = 1, with prior model weights P(M1) = P(M2) = 0.5; when When ≥2, the posterior model weights obtained by updating the previous time step using equation (11) are used. The prior model weights are used as the weights for the current time step. The cumulative displacement prediction values ​​of each model obtained from the prior model weights and equation (6) are substituted into equation (7) to calculate the cumulative displacement fusion prediction value for time step t.

[0113] Step S7, obtain the time step The cumulative displacement observations are substituted together with the cumulative displacement predictions of each model into equation (8), where the prediction error variances of the limit equilibrium model and the finite element model are respectively taken as... =0.0210mm², =0.0980mm². Calculate the two models at time step. The likelihood function value is obtained; then the nonnormalized weights, nonnormalized constants and posterior model weights are calculated in sequence according to equations (9) to (11).

[0114] Step S8, set the time step The cumulative displacement observations are added to the time series window of the observation data, and then... = +1, return to step S3 to continue the recursive calculation. The monthly effective rainfall, cumulative displacement observations and corresponding soil parameters from March 2021 to February 2025 are sequentially input into the limit equilibrium model M1 and the finite element model M2. The cumulative displacement prediction results of each single model and the multi-model collaborative fusion prediction results given by equation (7) are shown in Table 2.

[0115] Table 2. Cumulative displacements predicted by different models

[0116]

[0117]

[0118]

[0119] As shown in Table 2, the error between the cumulative displacement and the observed cumulative displacement obtained by multi-model collaborative prediction is significantly smaller than that of the prediction results of the limit equilibrium method and the finite element method alone, which proves the superiority of the multi-model collaborative prediction method.

[0120] Step S9: Calculate the prediction performance indicators of the weighted fusion model and the single model, including normalized root mean square error, mean absolute error and Nash efficiency coefficient, and quantitatively evaluate and compare the prediction accuracy of each model.

[0121] To compare the prediction performance of the multi-model collaborative prediction method proposed in this invention, its prediction performance (normalized root mean square error, mean absolute error, and Nash efficiency coefficient) is compared and analyzed with that of the finite element method and the limit equilibrium method. The comparison results of the performance indicators are shown in Table 3.

[0122] Table 3 Comparison of Predictive Performance Indicators of Each Model

[0123]

[0124] The comparative results quantitatively demonstrate the superiority of the multi-model collaborative prediction method. Regarding error metrics, the normalized root mean square error and mean absolute error (MAO) of the multi-model collaborative prediction method are lower than those of the limit equilibrium method and the finite element method. Its MAO is only about one-third that of a single model. In terms of efficiency coefficient, the Nash efficiency coefficient of the multi-model collaborative prediction method is closest to 1, proving that the prediction results of the multi-model collaborative prediction method have the highest degree of agreement with the actual monitoring sequence and can perfectly explain the actual displacement changes. Therefore, whether considering prediction error or the ability to explain data variation patterns, the multi-model collaborative prediction method consistently outperforms any single model across all evaluation dimensions. This result confirms that by dynamically integrating the advantages of different models and neutralizing their inherent biases, the multi-model collaborative prediction method can generate prediction results that are far more accurate and reliable than those of a single model.

[0125] The slope displacement multi-model collaborative prediction method and system considering the dynamic coupling of rainfall and intensity degradation provided by this invention has the following characteristics:

[0126] 1. Eliminate systematic biases in single models and significantly improve prediction accuracy.

[0127] This invention uses a multi-model averaging framework to weight and fuse the prediction results of various physical models, including the limit equilibrium method and the finite element method, and uses real-time monitoring data to drive the dynamic evolution of model weights.

[0128] 2. Enable real-time dynamic updates of model weights to avoid subjective weight assignment.

[0129] This invention is based on a recursive probability estimation scheme, which uses the posterior probability of the previous time step as the prior of the current time step. This allows the model weights to be automatically adjusted as new monitoring data arrives. When a model has higher prediction accuracy in the near future, its weight naturally increases, and vice versa. This mechanism achieves data-driven objective weighting and avoids interference from subjective human factors.

[0130] 3. A damage degradation model based on material strength parameters is introduced, which conforms to physical reality.

[0131] Traditional slope reliability analysis typically assumes that the strength parameters of the soil and rock mass are time-invariant deterministic values ​​or static random variables, neglecting the crucial physical process of the shear strength of the slip zone soil gradually decreasing from its peak value to its residual strength during shearing. This invention uses cumulative displacement as a damage metric and constructs an exponential decay model to describe the deterioration of cohesion and internal friction angle with displacement. This makes the evolution of strength parameters more consistent with the actual physical process, thereby improving the reliability of long-term deformation prediction.

[0132] 4. Establish a dynamic creep scaling factor coupled with rainfall to capture short-term fluctuations.

[0133] Traditional creep models can only describe long-term trends dominated by intensity degradation and cannot reflect displacement fluctuations caused by short-term stimuli such as rainfall. This invention constructs creep scaling factors that dynamically change with effective rainfall for multiple models, directly coupling the rainfall effect into the displacement rate prediction formula. This enables the models to capture both long-term degradation trends and respond to short-term rainfall fluctuations, improving the models' adaptability to complex environmental conditions.

[0134] 5. Construct an open probabilistic fusion framework with good scalability.

[0135] This invention constructs an open probabilistic fusion framework. This framework is not only applicable to the fusion of two types of physical models—limit equilibrium method and finite element method—but can also be extended to: ① more types of numerical models (such as discrete element method, material point method, etc.); ② the fusion of different qualitative evaluation methods (such as analytic hierarchy process, fuzzy comprehensive evaluation, expert scoring method) in the disaster chain transmission process; ③ the comprehensive evaluation of the results of different expert groups. This openness and scalability give this invention broad application prospects.

[0136] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation, characterized in that, Includes the following steps: Step S1: Obtain engineering geological survey data of the target slope, including physical and mechanical parameters of the sliding body and sliding zone soil and slope geometric parameters. And obtain the time step relative to the time to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step; Step S2: Establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions, denoted as slope stability analysis models. , , This indicates the number of types of slope stability analysis models; Step S3: Construct a damage degradation model for the strength parameters of the slip zone soil. An exponential decay model is used to describe the degradation law of the slip zone soil strength parameters with cumulative displacement, based on time steps. Cumulative displacement fusion prediction value Update time step The strength parameters of the slip zone soil were determined and substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators; Step S4: Construct stability analysis models for each type of slope. The corresponding rainfall-coupled dynamic displacement rate prediction model, based on each slope stability analysis model Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ; Step S5, according to the time step Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value ; Step S6: Obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; Based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value ; Step S7, obtain the target slope at time step Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations The deviation is calculated for each slope stability analysis model. At time step The likelihood function value is obtained, and the slope stability analysis model is dynamically updated based on the recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ; Step S8, set the time step Cumulative displacement observations Add to timing window, make Return to step S3.

2. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, The slope stability analysis model includes at least a limit equilibrium model and a finite element model; the slope stability analysis model outputs slope stability indices for each time step through Monte Carlo simulation or surrogate model methods; the slope stability indices include a safety factor or an average reliability index.

3. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, The expression for the damage deterioration model of the slip zone soil strength parameters is as follows: （1） （2） in: and The strength parameters of the slip zone soil are as follows: time step, etc. The cohesive force and internal friction angle; and These are the residual strength parameters of cohesion and the residual strength parameters of internal friction angle, respectively. and These are the peak strength parameters of cohesion and the peak strength parameters of internal friction angle, respectively. and These are the cohesive degradation constant and the internal friction angle degradation constant, respectively, which control the rate of strength decline. For time step Cumulative displacement fusion prediction value.

4. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, Time step Dynamic creep scaling factor The expression is: （3） in: The creep state memory coefficient, ; This is the time memory decay coefficient; The duration of each time step; For time step The dynamic creep scaling factor; This represents the maximum driving force of rainfall. This is the rainfall sensitivity coefficient; For time step The predicted effective rainfall; It is the basic creep scale factor, representing the basic creep rate under rainless conditions; This is a long-term inertia term, representing the degree to which the deviation of the dynamic creep scale factor from the baseline creep state in the previous time step is retained in the current time step. It is used to characterize the memory effect of the target slope on historical rainfall and existing creep state. As a short-term driving term, it reflects the immediate excitation effect of current rainfall and controls the short-term fluctuation range of creep rate. When rainfall suddenly increases, the short-term driving term responds quickly, while the long-term inertial term changes relatively slowly. The product of the two reflects the physical state of instantaneous disturbance based on historical state, which is more consistent with the response characteristics of creep rate to rainfall.

5. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, When slope stability analysis model When it is a limit equilibrium model, its time step Predicted displacement rate The expression is: （4） in: The creep decay coefficient; For the limit equilibrium model at time step The average reliability index output; The exponential function relationship between displacement rate and average reliability index; When slope stability analysis model When it is a finite element model, its time step Predicted displacement rate The expression is: （5） in: For the finite element model at time step Output safety factor; The power-law exponent; The functional relationship between displacement rate and safety factor.

6. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, Each slope stability analysis model At time step Cumulative displacement prediction value The expression is: （6） in: The duration of each time step.

7. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, Target slope in time step Cumulative displacement fusion prediction value The expression is: （7） By constructing a dynamic entropy exponential nonlinear power-mean fusion formula, the cumulative displacement prediction fusion result is automatically adjusted for nonlinearity based on the concentration of weights in each slope stability analysis model, reflecting the relative reliability differences among slope stability analysis models.

8. The multi-model collaborative prediction method for slope displacement considering the dynamic coupling of rainfall and intensity degradation as described in claim 1, characterized in that, Calculate the stability analysis model for each slope At time step likelihood function value The expression is: （8） in: For slope stability analysis model The prediction error variance, based on the time-series window The fitting residuals are determined; For slope stability analysis model At time step The likelihood function value means: in the time window Given the given conditions, slope stability analysis model Time step The goodness of fit of the cumulative displacement prediction values For time step The cumulative displacement observations, and They have the same meaning.

9. The multi-model collaborative prediction method for slope displacement considering dynamic coupling of rainfall and intensity degradation as described in claim 8, characterized in that, The recursive probability estimation scheme dynamically updates each slope stability analysis model. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ,include: Calculate the nonnormalized weights: （9） in: For slope stability analysis model At time step The posterior model weights; For slope stability analysis model At time step The non-normalized weights; Calculate the nonnormalization constant: （10） in: For time step The nonnormalization constant; For slope stability analysis model At time step The likelihood function value; , This indicates the number of types of slope stability analysis models; For slope stability analysis model At time step The posterior model weights; For slope stability analysis model At time step The non-normalized weights; Weight update expression: （11） in: For slope stability analysis model At time step The posterior model weights; in When the initial model weights of all slope stability analysis models are equal (i.e., =1 and there is no prior information), the initial model weights are set to be equal. .

10. A multi-model collaborative prediction system for slope displacement considering the dynamic coupling of rainfall and intensity degradation, characterized in that, The method for collaborative prediction of slope displacement using multiple models considering the dynamic coupling of rainfall and intensity degradation as described in any one of claims 1 to 9 includes: The engineering geological survey data and monitoring data acquisition module is used to acquire engineering geological survey data of the target slope, including the physical and mechanical parameters of the sliding body and sliding zone soil and the slope geometric parameters; and to acquire the data relative to the time step to be predicted. Timing window , These represent the historical cumulative displacement observations at each time step; A slope stability analysis model is used to establish at least two types of slope stability analysis models with the same geometric dimensions and boundary conditions. This is represented as a slope stability analysis model. , , This indicates the number of types of slope stability analysis models; A damage degradation model for the strength parameters of slip zone soil is used to describe the degradation law of slip zone soil strength parameters with cumulative displacement in an exponential decay form, based on time steps. Cumulative displacement fusion prediction value Update time step The strength parameters of the slip zone soil were determined and substituted into each slope stability analysis model. In this process, each slope stability analysis model is obtained. At time step Slope stability indicators; A rainfall-coupled dynamic displacement rate prediction model is used to predict slope stability based on each slope stability analysis model. Rainfall response characteristics and time steps The predicted effective rainfall amount is obtained by time step. Dynamic creep scaling factor According to each slope stability analysis model The relationship between slope stability indices and dynamic displacement rate is investigated, a dynamic displacement rate expression is constructed, and a time step is used. Dynamic creep scaling factor By revising the dynamic displacement rate expression, we obtain the stability analysis model for each slope. At time step Predicted displacement rate ; The cumulative displacement prediction module is used to predict displacement based on time steps. Predicted displacement rate Combined with time steps Cumulative displacement fusion prediction value Each slope stability analysis model was obtained. At time step Cumulative displacement prediction value ; The cumulative displacement fusion prediction module is used to obtain the stability analysis model for each slope. At time step Posterior model weights As a time step Prior model weights; based on each slope stability analysis model At time step The prior model weights are used to construct a dynamic entropy exponential nonlinear power-mean fusion formula for each slope stability analysis model. At time step Cumulative displacement prediction value Perform weighted fusion and output the target slope at time step Cumulative displacement fusion prediction value ; The model weight update module is used to obtain the target slope at time step. Cumulative displacement observations According to each slope stability analysis model At time step Cumulative displacement prediction value and time step Cumulative displacement observations The deviation is calculated for each slope stability analysis model. At time step The likelihood function value is obtained, and the slope stability analysis model is dynamically updated based on the recursive probability estimation scheme. At time step The prior model weights are used to obtain their weights at time step. Posterior model weights ; The model accuracy evaluation module is used to quantitatively evaluate and compare the prediction accuracy of each model by using normalized root mean square error, mean absolute error, and Nash efficiency coefficient.

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