Method for evaluating stability of tailing dam and predicting dam break risk

Abstract

The invention is suitable for the technical field of tailing dam risk prediction, and particularly relates to a tailing dam stability evaluation and dam break risk prediction method, which comprises the following steps: S1, establishing a tailing dam displacement prediction model, analyzing historical displacement data, constructing a shadow equation and a time response function, generating a vertical settlement displacement prediction sequence, and calculating a vertical settlement displacement prediction model; error checking is carried out; s2, calculating the normalized weight of each influence index, forming an index weight matrix, calculating the grey correlation degree of each factor, obtaining an overall grey effect measurement value in combination with the index weight, and dividing the safety state of the tailing dam; and S3, determining a risk level by integrating the evaluation system and risk early warning and combining the prediction model and a gray effect measurement method. According to the method, the improved Verhulst model is adopted, the shadow equation and the time response function are combined, the parameters are optimized through the least square method, the vertical settlement displacement of the tailing dam can be predicted more accurately, and the displacement prediction precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of tailings dam risk prediction, and in particular relates to a method for tailings dam stability assessment and dam break risk prediction. Background Art

[0002] Tailings dams, as a crucial component of mining operations, have long garnered significant attention worldwide for the safety issues they raise. A dam failure can easily trigger secondary disasters such as debris flows, landslides, and soil and water pollution, further exacerbating the hazards of the accident and causing immeasurable damage to people's lives, property, and the ecological environment. Currently, some tailings dam disaster prevention and control efforts suffer from a disconnect between theory and practice, and a separation between prediction and evaluation models, leading to frequent tailings dam instability and failures.

[0003] At present, most of the existing technologies are aimed at dam stability analysis based on safety factor calculation, single factor qualitative safety evaluation, local safety monitoring, etc., but it is difficult to achieve a comprehensive assessment and prediction of the overall stability of the dam. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for tailings dam stability assessment and dam break risk prediction, aiming to solve the problem that the existing technology is difficult to achieve a comprehensive assessment and prediction of the overall stability of the dam body.

[0005] The present invention is achieved by providing a method for tailings dam stability assessment and dam failure risk prediction, the method comprising:

[0006] Step S1: Establish a tailings dam displacement prediction model, use the improved Verhulst model to analyze historical displacement data, construct shadow equations and time response functions, use the least squares method to estimate parameters, generate vertical settlement displacement prediction sequences, and perform error testing;

[0007] Step S2: Introduce the relative importance grey correlation method, calculate the normalized weight of each influencing indicator by constructing a judgment matrix and normalization processing, and form an indicator weight matrix. Use the grey effect measurement method to construct a decision matrix, calculate the grey correlation degree of each factor, and combine the indicator weights to obtain the overall grey effect measurement value, divide the safety status of the tailings dam, and provide a quantitative basis for dam break risk warning;

[0008] Step S3: Comprehensive evaluation system and risk warning, combining prediction model and grey effect measurement method, to build an integrated tailings dam safety assessment system and determine the risk level.

[0009] Preferably, in step S1, the Verhulst model is improved:

[0010] Assume that the initial observation value of dam displacement is X (0)=(x (0) (1),x (0) (2),…,x (0) (n)), then there is a 1-IAGO sequence X(1) * =(x * (1),x * (2),…,x * (n));

[0011] Among them, X (0) =(x (0) (1),x (0) (2),…,x (0) (n)) represents the original observation value sequence of the system; X * =(x * (1),x * (2),…,x * (n)) is a cumulative generation sequence; x * (1) = x (0) (1), x * (k) = x (0) (k)-x (0) (k-1), k=2,3,…,n;

[0012] Generate sequence G next to the mean (0) =(g (0) (1),g (0) (2),…,g (0) (n)), where:

[0013] x (0) (1) = x * (1); k = 1

[0014] x * (k) = x (0) (k)-x (0) (k-1); k=2,3,…,n

[0015] g (1) (k) = 0.5 g (1) (k)+0.5g (1) (k-1); k=2,3,…,n

[0016] Then we have:

[0017]

[0018] Where a and b are the parameter columns of the difference Verhulst model, estimated by the least squares method; g (1) (k) is the kth item in the background value generation sequence; x (0) (k) is the kth item in the original sequence; x* (k) is the difference sequence of the original sequence.

[0019] Preferably, in step S1,

[0020] If there is a matrix

[0021]

[0022] The least squares estimated parameters of the improved Verhulst model are:

[0023]

[0024] Then the shadow equation of the improved Verhulst model is:

[0025]

[0026] is the continuous form of the Verhulst model, representing a growth process with nonlinear positive feedback.

[0027] The solution to the shadow equation, that is, the time response function, is:

[0028]

[0029] The time response series of the improved Verhulst model is:

[0030]

[0031] In the above formula, k = 1, 2, ..., n, and the theoretical value is:

[0032]

[0033] Among them, vector Y is a sequence generated by inverse accumulation x * (k), a column vector consisting of the 2nd to the nth item; the matrix B is the modeling design matrix, the first column is the negative background value g (0) (k), the second column is the mean of the squares of the two adjacent terms; the least squares estimated parameter a of the model is the linear attenuation parameter of the Verhulst model; b is the nonlinear term coefficient in the Verhulst model; x in the time response function (0) (1) is the initial value; t is the time; is the predicted value at the k+1th moment; is the difference value predicted at the k+1th moment.

[0034] Preferably, in step S1, an error check is performed on the dam body historical displacement monitoring data value sequence and the predicted value sequence, and the difference between the actual value and the theoretical value is set to λ:

[0035]

[0036] Among them, x (0) (1) is the kth item of original monitoring data; is the kth predicted value.

[0037] The relative error is:

[0038]

[0039] The average relative error is:

[0040]

[0041] Get the sum of squared differences:

[0042] s=λ T λ

[0043] Where λ is the residual vector.

[0044] The prediction models of the vertical displacement of the tailings dam and the horizontal displacement of the tailings dry beach are tested with a posteriori difference test, and the mean and variance of the original series are calculated:

[0045]

[0046] Compute the residual mean and variance:

[0047]

[0048] Among them, λ (0) (k) is the kth residual (the difference between the observed value and the model predicted value);

[0049] The mean square error ratio is also called the posterior ratio c. The mean square error ratio and the small error probability p are expressed as:

[0050]

[0051]

[0052] The smaller the c value, the larger the p value, which indicates higher accuracy, and vice versa. The accuracy of the prediction model is comprehensively evaluated by the c and p values.

[0053] Preferably, in step S1, the standard for evaluating the accuracy of the tailings dam displacement prediction model is:

[0054] When the posterior ratio c is less than 0.35 and the probability of small error p is greater than 0.95, the model accuracy is level one;

[0055] When the posterior ratio c is less than 0.5 and the probability of small error p is greater than 0.80, the model accuracy is level 2;

[0056] When the posterior ratio c is less than 0.65 and the probability of small error p is greater than 0.70, the model accuracy is level three;

[0057] When the posterior ratio c ≥ 0.80 and the small error probability p ≥ 0.60, the model accuracy is level four.

[0058] Preferably, in step S2, the step of introducing the relative importance grey correlation method includes:

[0059] Integrating relative importance analysis and grey validity methods, an evaluation framework for complex systems is constructed: first, key influencing factors are screened out based on the weight calculation results, and then these high-importance indicators are substituted into the grey correlation model to construct a relative importance correlation level table and a factor relative importance comparison table.

[0060] Preferably, in step S2, the lower limit effect measurement is used for evaluation:

[0061]

[0062] In the above formula: Q min , Q i are the sets of coefficient values ​​for different periods {Q i The minimum value and general value of the coefficient are as follows: For coefficients with larger values, there are more unstable phenomena in the tailings dam, the displacement of the dam body may be larger, and the possibility of dam failure is also greater. For such indicators, the upper limit effect measurement is used for evaluation:

[0063]

[0064] In the above formula: Q max , Q i are the sets of the coefficients in different periods {Q i} the maximum value and the general value.

[0065] Preferably, in step S2, the grey effect measurement value is calculated by grey correlation, grey clustering and other methods in grey system theory, and ranges from 0 to 1. The larger the value, the greater the influence of the factor on the stability of the tailings dam, and the worse the stability of the tailings dam. According to the results of the grey effect measurement of each factor, a statistical decision matrix R of all monitoring points is established. The decision matrix is ​​used, and the influence of each factor on the stability of the tailings dam is considered to perform an overall grey effect measurement of multiple factors. The weight matrix W obtained based on the entropy method is synthesized with the decision matrix R to finally obtain the total grey effect measurement matrix A:

[0066] A=RW

[0067] Among them, A is the grey effect measurement matrix, which represents the overall stability risk of the tailings dam by weighted integration of the influence of various factors; R is the statistical decision matrix of the monitoring points, which is used to reflect the specific conditions of each monitoring point; W is the influencing factor weight matrix, which is used to reflect the influence weight of each factor on the stability of the tailings dam.

[0068] Preferably, in step S2, for the tailings dam, when the displacement of the dam body at a certain monitoring point exceeds a value ζ, the dam body is determined to be in an unsafe state at that position, and the difference between the final displacement prediction value of the dam body and the monitoring value of the previous period is compared with ζ. When it is greater than ζ, the dam is determined to be in a dangerous state; when it is less than ζ, the dam is determined to be in a safe state.

[0069] Preferably, in step S2, by analyzing the comprehensive grey effect measurement value of the dam body, its safety status can be divided into three levels: when the comprehensive grey effect measurement value is greater than α1, the dam body is in a dangerous state; when the comprehensive grey effect measurement value is between α2 and α1, the dam body is between a dangerous state and a safe state; when the comprehensive grey effect measurement value is less than α2, the dam body is in a safe state.

[0070] In step S2, by analyzing the comprehensive gray effect measurement value of the dam body, its safety status can be divided into three levels: when the comprehensive gray effect measurement value is greater than α1, the dam body is in a dangerous state; when the comprehensive gray effect measurement value is between α2 and α1, the dam body is between the dangerous state and the safe state; when the comprehensive gray effect measurement value is less than α2, the dam body is in a safe state.

[0071] The beneficial effects of the present invention are:

[0072] By using the improved Verhulst model, combined with the shadow equation and time response function, and optimizing the parameters using the least squares method, the vertical settlement displacement of the tailings dam can be predicted more accurately, thus improving the displacement prediction accuracy.

[0073] The weights of key indicators such as downstream slope ratio, flood discharge coefficient, and drainage and infiltration coefficient were quantified through the relative importance grey correlation method to comprehensively evaluate the influencing factors.

[0074] The grey effect measurement method is used to construct a decision matrix, calculate the grey correlation of each factor, and combine the weights to obtain the overall measurement value to achieve quantitative risk warning;

[0075] Combining the displacement prediction model with the grey effect measurement method, a systematic evaluation framework is formed. This system can not only predict displacement, but also comprehensively analyze multiple indicators to ultimately determine the risk level. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1A flowchart of a method for tailings dam stability assessment and dam break risk prediction provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0078] like Figure 1 FIG. 1 is a flow chart of a method for tailings dam stability assessment and dam failure risk prediction provided by an embodiment of the present invention, the method comprising:

[0079] Step S1: Establish a tailings dam displacement prediction model, use the improved Verhulst model to analyze historical displacement data, construct shadow equations and time response functions, use the least squares method to estimate parameters, generate vertical settlement displacement prediction sequences, and perform error testing.

[0080] Step S11: Improved Verhulst model

[0081] Assume that the initial observation value of dam displacement is X (0) =(x (0) (1),x (0) (2),…,x (0) (n)), then there is a 1-IAGO sequence X(1) * =(x * (1),x * (2),…,x * (n)), the sequence G is generated next to the mean (0) =(g (0) (1),g (0) (2),…,g (0) (n)).

[0082] in:

[0083] x (0) (1) = x * (1); k = 1

[0084] x * (k) = x (0) (k)-x (0) (k-1); k=2,3,…,n

[0085] g (1) (k) = 0.5 g (1) (k)+0.5g (1) (k-1); k=2,3,…,n

[0086] Then there is

[0087]

[0088] is the improved Verhulst model, where a and b are the parameter lists of the difference Verhulst model.

[0089] If there is a matrix

[0090]

[0091] The least squares estimated parameters of the improved Verhulst model are:

[0092]

[0093] Then the shadow equation of the improved Verhulst model is:

[0094]

[0095] The solution to the shadow equation, that is, the time response function, is:

[0096]

[0097] The time response series of the improved Verhulst model is:

[0098]

[0099] In the above formula, k = 1, 2, ..., n, and the theoretical value is:

[0100]

[0101] Step S12: Model verification

[0102] For the dam body historical displacement monitoring data value sequence and the predicted value sequence, an error test is performed. Assume that the difference between the actual value and the theoretical value is λ:

[0103]

[0104] The relative error is:

[0105]

[0106] The average relative error is:

[0107]

[0108] Get the sum of squared differences:

[0109] s=λ T λ

[0110] The prediction models of the vertical displacement of the tailings dam and the horizontal displacement of the tailings dry beach are tested with a posteriori difference test, and the mean and variance of the original series are calculated:

[0111]

[0112] Compute the residual mean and variance:

[0113]

[0114] The mean square error ratio is also called the posterior ratio c, which and the small error probability p can be calculated according to the following formula:

[0115]

[0116] A smaller c value and a larger p value indicate higher accuracy, and vice versa. Specific evaluation criteria are shown in the table below. Therefore, the c and p values ​​can be used to comprehensively assess the accuracy of the prediction model.

[0117] Grey prediction model accuracy test grade table

[0118]

[0119] The accuracy of the GM(1,1) model is considered qualified only when the relative error, average relative error, residual sum of squares and posterior difference tests are all qualified. When the random fluctuations of statistical data are large and the regularity is not strong, and the accuracy of the GM(1,1) model is not high, the residual sequence can be used to establish a GM(1,1) model to correct the original model to improve the accuracy.

[0120] Step S2: Introduce the relative importance grey correlation method, calculate the normalized weight of each influencing indicator by constructing a judgment matrix and normalization processing, and form an indicator weight matrix. Use the grey effect measurement method to construct a decision matrix, calculate the grey correlation degree of each factor, and combine the indicator weights to obtain the overall grey effect measurement value, divide the safety status of the tailings dam, and provide a quantitative basis for dam break risk warning;

[0121] In step S2, the grey effect measurement method includes the following steps:

[0122] The displacement analysis in step S1 above shows that it significantly impacts the stability of the tailings dam and can indirectly determine its hazardous condition. Therefore, based on the results of the dam displacement prediction on the hazardous condition of the tailings dam, we select the most heavily weighted indicators and conduct a comprehensive analysis of the tailings dam's stability using the grey effect measurement method.

[0123] Step S21: Relative Importance Grey Correlation Method

[0124] Relative importance analysis and grey validity method are integrated to construct an evaluation framework for complex systems: first, key influencing factors are screened out based on the weight calculation results, and then these high-importance indicators are substituted into the grey correlation model.

[0125] Relative importance correlation level calculation method

[0126]

[0127] Comparison of relative importance of factors

[0128]

[0129] Step S22: Measure the effect of influencing factors

[0130] Among the selected influencing factors, the smaller the value of some coefficients, the more unstable the tailings dam is, the greater the displacement of the dam body is likely to be, and the greater the possibility of dam failure. Conversely, the larger the value, the less stable the tailings dam is, the smaller the displacement of the dam body is likely to be, and the more stable the tailings dam is. Therefore, the lower limit effect measurement is used to evaluate these indicators:

[0131]

[0132] In the above formula: Q min , Q i are the sets of coefficient values ​​for different periods {Q i} minimum value and general value.

[0133] The larger the coefficient value, the more unstable phenomena exist in the tailings dam, the greater the dam displacement may be, and the greater the possibility of dam failure. Therefore, this type of indicator is evaluated using the upper limit effect measurement:

[0134]

[0135] In the above formula: Q max , Q i are the sets of the coefficients in different periods {Q i} the maximum value and the general value.

[0136] The grey effect measure is calculated using grey correlation and grey clustering methods from grey system theory. It reflects the degree of influence of each factor on the stability of the tailings dam. This value typically ranges from 0 to 1, with larger values ​​indicating a greater impact on the stability of the tailings dam and worse stability.

[0137] According to the results of the grey effect measurement of each factor, the statistical decision matrix R of all monitoring points is established.

[0138] Using the decision matrix and considering the impact of various factors on the stability of the tailings dam, the overall grey effect measurement of multiple factors is carried out. The weight matrix obtained based on the entropy method is combined with the decision matrix R to obtain the overall grey effect measurement matrix A:

[0139] A=RW

[0140] Step S23: Grey effect measurement evaluation based on dam displacement prediction

[0141] For tailings dams, displacement changes at each location are within a certain range. When the displacement change exceeds a certain value, the dam body at that location may be unstable, or even dangerous. In other words, when the displacement of the dam body at a certain monitoring point exceeds the value ζ, the dam body at that location may be in an unsafe state.

[0142] The difference between the predicted final displacement of the dam and the monitoring value of the previous period is compared with ζ. When it is greater than ζ, the dam is in a dangerous state; when it is less than ζ, the dam is in a safe state. The dangerous state of the tailings dam corresponds to the total gray effect measurement value of the tailings dam. Through analysis, it is found that the total gray effect measurement value is α1. When the total gray effect measurement value is not less than this value, the dam must be in a relatively dangerous state, that is:

[0143] γ i ≥α1

[0144] Find another gray effect measure value α2. When the total gray effect measure value is greater than or equal to α2 and less than α1, the dam may be in a relatively dangerous state, that is:

[0145] α2≤γ i <α1

[0146] By analyzing the comprehensive gray effect measurement value of the dam body, its safety status can be divided into three levels: when the measurement value is greater than α1, the dam body is in a dangerous state; when the measurement value is between α2 and α1, the dam body may be in a dangerous state; when the measurement value is less than α2, the dam body is generally in a safe state. This method provides a scientific judgment basis for on-site safety assessment personnel, helping to promptly identify potential risks and take appropriate preventive measures.

[0147] Step S3: Comprehensive evaluation system and risk warning, combining prediction model and grey effect measurement method, to build an integrated tailings dam safety assessment system and determine the risk level.

[0148] In a specific embodiment of the present invention, the arrangement of monitoring points and monitoring data:

[0149] Six monitoring points are arranged at the potential sliding surface, and their horizontal and vertical displacements are monitored at different time intervals. Although there are certain errors in the source of the collected data, it does not affect the effective prediction of the dam displacement by the improved Verhulst model. There will only be certain errors in the prediction accuracy.

[0150] The monitoring data of the vertical settlement displacement of the dam body are shown in Table 1. The data are calculated using point coordinates.

[0151] Table 1 Monitoring data of vertical settlement displacement of dam body

[0152]

[0153] The monitoring data of the horizontal displacement of the dam body are shown in Table 2.

[0154] Table 2 Monitoring data of horizontal displacement of dam body

[0155]

[0156] Note: The observed displacement values ​​in Table 1 and Table 2 are the average values ​​of the observed values ​​at the monitoring point at that time, in meters.

[0157] Improved Verhulst model for prediction of dam displacement

[0158] The calculation principle of Verhulst is improved by step S2. Combining the monitoring displacements in Tables 1 and 2, the displacement of the entire target tailings dam is predicted by the Verhulst model in the same period, and compared with the original monitoring values. The predicted values ​​of the vertical settlement monitoring displacement and the horizontal displacement are shown in Tables 3 and 4. The calculation formula of the Verhulst model is easy to obtain

[0159]

[0160] The displacement prediction value is taken from period two and its value is the same as the displacement value of period one.

[0161] Table 3a Improved Verhulst prediction results and comparative analysis of vertical settlement displacement of target tailings dam

[0162]

[0163] Table 3b Improved Verhulst prediction results and comparative analysis of vertical settlement displacement of target tailings dam

[0164]

[0165] Table 4a Improved Verhulst prediction results and comparative analysis of horizontal displacement of target tailings dam

[0166]

[0167] Table 4b Improved Verhulst prediction results and comparative analysis of horizontal displacement of target tailings dam

[0168]

[0169] Historical data indicates that a dam is considered dangerous if its final lateral displacement exceeds 800mm or its final longitudinal displacement exceeds 1000mm at a certain location. However, field monitoring data obtained in this study indicates that the dam is not in a dangerous state. However, to explore the feasibility of the proposed method, this study assumes that the critical displacement is set at 500mm in the vertical settlement direction and 300mm in the horizontal direction.

[0170] Before analysis, an accuracy test is required to determine whether the accuracy of the model under this data is suitable for long-term data prediction. The displacement data of monitoring point I at different periods are used as an example to conduct an error test on the improved Verhulst model. The accuracy in the settlement direction and horizontal direction is shown in Table 5.

[0171] Table 5a Model prediction accuracy of the improved Verhulst model for settlement direction at monitoring point I

[0172]

[0173] Table 5b Model prediction accuracy of the improved Verhulst model for settlement direction at monitoring point I

[0174]

[0175] The accuracy test table and Table 1 show that the improved Verhulst model in the settlement direction has high data accuracy, reaching level 1, making it suitable for long-term prediction. However, the improved Verhulst model in the horizontal direction has low accuracy, making it unsuitable for long-term prediction. This is due to the lack of horizontal displacement data points, resulting in unclear variations and low prediction accuracy. Therefore, to improve the reliability of the model and ensure the scientific and feasible nature of the method, this study used raw data from the tailings dam settlement direction to predict the displacement of the dam at different monitoring points during different periods. The displacement of the target dam in the settlement direction was predicted at different monitoring points after the same time interval, i.e., period VII. The difference between the displacement value and the displacement value during period VI was calculated. Based on the previously assumed dangerous displacement change, i.e., a settlement exceeding 500 mm is considered dangerous, the safety status of different monitoring points during period VII was determined.

[0176] Table 6 Deformation of the dam body at six different monitoring points during period VII

[0177]

[0178] Gray effect measurement of tailings dam stability:

[0179] Selection of influencing factors:

[0180] (1) Downstream slope ratio: This parameter is one of the important components of the tailings dam data size. The value of the downstream slope ratio directly affects the stability of the seepage field and stress field inside the dam body. The higher the downstream slope ratio, the greater the possibility of dam failure. Therefore, the gray upper limit gray effect measurement method is also used to measure this indicator.

[0181] (2) Flood drainage facility integrity coefficient: This indicator is used to measure the design function of the flood drainage facility, but more importantly, to measure its normal operation in actual on-site engineering. Generally, a qualitative evaluation is performed using an expert scoring method. The grading method for this indicator is shown in Table 7. Analysis shows that the higher the expert rating, the better the working condition of the tailings dam's flood drainage facilities and the higher the stability of the tailings dam. Therefore, the gray lower limit evaluation method is used to measure this indicator.

[0182] Table 7 Integrity coefficient of flood drainage facilities

[0183]

[0184] (3) Drainage facility integrity coefficient: This indicator is used to measure the design function of the drainage facility, but more importantly, to measure its normal operation in actual on-site engineering. Generally, a qualitative evaluation is performed using an expert scoring method. The grading method for this indicator is shown in Table 8. Analysis shows that the higher the expert rating, the better the working condition of the tailings dam's drainage facilities and the higher the stability of the tailings dam. Therefore, the gray lower limit evaluation method is used to measure this indicator.

[0185] Table 8 Drainage facility integrity coefficient table

[0186]

[0187] (4) Monitoring facility integrity coefficient: This indicator is used to measure the operation of the tailings dam monitoring facilities and the effectiveness of the tailings dam early warning method. Among them, the height of the infiltration line in the monitoring dam body and the height of the reservoir water level are important links in the stability analysis of the tailings dam. Therefore, the normal operation of the monitoring facilities plays a very important role in the safety management of the entire tailings dam. Generally, the expert scoring method is used to score this indicator, and its classification standard is shown in Table 9. Analysis shows that the better the working condition of the tailings dam's monitoring facilities, the higher the stability of the tailings dam. Therefore, the gray lower limit evaluation method is used to measure this indicator.

[0188] Table 9 Monitoring facility completeness coefficient table

[0189]

[0190] Gray effect measurement of influencing factors:

[0191] For the four grey effect measurement indicators selected in the previous article, the actual survey data of the corresponding projects are shown in Table 10.

[0192] Table 10 Field survey data of corresponding measurement indicators in different periods

[0193]

[0194] The grey effect measurement method is used to conduct grey measurement on the four different influencing factors in different periods. The specific grey effect measurement table is shown in Table 11.

[0195] Table 11 Grey effect measurement table of factors affecting sample dam displacement

[0196]

[0197] Analysis of dam displacement failure law:

[0198] According to the relative importance calculation method, the weights of the four selected indicators: downstream slope ratio, flood discharge coefficient, seepage coefficient, and monitoring coefficient are 0.35, 0.23, 0.24, and 0.18 respectively. The decision matrix is ​​established using the gray effect measurement value of the factors affecting dam displacement, according to the following formula:

[0199]

[0200] A comprehensive grey effect measurement was conducted on different indicators at different periods, and the results were compared with the previously obtained damage conditions of the tailings dam. Since the error of the predicted data in the horizontal direction was too large, the data when the displacement was in a dangerous state was analyzed using the predicted value in the vertical direction. Finally, the damage law analysis table of the tailings dam was obtained, as shown in Table 12 below:

[0201] Table 12 Analysis of displacement safety rules of tailings dam body

[0202]

[0203] Table 12 shows that the minimum comprehensive effect measure value for the tailings dam is 0.7034. This means that as long as the comprehensive gray effect measure value for the tailings dam is above 0.7034, the tailings dam may be in a relatively dangerous state due to excessive displacement. During periods without danger, the maximum gray effect measure value is 0.7332, and the minimum comprehensive effect measure value greater than this value during dangerous periods is 0.9053. Therefore, the following pattern can be obtained:

[0204] (1) When the comprehensive effect measurement value of the dam body belongs to [0.9053, 1], the dam body is very likely to be damaged due to being in a dangerous state for a long time.

[0205] (2) When the total grey effect measurement value of the dam body belongs to [0.7034, 0.9053], the dam body may be destroyed because it is in a dangerous state for a long time.

[0206] (3) When the total grey effect measurement value of the dam body belongs to [0, 0.7034], the final displacement of the dam body is still within a relatively safe range and will not be damaged due to being in a dangerous state for a long time.

[0207] Based on the above conclusions, during the operation of this tailings dam, by analyzing the monitoring data of key parameters such as tailings dam displacement and predicting the overall stability of the tailings dam based on the constructed evaluation model, it is possible to determine the dangerous state of the dam body and then implement relevant prevention and control measures based on the state level. Therefore, this method has certain practical engineering application value.

[0208] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

[0209] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for tailings dam stability assessment and dam failure risk prediction, characterized in that: The method comprises: Step S1: Establish a tailings dam displacement prediction model, use the improved Verhulst model to analyze historical displacement data, construct shadow equations and time response functions, use the least squares method to estimate parameters, generate vertical settlement displacement prediction sequences, and perform error testing; Step S2: Introduce the relative importance grey correlation method, calculate the normalized weight of each influencing indicator by constructing a judgment matrix and normalization processing, and form an indicator weight matrix. Use the grey effect measurement method to construct a decision matrix, calculate the grey correlation degree of each factor, and combine the indicator weights to obtain the overall grey effect measurement value, divide the safety status of the tailings dam, and provide a quantitative basis for dam break risk warning; Step S3: Comprehensive evaluation system and risk warning, combining prediction model and grey effect measurement method, to build an integrated tailings dam safety assessment system and determine the risk level.

2. The method for tailings dam stability assessment and dam failure risk prediction according to claim 1, characterized in that: In step S1, the Verhulst model is improved: Assume that the initial observation value of dam displacement is X (0) =(x (0) (1),x (0) (2),…,x (0) (n)), then there is a 1-IAGO sequence X(1) * =(x * (1),x * (2),…,x * (n)); Among them, X (0) =(x (0) (1),x (0) (2),…,x (0) (n)) represents the original observation value sequence of the system; X * =(x * (1),x * (2),…,x * (n)) is a cumulative generation sequence; x * (1) = x (0) (1), x * (k) = x (0) (k)-x (0) (k-1), k=2,3,…,n; Generate sequence G next to the mean (0) =(g (0) (1),g (0) (2),…,g (0) (n)), where: x (0) (1)=x * (1);k=1 x * (k)=x (0) (k)-x (0) (k-1);k=2,3,…,n g (1) (k)=0.5g (1) (k)+0.5g (1) (k-1);k=2,3,…,n Then we have: Where a and b are the parameter columns of the difference Verhulst model, estimated by the least squares method; g (1) (k) is the kth item in the background value generation sequence; x (0) (k) is the kth item in the original sequence; x * (k) is the difference sequence of the original sequence.

3. The method for tailings dam stability assessment and dam failure risk prediction according to claim 2, characterized in that: In the step S1, If there is a matrix The least squares estimated parameters of the improved Verhulst model are: Then the shadow equation of the improved Verhulst model is: is the continuous form of the Verhulst model, representing a growth process with nonlinear positive feedback. The solution to the shadow equation, that is, the time response function, is: The time response series of the improved Verhulst model is: In the above formula, k = 1, 2, ..., n, and the theoretical value is: Among them, vector Y is a sequence x generated by an inverse accumulation * (k), a column vector consisting of the 2nd to the nth item; the matrix B is the modeling design matrix, the first column is the negative background value g (0) (k), the second column is the mean of the squares of the two adjacent terms; the least squares estimated parameter a of the model is the linear attenuation parameter of the Verhulst model; b is the nonlinear term coefficient in the Verhulst model; x in the time response function (0) (1) is the initial value; t is the time; is the predicted value at the k+1th moment; is the difference value predicted at the k+1th moment.

4. The method for tailings dam stability assessment and dam failure risk prediction according to claim 1, characterized in that: In step S1, the error test is performed on the dam body historical displacement monitoring data value sequence and the predicted value sequence, and the difference between the actual value and the theoretical value is set to λ: Among them, x (0) (1) is the kth item of original monitoring data; is the kth predicted value. The relative error is: The average relative error is: Get the sum of squared differences: s=λ T l Where λ is the residual vector. The prediction models of the vertical displacement of the tailings dam and the horizontal displacement of the tailings dry beach are tested with a posteriori difference test, and the mean and variance of the original series are calculated: Compute the residual mean and variance: Among them, λ (0) (k) is the kth residual (the difference between the observed value and the model predicted value); The mean square error ratio is also called the posterior ratio c. The mean square error ratio and the small error probability p are expressed as: The smaller the c value, the larger the p value, which indicates higher accuracy, and vice versa. The accuracy of the prediction model is comprehensively evaluated by the c and p values.

5. The method for tailings dam stability assessment and dam failure risk prediction according to claim 4, characterized in that: In step S1, the criteria for evaluating the accuracy of the tailings dam displacement prediction model are: When the posterior ratio c is less than 0.35 and the probability of small error p is greater than 0.95, the model accuracy is level one; When the posterior ratio c is less than 0.5 and the probability of small error p is greater than 0.80, the model accuracy is level 2; When the posterior ratio c is less than 0.65 and the probability of small error p is greater than 0.70, the model accuracy is level three; When the posterior ratio c ≥ 0.80 and the small error probability p ≥ 0.60, the model accuracy is level four.

6. The method for tailings dam stability assessment and dam failure risk prediction according to claim 1, characterized in that: In step S2, the steps of introducing the relative importance grey correlation method include: Integrating relative importance analysis and grey validity methods, an evaluation framework for complex systems is constructed: first, key influencing factors are screened out based on the weight calculation results, and then these high-importance indicators are substituted into the grey correlation model to construct a relative importance correlation level table and a factor relative importance comparison table.

7. The method for tailings dam stability assessment and dam failure risk prediction according to claim 1, characterized in that: In step S2, the lower limit effect measure is used for evaluation: In the above formula: Q min , Q i are the sets of coefficient values ​​for different periods {Q i The minimum value and general value of the coefficient are as follows: For coefficients with larger values, there are more unstable phenomena in the tailings dam, the displacement of the dam body may be larger, and the possibility of dam failure is also greater. For such indicators, the upper limit effect measurement is used for evaluation: In the above formula: Q max , Q i are the sets of the coefficients in different periods {Q i } the maximum value and the general value.

8. The method for tailings dam stability assessment and dam failure risk prediction according to claim 7, characterized in that: In step S2, the grey effect measurement value is calculated by grey correlation and grey clustering in grey system theory, and ranges from 0 to 1. The larger the value, the greater the influence of the factor on the stability of the tailings dam, and the worse the stability of the tailings dam. According to the results of the grey effect measurement of each factor, a statistical decision matrix R of all monitoring points is established. Using the decision matrix and considering the influence of each factor on the stability of the tailings dam, the overall grey effect measurement of multiple factors is performed. The weight matrix W obtained based on the entropy method is synthesized with the decision matrix R to finally obtain the total grey effect measurement matrix A: A=RW Among them, A is the grey effect measurement matrix, which represents the overall stability risk of the tailings dam by weighted integration of the influence of various factors; R is the statistical decision matrix of the monitoring points, which is used to reflect the specific conditions of each monitoring point; W is the influencing factor weight matrix, which is used to reflect the influence weight of each factor on the stability of the tailings dam.

9. The method for tailings dam stability assessment and dam failure risk prediction according to claim 1, characterized in that: In step S2, for the tailings dam, when the displacement of the dam body at a certain monitoring point exceeds the value ζ, the dam body is determined to be in an unsafe state at that position, and the difference between the final displacement prediction value of the dam body and the monitoring value of the previous period is compared with ζ. When it is greater than ζ, the dam is determined to be in a dangerous state; when it is less than ζ, the dam is determined to be in a safe state.

10. The method for tailings dam stability assessment and dam failure risk prediction according to claim 9, characterized in that: In step S2, by analyzing the comprehensive gray effect measurement value of the dam body, its safety status can be divided into three levels: when the comprehensive gray effect measurement value is greater than α1, the dam body is in a dangerous state; when the comprehensive gray effect measurement value is between α2 and α1, the dam body is between the dangerous state and the safe state; when the comprehensive gray effect measurement value is less than α2, the dam body is in a safe state.

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