A landslide prediction method based on landslide deformation and damage type adaptive prediction model

Abstract

The present application relates to a kind of landslide prediction methods based on landslide deformation damage type adaptation prediction model, belong to landslide prediction and forecasting technical field.The specific steps of the method of the present application are as follows: determine its deformation damage type by landslide monitoring curve characteristics and formation influencing factor;According to the sudden type landslide adaptation Verhulst inverse function model, the gradual change type landslide adaptation GM (1,1) power model selects appropriate model;Finally, extract the displacement monitoring data in the acceleration stage of landslide, substitute into corresponding model, determine parameter using nonlinear fitting, finally solve the landslide occurrence time prediction value.The present application can establish the accurate corresponding relationship between landslide deformation damage type and prediction model, and can improve the prediction accuracy of the occurrence time of different types of landslides.

Description

Technical Field

[0001] This invention relates to a landslide prediction method based on a landslide deformation and failure type adaptation prediction model, belonging to the field of landslide prediction and forecasting technology. Background Technology

[0002] Landslides, as a common geological hazard, often pose a serious threat to people's lives and property, transportation infrastructure, and the ecological environment due to their suddenness and destructiveness. Although significant progress has been made in the field of landslide prediction and forecasting, with successful prediction cases such as the Xintan landslide, Jimingsi landslide, and Huangci landslide effectively preventing numerous casualties and property losses, accurate prediction of landslide timing remains a global challenge, and the actual challenges faced in forecasting work far outweigh the achievements already made.

[0003] Displacement monitoring data can intuitively reflect the changes and development trends of slopes. Landslide prediction research based on displacement monitoring data can provide crucial evidence for the formulation of disaster reduction and prevention strategies, possessing significant practical importance and substantial economic and social benefits. Therefore, it has become one of the core directions of landslide prediction research. Currently, various landslide prediction models have been proposed in the field, such as the Saito model, the Fukuzono model, the Su Aijun model, and the biological growth model. Most of these models are based on creep theory. However, the causes of landslides are complex and diverse. Under the influence of human factors or natural factors such as excavation loading, reservoir water level fluctuations, and irrigation, their deformation and failure behaviors exhibit various types, and the corresponding displacement-time curves differ significantly from the landslide curves generated by natural creep under gravity. Some scholars have classified landslides into stable, gradual, and sudden types, and clarified the mechanical conditions for various deformation behaviors, confirming the diverse characteristics of landslide deformation and failure behaviors.

[0004] Most existing traditional landslide prediction methods are based on fitting and extrapolating from conventional monitoring data. They generally assume that landslide deformation exhibits three stages: deceleration, isokinesis, and acceleration, with the corresponding displacement curves being inverted "S" shapes. However, not all landslides follow this pattern in reality. Furthermore, the selection of prediction models often fails to adequately consider the specific type, formation pattern, and triggering factors of landslides. There is a lack of targeted research on landslides with different deformation evolution processes and formation mechanisms, and no established correspondence between early warning and prediction models and landslide deformation behavior. This leads to the blind selection of prediction models, making it difficult to achieve accurate predictions for various types of landslides and severely impacting the success rate of landslide prediction. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a landslide prediction method based on a landslide deformation and failure type adaptation prediction model. This invention can establish an accurate correspondence between landslide deformation and failure types and prediction models, and can also improve the prediction accuracy of the occurrence time of different types of landslides.

[0006] To achieve the above objectives, the technical solution provided by this invention is a landslide prediction method based on a landslide deformation and failure type adaptation prediction model, comprising the following steps:

[0007] (1) Determination of landslide deformation and failure type: Based on the characteristics of the landslide monitoring curve and the influencing factors, the deformation and failure type of the landslide is determined; among them, the deformation and failure types of landslides include sudden landslides and gradual landslides.

[0008] (2) Prediction model selection: Select the corresponding prediction model for the determined landslide deformation and failure type; among them, sudden landslides are adapted to the Verhulst inverse function model, and gradual landslides are adapted to the GM(1,1) power model.

[0009] (3) Model parameter determination and landslide prediction:

[0010] For sudden landslides, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the Verhulst inverse function model, and the model parameters are determined using a nonlinear fitting method. According to the formula Calculate the predicted time of landslide occurrence;

[0011] For a gradually changing landslide, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the GM(1,1) power model, and the model parameters are determined using a nonlinear fitting method. Power index Calculate the displacement value corresponding to the maximum acceleration criterion, substitute it into the time response function of the GM(1,1) power model, and apply the formula... Solve for the predicted time of landslide occurrence.

[0012] A further improvement to the above method is as follows:

[0013] The method for determining the deformation and failure type of a landslide in step (1) is as follows: if the landslide is caused by excavation and loading, human irrigation and / or changes in reservoir water level, the landslide is judged to be sudden; if the landslide is caused by natural creep of rock and soil under gravity, the landslide is judged to be gradual.

[0014] The principle of the Verhulst inverse function model in step (2) is as follows:

[0015] A non-negative, equally spaced displacement monitoring data sequence is provided. , ,right Performing a cumulative generation transformation yields:

[0016] ;

[0017] In the formula, t is the time sequence number at equal time intervals, corresponding to the time progress of landslide displacement monitoring. ; n is the equally spaced displacement monitoring data sequence The total number of data points, i.e. the total number of displacement monitoring data collected at equal intervals;

[0018] ; ;

[0019] Will Fitting the Verhulst first-order whitening nonlinear differential equation yields:

[0020] ;

[0021] In the formula, For parameters;

[0022] The general solution fitted to the Verhulst first-order whitening nonlinear differential equation is:

[0023] ;

[0024] Solving for the general solution, we obtain the inverse function:

[0025] ;

[0026] when hour, That is, through Calculate the predicted time of landslide occurrence.

[0027] The principle of the GM(1,1) power model in step (2) is as follows:

[0028] set up ) The original data sequence is a non-negative unimodal. for 1-AGO sequence, for The sequence is generated from the nearest mean, and , and If all numbers are sequences, then the nonlinear model that satisfies the grey modeling conditions, i.e., the GM(1,1) power model, is:

[0029] ;

[0030] In the formula, It is a sequence Data elements in; It is a sequence Data elements in; It is a sequence Data elements in; Displacement monitoring data sequences at equal time intervals Time sequence number; It is a power exponent;

[0031] Displacement sequences monitored at equal time intervals during landslides , displacement sequence The expression format of displacement monitoring values ​​at various time intervals. ;

[0032] A sequence generated by a single accumulation ,in, , ;Right now This is to generate the sequence after AGO processing by accumulating the original displacement data once. The representation of each data element in the text;

[0033] for The sequence generated by the nearest mean ,in, , ;Right now For sequence The nearest neighbor mean generation sequence The representation of each data element in the text;

[0034] In the formula, Displacement monitoring data sequences representing equal time intervals Time sequence number;

[0035] The whitening equation for the GM(1,1) power model is:

[0036] ;

[0037] The general solution to the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, is:

[0038] ;

[0039] In the formula, a and b are coefficients; c is a constant of the general solution of the differential equation; It is a power exponent, and ; Displacement monitoring data sequences at equal time intervals Time sequence number;

[0040] make:

[0041] ;

[0042] Then the parameter list of the GM(1,1) power model The least squares estimate is:

[0043] ;

[0044] Taking the derivative of the whitening equation for the GM(1,1) power model, we get:

[0045] ;

[0046] The moment when the maximum value is reached is the moment when the speed reaches its maximum value, because hour, Having obtained an extreme value, let Solving the equation, we get:

[0047] ;

[0048] right Taking the derivative, we get:

[0049] ;

[0050] The moment when the acceleration reaches its maximum value is At the moment when the maximum value is reached, because hour, Having obtained an extreme value, let Solving the equation, we get:

[0051] ;

[0052] Power index When the values ​​of a and b obtained through grey system theory are both greater than 0, then:

[0053] ;

[0054] Since the displacement at the moment of maximum acceleration should be less than the displacement at the moment of maximum velocity, the displacement at the moment when acceleration reaches its maximum value is:

[0055] ;

[0056] Substituting the displacement at the moment when the acceleration reaches its maximum value into the general solution of the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, we can solve the equation to obtain:

[0057] ;

[0058] The predicted time of occurrence of the asymptotic landslide, t, is calculated by solving the equation. B This is the predicted time of occurrence for the asymptotic landslide.

[0059] The nonlinear fitting methods for sudden landslides and gradual landslides in step (3) are as follows:

[0060] Method 1: An optimization algorithm combining the Marquardt method and the general global optimization method is adopted, and the measured displacement data is nonlinearly fitted using 1stOpt software to obtain the model parameters;

[0061] Method 2: Let The grey system principle is used to obtain and The value is obtained by substituting the optimal data point determined by the principle of minimum error into the general solution as known conditions. The value is then determined based on the principle of minimizing error. value.

[0062] As can be seen from the above technical solution, the landslide prediction method provided by this invention, based on a landslide deformation and failure type adaptation prediction model, determines the deformation and failure type by analyzing the characteristics of landslide monitoring curves and influencing factors; it selects a suitable model by adapting the Verhulst inverse function model for sudden landslides and the GM (1,1) power model for gradual landslides; finally, it extracts displacement monitoring data from the landslide acceleration stage, substitutes it into the corresponding model, uses nonlinear fitting to determine the parameters, and finally solves for the predicted landslide occurrence time. This invention has the following advantages over existing technologies:

[0063] (1) The technical solution adopted in this invention establishes for the first time the adaptation relationship between sudden and gradual landslides and corresponding prediction models, which completely solves the problem of blind model selection in traditional methods.

[0064] (2) The technical solution adopted in this invention selects a model with matching curve characteristics (GM(1,1) power model, Verhulst inverse function model) for different landslide types, which provides more sufficient modeling basis and stronger fitting.

[0065] (3) The technical solution adopted in this invention determines the model parameters and power exponent through nonlinear fitting, which avoids the limitations of fixed power exponent, better fits the actual displacement data change trend, and improves the accuracy of parameters.

[0066] (4) The technical solution adopted in this invention has been verified by actual landslide cases, and the prediction error has been significantly reduced, the probability of successful prediction has been greatly improved, and it can provide a more reliable decision-making basis for disaster reduction and prevention. Attached Figure Description

[0067] Figure 1 Flowchart of a landslide prediction method based on a landslide deformation and failure type adaptation prediction model. Detailed Implementation

[0068] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0069] The landslide prediction method based on a landslide deformation and failure type adaptation prediction model provided by this invention includes the following steps:

[0070] (1) Determination of landslide deformation and failure type: Based on the characteristics of the landslide monitoring curve and the influencing factors, the deformation and failure type of the landslide is determined; among them, the deformation and failure types of landslides include sudden landslides and gradual landslides.

[0071] The method for determining the deformation and failure type of a landslide is as follows: if the landslide is caused by excavation and loading, human irrigation and / or reservoir water level changes, it is judged as a sudden landslide; if the landslide is caused by the natural creep of the rock and soil mass under gravity, it is judged as a gradual landslide.

[0072] (2) Prediction model selection: Select the corresponding prediction model for the determined landslide deformation and failure type; among them, sudden landslides are adapted to the Verhulst inverse function model, and gradual landslides are adapted to the GM(1,1) power model.

[0073] The principle of the Verhulst inverse function model is as follows:

[0074] A non-negative, equally spaced displacement monitoring data sequence is provided. , ,right Performing a cumulative generation transformation yields:

[0075] ;

[0076] In the formula, t is the time sequence number at equal time intervals, corresponding to the time progress of landslide displacement monitoring. ; n is the equally spaced displacement monitoring data sequence The total number of data points, i.e. the total number of displacement monitoring data collected at equal intervals;

[0077] ; ;

[0078] Will Fitting the Verhulst first-order whitening nonlinear differential equation yields:

[0079] ;

[0080] In the formula, For parameters;

[0081] The general solution fitted to the Verhulst first-order whitening nonlinear differential equation is:

[0082] ;

[0083] Solving for the general solution, we obtain the inverse function:

[0084] ;

[0085] when hour, That is, through Calculate the predicted time of landslide occurrence.

[0086] The principle of the GM(1,1) power model is as follows:

[0087] set up ) The original data sequence is a non-negative unimodal. for 1-AGO sequence, for The sequence is generated from the nearest mean, and , and If all numbers are sequences, then the nonlinear model that satisfies the grey modeling conditions, i.e., the GM(1,1) power model, is:

[0088] ;

[0089] In the formula, It is a sequence Data elements in; It is a sequence Data elements in; It is a sequence Data elements in; Displacement monitoring data sequences at equal time intervals Time sequence number; It is a power exponent;

[0090] Displacement sequences monitored at equal time intervals during landslides , displacement sequence The expression format of displacement monitoring values ​​at various time intervals. ;

[0091] A sequence generated by a single accumulation ,in, , ;Right now This is to generate the sequence after AGO processing by accumulating the original displacement data once. The representation of each data element in the text;

[0092] for The sequence generated by the nearest mean ,in, , ;Right now For sequence The nearest neighbor mean generation sequence The representation of each data element in the text;

[0093] In the formula, Displacement monitoring data sequences representing equal time intervals Time sequence number;

[0094] The whitening equation for the GM(1,1) power model is:

[0095] ;

[0096] The general solution to the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, is:

[0097] ;

[0098] In the formula, a and b are coefficients; c is a constant of the general solution of the differential equation; It is a power exponent, and ; Displacement monitoring data sequences at equal time intervals Time sequence number;

[0099] make:

[0100] ;

[0101] Then the parameter list of the GM(1,1) power model The least squares estimate is:

[0102] ;

[0103] Taking the derivative of the whitening equation for the GM(1,1) power model, we get:

[0104] ;

[0105] The moment when the maximum value is reached is the moment when the speed reaches its maximum value, because hour, Having obtained an extreme value, let Solving the equation, we get:

[0106] ;

[0107] right Taking the derivative, we get:

[0108] ;

[0109] The moment when the acceleration reaches its maximum value is At the moment when the maximum value is reached, because hour, Having obtained an extreme value, let Solving the equation, we get:

[0110] ;

[0111] Power index When the values ​​of a and b obtained through grey system theory are both greater than 0, then:

[0112] ;

[0113] Since the displacement at the moment of maximum acceleration should be less than the displacement at the moment of maximum velocity, the displacement at the moment when acceleration reaches its maximum value is:

[0114] ;

[0115] Substituting the displacement at the moment when the acceleration reaches its maximum value into the general solution of the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, we can solve the equation to obtain:

[0116] ;

[0117] The predicted time of occurrence of the asymptotic landslide, t, is calculated by solving the equation. B This is the predicted time of occurrence for the asymptotic landslide.

[0118] (3) Model parameter determination and landslide prediction:

[0119] For sudden landslides, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the Verhulst inverse function model, and the model parameters are determined using a nonlinear fitting method. According to the formula Calculate the predicted time of landslide occurrence;

[0120] For a gradually changing landslide, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the GM(1,1) power model, and the model parameters are determined using a nonlinear fitting method. Power index Calculate the displacement value corresponding to the maximum acceleration criterion, substitute it into the time response function of the GM(1,1) power model, and apply the formula... Solve for the predicted time of landslide occurrence.

[0121] The nonlinear fitting methods for sudden landslides and gradual landslides are as follows:

[0122] Method 1: An optimization algorithm combining the Marquardt method and the general global optimization method is adopted, and the measured displacement data is nonlinearly fitted using 1stOpt software to obtain the model parameters;

[0123] Method 2: Let The grey system principle is used to obtain and The value is obtained by substituting the optimal data point determined by the principle of minimum error into the general solution as known conditions. The value is then determined based on the principle of minimizing error. value.

[0124] The Huangci landslide, a sudden landslide, and the Salershan new landslide, a gradual landslide, were used as experimental subjects. The above steps were used to predict the timing of the landslides, thus verifying the landslide prediction effectiveness of the method of the present invention.

[0125] The Huangci landslide is located on the southern edge of Heifangtai, north of Huangci Village, Yangguoxia Town. The elevation difference between the foot of the slope and the top of the tundra is approximately 100 meters. At the foot of the slope is a perennial irrigation canal, and a densely populated residential area lies just south of the canal. A hundred meters from the foot of the slope is the Yangguoxia Hydropower Station, a road connecting Lanzhou to the Yangguoxia Chemical Plant. There were originally 63 households and over 300 residents between the landslide and the road. The leading edge of the landslide reaches directly to Huangci Village, posing a direct threat to the lives and property of the villagers. The landslide was controlled by multiple factors, and its scale and complexity are significant. The landslide volume is nearly 60 mm. 3 The bedrock surface dips towards the free face at an angle of 100° to 200°, easily leading to bedding-parallel sliding along the bedrock surface. Extensive irrigation activities have increased the water volume in the work area to twice the rainfall, raising the groundwater level. The weak structural surfaces are continuously soaked and softened, reducing soil strength. Under its own weight, the soil creeps and deforms towards the free face. Based on relevant literature, the displacement monitoring data at monitoring point B2 of the Huangci landslide are shown in Table 1.

[0126] Table 1 Monitoring data from monitoring point B2 of Huangci landslide

[0127]

[0128] The Huangci landslide occurred at 2:30 AM on January 30, 1995. Since the Huangci landslide was a typical irrigation-induced landslide, as shown by the deformation monitoring data in Table 1, the deformation increased rapidly in a short period. This indicates that the Huangci landslide was a sudden landslide. According to the landslide prediction approach of this invention, the Verhulst inverse function model should be used for prediction.

[0129] The last data point was discarded, meaning that displacement monitoring data from January 23 to January 28, 1995, were selected for prediction and forecasting. In this embodiment, nonlinear fitting was performed using 1stOpt software, yielding the following values: a=0.1181, b=0.0176, c=7.1480.

[0130] Substitute the parameters obtained from the nonlinear fitting into have to:

[0131] ;

[0132] The Verhulst inverse function model predicted the landslide to occur on January 29, 1995, one day earlier than the actual occurrence. For comparison, the GM(1,1) power model was also used for prediction. Calculations showed that the acceleration maximum criterion predicted the landslide to occur on January 24, 1995, six days earlier than the actual occurrence. The prediction results using both models are shown in Table 2.

[0133] Table 2. Prediction results of the Huangci landslide sudden landslide time based on monitoring data from monitoring point B2.

[0134]

[0135] As shown in Table 2, the prediction results of the GM(1,1) power model have a larger gap with the actual time of landslide occurrence. This indicates that when predicting and forecasting sudden landslides in Huangci caused by human irrigation, the Verhulst inverse function model should be selected for prediction.

[0136] The Salershan landslide is located on the north bank of the Baxie River in Guoyuan Township, Dongxiang Autonomous County, Linxia Prefecture, Gansu Province. Frequent seismic activity, complex geological structure, fractured rock mass, and continuous rainfall prior to the landslide were the main causes of its occurrence. The landslide occurred on March 25, 1986.

[0137] The deformation and development process of the new landslide at Salershan is as follows: In early 1979, a discontinuous east-west tensional crack L1, several hundred meters long, appeared on the rear part of the northern slope of the Salershan summit. By 1982, a ground fissure L2 had also appeared behind Saler Village. In February 1983, a new fissure L3 appeared in the area of ​​Kushun Village on the Class IV platform. Subsequently, all fissures developed rapidly. On March 7, 1983, a landslide occurred. The final landslide occurred on March 25, 1986. Displacement monitoring data of the new Salershan landslide are shown in Table 3.

[0138] Table 3 Displacement monitoring data of the new landslide at Salershan.

[0139]

[0140] Based on the causes of the landslide and the entire process of its deformation and instability, it can be determined that this landslide is an asymptotic landslide. According to the prediction approach of this invention, the GM(1,1) power model and the acceleration maximum criterion should be selected for prediction. For comparison, the prediction results of the Verhulst inverse function model were also calculated, and the results are shown in Table 4.

[0141] Table 4. Prediction results of the dramatic landslide time of the new landslide at Salershan based on displacement monitoring data.

[0142]

[0143] As shown in Table 4, the prediction results of the GM(1,1) power model are more accurate, while the prediction time of the Verhulst inverse function model differs significantly from the actual occurrence time of the landslide. This indicates that when predicting and forecasting progressive landslides caused by natural creep under gravity, the GM(1,1) power model should be selected as much as possible.

[0144] The experimental results show that this invention can establish a precise correspondence between landslide deformation and failure types and prediction models, avoiding the blind selection of models. Moreover, it can significantly improve the prediction accuracy of the occurrence time of different types of landslides by optimizing the parameters through nonlinear fitting, providing a reliable basis for disaster reduction and prevention.

Claims

1. A landslide prediction method based on a landslide deformation and failure type adaptation prediction model, characterized in that, Includes the following steps: (1) Determination of landslide deformation and failure type: Based on the characteristics of the landslide monitoring curve and the influencing factors, the deformation and failure type of the landslide is determined; among them, the deformation and failure types of landslides include sudden landslides and gradual landslides. (2) Prediction model selection: Select the corresponding prediction model for the determined landslide deformation and failure type; among them, sudden landslides are adapted to the Verhulst inverse function model, and gradual landslides are adapted to the GM(1,1) power model. (3) Model parameter determination and landslide prediction: For sudden landslides, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the Verhulst inverse function model, and the model parameters are determined using a nonlinear fitting method. According to the formula Calculate the predicted time of landslide occurrence; For a gradually changing landslide, displacement monitoring data from the acceleration phase of the landslide are extracted, substituted into the GM(1,1) power model, and the model parameters are determined using a nonlinear fitting method. Power index Calculate the displacement value corresponding to the maximum acceleration criterion, substitute it into the time response function of the GM(1,1) power model, and apply the formula... Solve for the predicted time of landslide occurrence.

2. The landslide prediction method based on a landslide deformation and failure type adaptation prediction model according to claim 1, characterized in that, The method for determining the deformation and failure type of a landslide in step (1) is as follows: if the landslide is caused by excavation and loading, human irrigation and / or changes in reservoir water level, the landslide is judged to be sudden; if the landslide is caused by natural creep of rock and soil under gravity, the landslide is judged to be gradual.

3. The landslide prediction method based on a landslide deformation and failure type adaptation prediction model according to claim 1, characterized in that, The principle of the Verhulst inverse function model in step (2) is as follows: A non-negative, equally spaced displacement monitoring data sequence is provided. , ,right Performing a cumulative generation transformation yields: ； In the formula, t is the time sequence number at equal time intervals, corresponding to the time progress of landslide displacement monitoring. ; n is the equally spaced displacement monitoring data sequence The total number of data points, i.e. the total number of displacement monitoring data collected at equal intervals; ； ； Will Fitting the Verhulst first-order whitening nonlinear differential equation yields: ； In the formula, For parameters; The general solution fitted to the Verhulst first-order whitening nonlinear differential equation is: ； Solving for the general solution, we obtain the inverse function: ； when hour, That is, through Calculate the predicted time of landslide occurrence.

4. The landslide prediction method based on a landslide deformation and failure type adaptation prediction model according to claim 1, characterized in that, The principle of the GM(1,1) power model in step (2) is as follows: set up ) The original data sequence is a non-negative unimodal. for 1-AGO sequence, for The sequence is generated from the nearest mean, and , and If all numbers are sequences, then the nonlinear model that satisfies the grey modeling conditions, i.e., the GM(1,1) power model, is: ； In the formula, It is a sequence Data elements in; It is a sequence Data elements in; It is a sequence Data elements in; Displacement monitoring data sequences at equal time intervals Time sequence number; It is a power exponent; Displacement sequences monitored at equal time intervals during landslides , displacement sequence The expression format of displacement monitoring values ​​at various time intervals. ; A sequence generated by a single accumulation ,in, , ;Right now This is to generate the sequence obtained after AGO processing by accumulating the original displacement data once. The representation of each data element in the text; for The sequence generated by the nearest mean, ,in, , ;Right now For sequence Neighboring mean generation sequence The representation of each data element in the text; In the formula, Displacement monitoring data sequences representing equal time intervals Time sequence number; The whitening equation for the GM(1,1) power model is: ； The general solution to the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, is: ； In the formula, a and b are coefficients; c is a constant of the general solution of the differential equation; It is a power exponent, and ; Displacement monitoring data sequences at equal time intervals Time sequence number; make: ； Then the parameter list of the GM(1,1) power model The least squares estimate is: ； Taking the derivative of the whitening equation for the GM(1,1) power model, we get: ； The moment when the maximum value is reached is the moment when the speed reaches its maximum value, because hour, Having obtained an extreme value, let Solving the equation, we get: ； right Taking the derivative, we get: ； The moment when the acceleration reaches its maximum value is At the moment when the maximum value is reached, because hour, Having obtained an extreme value, let Solving the equation, we get: ； Power index When the values ​​of a and b obtained through grey system theory are both greater than 0, then: ； Since the displacement at the moment of maximum acceleration should be less than the displacement at the moment of maximum velocity, the displacement at the moment when acceleration reaches its maximum value is: ； Substituting the displacement at the moment when the acceleration reaches its maximum value into the general solution of the whitening equation of the GM(1,1) power model, i.e., the time response function of the GM(1,1) power model, we can solve the equation to obtain: ； The predicted time of occurrence of the asymptotic landslide, t, is calculated by solving the equation. B This represents the predicted time of occurrence for asymptotic landslides.

5. The landslide prediction method based on a landslide deformation and failure type adaptation prediction model according to claim 1, characterized in that, The nonlinear fitting methods for sudden landslides and gradual landslides in step (3) are as follows: Method 1: An optimization algorithm combining the Marquardt method and the general global optimization method is adopted, and the measured displacement data is nonlinearly fitted using 1stOpt software to obtain the model parameters; Method 2: Let The grey system principle is used to obtain and The value is obtained by substituting the optimal data point determined by the principle of minimum error into the general solution as known conditions. The value is then determined based on the principle of minimizing error. value.

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