Dynamic prediction time function model for surface mining subsidence and parameter solving method thereof

Abstract

The invention relates to a dynamic prediction time function model for surface mining subsidence and a parameter solving method thereof, which are characterized in that on the basis of a Sigmoid function, all expressions of dynamic subsidence rule characteristics of mining surface points can be realized by carrying out related optimization and improvement on the Sigmoid function and improving an interval estimation method based on a main influence radius of a probability integral prediction parameter. According to the method, the ground surface subsidence track feature, the total subsidence time feature, the subsidence speed feature and the acceleration feature can be accurately and dynamically predicted, a time function parameter solving method is simple, parameters used for parameter solving are all related prediction parameters of a common ground surface mining subsidence static prediction model-probability integral method, and therefore the method has the advantages that the method is easy to implement. In an actual operation level, parameters of the time function are easier to obtain.

Description

Technical Field

[0001] The invention relates to the technical field of mining subsidence research, and in particular to a surface mining subsidence dynamic prediction time function model and a parameter calculation method thereof. Background Art

[0002] Mining subsidence is a complex four-dimensional problem that varies with space and time. When mining under buildings, mining damage to buildings is also a complex dynamic process, during which the buildings will be subjected to compression, tension and shear damage. Therefore, providing the dynamic process of surface subsidence caused by coal mining is very important for reducing and preventing mining damage to buildings. Since the static prediction model of surface mining subsidence is relatively mature, the key to affecting the accuracy of dynamic prediction of surface mining subsidence is to determine a high-precision dynamic prediction time function of surface mining subsidence and accurately obtain and determine the parameters related to the time function.

[0003] Regarding the time function for dynamic prediction of surface subsidence, Knothe established the Knothe time function model in 1952. This model has only one parameter and realizes the dynamic subsidence prediction of surface subsidence, but it is not very effective in reflecting the changing laws of surface subsidence velocity and acceleration. In view of the shortcomings of the Knothe time function, Sroka (1982-1983) constructed a dual-parameter time function, which can better reflect the changing laws of surface subsidence velocity and acceleration. However, the impact of underground mining is not transmitted to the surface instantly. Generally, when the working face advances 0.25 to 0.5 times the mining depth from the opening of the cut, the impact of underground mining will appear on the surface. The dual-parameter time function cannot reflect this aspect well. For this reason, Kowalski (2001) proposed a generalized time function from the point of view that the surface mining lags behind the underground mining. This function has three parameters and can theoretically better reflect the entire process of surface movement and deformation. However, although the dual-parameter time function and the generalized time function are theoretically superior to the Knothe time function, the former two contain more parameters and it is relatively difficult to determine the parameters under different geological mining conditions. There are also very few research results on the methods for obtaining the time function parameters for dynamic prediction of surface mining subsidence. Cui Ximin mainly provided the graphical method and interval estimation method.

[0004] At present, the main methods for obtaining the time function include the graphical method, the least squares curve fitting method, the interval estimation method and its improved full mining angle method. The accuracy of the graphical method and the full mining angle method depends on the experience of the map maker. If the map maker is not experienced enough, the accuracy of the solution cannot be guaranteed; the least squares curve fitting method requires a large amount of measured data. If there is no or insufficient measured data, this method cannot be used to obtain reliable time function parameters. The interval estimation method is based on the general movement law of the mining surface. When there is a lack of measured data, general empirical values ​​can still be used, but the time function parameter value calculated by the interval estimation method is an interval value, and the result lacks precision. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a time function model for dynamic prediction of surface mining subsidence and a method for obtaining its parameters. The prediction method and model can not only realize accurate dynamic prediction of surface subsidence trajectory characteristics, total subsidence time characteristics, subsidence velocity characteristics and acceleration characteristics, but also the method for obtaining the time function parameters is simple. The parameters used for obtaining the parameters are all relevant prediction parameters of the commonly used static prediction model for surface mining subsidence - probability integral method. Therefore, at the practical operation level, the parameters of the time function are easier to obtain.

[0006] Specifically, the present invention is achieved through the following technical solutions:

[0007] A time function model for dynamic prediction of surface mining subsidence, the formula of the time function model is:

[0008] S(t)=(1+e (-nt+6) ) -1

[0009] Among them, n is the time influence coefficient, which is obtained by combining the time function model and the probability integral method theory; t is the duration of subsidence of the mining surface point.

[0010] Furthermore, the calculation formula of the time impact coefficient is:

[0011]

[0012] Among them, v is the advancing speed of the working face, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are respectively the main influencing radius and the inflection point offset distance at the stop line in the mining direction.

[0013] Furthermore, the time influence coefficient is obtained in the following manner:

[0014] According to the probability integral method theory, when the working face is fully mined, the maximum surface subsidence value is approximately equal to 0.98W 0 , assuming that the advancing speed of the working face is v, and the size of the goaf when it reaches full mining is L c , then the time when the surface movement reaches full mining can be obtained as L c / v, thus combining the formula of the time function model to obtain:

[0015]

[0016] Among them, W 0 is the final settlement value.

[0017] Furthermore, the size L of the goaf when it reaches full mining c Use the following formula to calculate:

[0018] L C =γ L +γ R +S L +S R

[0019] Among them, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are respectively the main influencing radius and the inflection point offset distance at the stop line in the mining direction.

[0020] The present invention also provides a method for obtaining parameters of a surface mining subsidence dynamic prediction time function model, comprising the following steps:

[0021] S1. Obtain the time influence coefficient n of the mining area to be predicted:

[0022]

[0023] Among them, v is the advancing speed of the working face, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are the main influence radius and the inflection point offset distance at the stop line in the mining direction respectively;

[0024] S2. Obtain the time function model of the mining area to be predicted:

[0025] S(t)=(1+e (-nt+6) ) -1

[0026] Where t is the duration of ground surface subsidence caused by mining.

[0027] Furthermore, it also includes step S3: obtaining the dynamic characteristics of surface mining subsidence in the mining area to be predicted through the above-mentioned time function model: including the surface sinking trajectory characteristics, total sinking time characteristics, sinking speed characteristics and acceleration characteristics of the mining area to be predicted.

[0028] Furthermore, after step S2, the method further includes a step of graphically expressing the time function model.

[0029] Further, in step S3, the surface subsidence trajectory characteristic corresponds to the graphical curve of the time function model, the total sinking time characteristic corresponds to the graphical horizontal coordinate of the time function model, the sinking speed characteristic corresponds to the first-order derivative of the time function model, and the acceleration characteristic corresponds to the second-order derivative of the time function model.

[0030] Beneficial effects:

[0031] 1. The present invention is based on the Sigmoid function. By optimizing and improving the Sigmoid function, it can fully express the dynamic subsidence law characteristics of mining surface points, including the surface subsidence trajectory characteristics, total subsidence time characteristics, subsidence velocity characteristics and acceleration characteristics.

[0032] 2. The present invention proposes an improved method of the interval estimation method based on the main influence radius of the probability integral prediction parameters. The parameters used for calculating the parameters are all relevant prediction parameters of the commonly used surface mining subsidence static prediction model-probability integral method. At the practical operation level, the parameters of the time function are easier to obtain.

[0033] 3. Compared with the series of functions based on Knothe time function, the present invention obtains a more stable single-parameter dynamic prediction time model. In particular, as in patent CN113435636A, the prediction time function proposed therein contains two time factor influence coefficients c and n, both of which are time factor influence coefficients related to the mechanical properties of the overlying rock formations. c mainly describes the dynamic characteristics of the sinking process of the surface point of coal mining subsidence, and n mainly describes the time characteristics of the surface point of mining lag behind underground mining. The two parameters contain the same influencing factors in the process of seeking parameters, and will affect each other when seeking parameters. In the improved Sigmoid dynamic prediction time function proposed by the present invention, a single-parameter dynamic prediction time function is proposed by comprehensively considering various influencing factors in the mining area, which has a more stable model structure and is more interpretable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a schematic diagram of the movement trajectory of surface points in the main section during mining;

[0035] Figure 2 It is a graphical expression diagram of the Sigmoid function;

[0036] Figure 3 It is a graphical expression of the first and second derivatives of the Sigmoid function;

[0037] Figure 4 It is a graphical representation of the time function model of the present invention;

[0038] Figure 5 It is a comparison diagram between the time function of the present invention and the measured value. DETAILED DESCRIPTION

[0039] The content of the present invention is further described below in conjunction with the drawings and embodiments, but the scope of protection claimed by the present invention is not limited to the following embodiments.

[0040] In mining subsidence, the ground starts to sink when the ground surface sinks to 10 mm. Generally, during the initial mining operation, the distance the working face advances from the opening of the cut is equivalent to 1 / 4 to 1 / 2 H. 0 (H 0 When the mining depth is 200 m, the mining impact will spread to the surface, causing the surface to sink. In the subsequent mining process, the surface point will experience a more complex time and space process, that is, from the beginning of movement to the violent movement, and then to the gradual cessation of movement, and will go through the following four movement stages. Now take the surface point A in the fully mined area of ​​the main section of the moving basin as an example. Figure 1 As shown (where H represents the mining depth):

[0041] (1) When the working face advances from a distant cut (such as point 1) to point A and the movement reaches point A, the ground subsidence speed gradually increases, and the movement direction of point A is opposite to the direction of the working face. This is the first stage of movement.

[0042] (2) When the working face passes directly below point A (such as point 2) and continues to move forward, the surface subsidence speed increases rapidly and gradually reaches the maximum subsidence speed. The moving direction of point A is close to the direction of the plumb bob. This is the second stage of movement.

[0043] (3) As the working face continues to advance and gradually moves away from point A on the ground surface, the ground subsidence speed decreases rapidly, and the moving direction of point A gradually becomes the same as the advancing direction of the working face. This is the third stage of movement.

[0044] (4) When the working face reaches a certain distance away from the surface point, the impact of the mining working face on point A gradually disappears, and the movement of point A stops. This is the fourth stage of movement.

[0045] In summary, the ideal time function that can accurately describe the subsidence characteristics of surface subsidence points in the fully mined area should have the following characteristics: it can accurately describe the characteristics of the surface subsidence trajectory, as well as the velocity and acceleration characteristics of the surface subsidence.

[0046] In order to effectively express the dynamic subsidence characteristics of mining surface points, the proposed model should be able to express all the above characteristics. When we conducted relevant deep learning theoretical research, we found that the Sigmoid function image, which is often used in the threshold function of neural networks, is similar to the characteristics of the subsidence law of mining surface points. If it is optimized and transformed, all the characteristics of the mining surface subsidence law can be effectively expressed. Therefore, this study proposes to construct a surface mining subsidence time function model based on the Sigmoid function.

[0047] The mathematical expression of the Sigmoid function is: S(x) = (1 + e -x ) -1 , its graphical expression is as follows Figure 2 As shown. Figure 2 It can be seen that: starting from x = -6, as the independent variable gradually increases, the Sigmoid function value gradually increases from 0 until x = 6, when the function value gradually approaches 1, and then as x increases, the function value tends to be stable. By taking the first-order derivative of the sigmoid function with respect to the independent variable x, the speed change function of the Sigmoid function value can be obtained, and the specific expression is: S'(x) = e -x ×(1+e -x ) -2 , whose graphical expression is as follows Figure 3 As shown, it can be seen that as the independent variable increases, the speed of the function value increases from 0 gradually, and then gradually decreases to 0 after reaching a certain level. If we further calculate the second-order derivative of the Sigmoid function with respect to the independent variable x, we can obtain the acceleration change function of the Sigmoid function value, the specific expression is: S"(x)=-e -x ×(1+e -x ) -2 +2×e -2x ×(1+e -x ) -3 , whose graphical expression is as follows Figure 3 shown.

[0048] From the above analysis, it can be seen that without any improvement, the Sigmoid function can formally express the first three characteristics of the dynamic subsidence of the aforementioned mining surface points, but it cannot effectively express the total subsidence time; nor can it effectively express the characteristic that the starting time of the subsidence of each point is greater than 0. Nevertheless, the author found through experimental research that if the Sigmoid function can be optimized and improved, the full expression of the dynamic subsidence law characteristics of the mining surface points can be achieved. For this reason, combining the dynamic subsidence law of the aforementioned mining surface points and the characteristics of the Sigmoid function, this study proposes the following function model: S(t) = (1+e (-nt+6) ) -1 For example, when n=14, the graphical expression is as follows Figure 4 As shown. Figure 4 It can be seen that the model is fully and effectively able to express the four characteristics of dynamic subsidence of surface points caused by mining mentioned above.

[0049] This study proposed an improved interval estimation method based on the main influence radius of probability integral prediction parameters.

[0050] The process of establishing the improved method is as follows:

[0051] According to the probability integral method theory, when the working face is fully mined, the maximum surface subsidence value is approximately equal to 0.98W 0 , assuming that the advancing speed of the working face is v, and the size of the goaf when it reaches full mining is L c , then the time when the surface movement reaches full mining can be obtained as L c / v, thus we get:

[0052]

[0053] According to the above formula, the critical sufficient mining length can be determined, and then the time function parameters can be determined.

[0054] When the size of a certain direction of the rectangular mining section reaches γ L +γ R +S L +S R When the mined area reaches the fully mined state, it is considered that the mined area has reached full mining along this direction. c It can be calculated using the following formula:

[0055] L C =γ L +γ R +S L +S R

[0056] Among them, γ L and S Lare the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are respectively the main influencing radius and the inflection point offset distance at the stop line in the mining direction.

[0057] Therefore, according to the combination of the above formulas, the precise determination formula of the time function parameters proposed in this paper can be obtained:

[0058]

[0059] Different geological mining conditions have different main impact radius (R) and inflection point offset (S) of surface mining subsidence, so the surface subsidence time impact coefficient n is also different. From the above formula, it can be seen that the model can be applied to various geological mining conditions, thereby helping to improve the accuracy of surface subsidence prediction in different mining areas.

[0060] Method validity verification:

[0061] In order to verify the effectiveness of the method of the present invention, six monitoring points in the fully mined area on the strike observation line of the Zhencheng bottom mine were selected for verification. The distance between each monitoring point is 30 meters, and the distance between A21 and the cut eye is 300 meters. According to the geological conditions of the mining area and the literature "Laws of surface movement and overburden failure in coal mines and their applications", it can be concluded that the main influence radius and inflection point offset distance at the cut eye are 218m and 22m respectively, and the main influence radius and inflection point offset distance at the stop line in the mining direction are 218m and 22m respectively. Therefore, according to formula L C =γ L +γ R +S L +S R The sufficient mining size L of the mining area can be obtained c It is 480m.

[0062] According to the advancement of the working face during mining, the average advancement speed v of the working face is calculated to be 865m / a. It can be concluded that under the geological conditions of the mining area, the optimal value of parameter n is 18. During the monitoring period, 9 settlement monitorings were carried out, and 8 settlement values ​​were calculated for each monitoring point. First, the settlement data of each monitoring point were normalized using the linear normalization method, and the settlement of each monitoring point was obtained as follows: Figure 5 shown.

[0063] Depend on Figure 5It can be seen that when the value of n is 18, the root mean square error of the monitoring point is 0.0356 and the goodness of fit is 0.9921. It can be seen that the dynamic time prediction function model of mining subsidence proposed in the present invention can accurately represent the actual settlement trend of the monitoring point in the mining area, verifying the effectiveness of the new time function method for dynamic prediction of surface mining subsidence of the present invention.

[0064] The above-mentioned embodiments only express several implementation methods of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A dynamic prediction time function model for surface mining subsidence, characterized in that: The formula of the time function model is: S(t)=(1+e (-nt+6 )) -1 Among them, n is the time influence coefficient, which is obtained by combining the time function model and the probability integral method theory; t is the duration of subsidence of the mining surface point.

2. The surface mining subsidence dynamic prediction time function model according to claim 1 is characterized in that: The calculation formula of the time influence coefficient is: Among them, v is the advancing speed of the working face, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are the main influencing radius and inflection point offset distance at the stop line in the mining direction respectively.

3. The surface mining subsidence dynamic prediction time function model according to claim 1 or 2 is characterized in that: The time influence coefficient is obtained in the following manner: According to the probability integral method theory, when the working face is fully mined, the maximum surface subsidence value is approximately equal to 0.98W0. Assuming that the advancing speed of the working face is v, the size of the goaf when it reaches full mining is L c , then the time when the surface movement reaches full mining can be obtained as L c / v, thus combining the formula of the time function model to obtain: Among them, W0 is the final settlement value.

4. The surface mining subsidence dynamic prediction time function model according to claim 3 is characterized in that: The size of the goaf when it reaches full mining c Use the following formula to calculate: L C =c L +g R +S L +S R Among them, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are the main influencing radius and inflection point offset distance at the stop line in the mining direction respectively.

5. The method for obtaining parameters of the time function model for dynamic prediction of surface mining subsidence according to any one of claims 1 to 4, characterized in that: The steps include: S1. Obtain the time influence coefficient n of the mining area to be predicted: Among them, v is the advancing speed of the working face, γ L and S L are the main influence radius and inflection point offset of the opening hole in the mining direction, γ R and S R They are the main influence radius and the inflection point offset distance at the stop line in the mining direction respectively; S2. Obtain the time function model of the mining area to be predicted: S(t)=(1+e (-nt+6) ) -1 Where t is the duration of ground surface subsidence caused by mining.

6. The parameter seeking method according to claim 5, characterized in that: The step S3 is also included: The dynamic characteristics of surface mining subsidence in the mining area to be predicted are obtained through the time function model: It includes the surface subsidence trajectory characteristics, total subsidence time characteristics, subsidence speed characteristics and acceleration characteristics of the mining area to be predicted.

7. The parameter seeking method according to claim 5 or 6, characterized in that: The step after step S2 also includes a step of graphically expressing the time function model.

8. The parameter seeking method according to claim 7, characterized in that: In step S3, the surface subsidence trajectory characteristics correspond to the graphical curve of the time function model, the total sinking time characteristics correspond to the graphical horizontal coordinate of the time function model, the sinking speed characteristics correspond to the first-order derivative of the time function model, and the acceleration characteristics correspond to the second-order derivative of the time function model.

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