Space-time coupled surface subsidence dynamic prediction method

Abstract

The invention discloses a space-time coupled surface subsidence dynamic prediction method. The method comprises the following steps: (1) collecting geological mining information of a mining area; (2) dividing a working face by taking a periodic caving step pitch as a division basis, and constructing a time function of each mining unit; (3) constructing the relationship between the surface subsidence sufficiency and the working face mining degree; (4) integrating the time function, the surface subsidence sufficiency function and the probability integral function; and (5) surface dynamic subsidence prediction. By the adoption of the method, the mining degree of the working face can be calculated according to the mining time and the working face advancing speed, the influence of the surface subsidence lag effect is obtained according to the time influence parameters, and the mining degree, the time lag effect and the surface final-state subsidence prediction method are combined to obtain the surface subsidence value at any moment. The method has rigorous theoretical property and wide applicability, and a scientific basis is provided for mining area surface subsidence prediction, building damage identification and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of coal mining subsidence control. Specifically, it is a dynamic prediction method for surface subsidence with spatio-temporal coupling. Background Art

[0002] The process of surface subsidence caused by coal seam mining is a complex four-dimensional problem concerning time and space. In terms of time, during a long period from the start to the end of the working face mining, the surface subsidence will experience a process from slow movement, to violent movement, then to gradual attenuation, and finally to stability. In terms of space, the surface movement and deformation are affected by factors such as the mining size of the working face and the mining depth, and are usually affected by the superposition of multiple working face mining. Moreover, the surface mining damage caused by different spatial relationships and mining sequences of the working face also varies. During the mining process, the time factor and the space factor are coupled with each other, and it is difficult to independently analyze their respective effects on the dynamic process of surface subsidence during coal seam mining. For example, the mining duration is closely related to the mining size, and the mining size increases with the mining duration. In addition, in actual production, the dynamic process of the damage degree of the surface and its buildings (structures) can guide the protection of buildings (structures) and ecological restoration, etc. For example, in the evaluation of surface building damage, the maximum damage suffered by the building during the whole process of surface movement and deformation should be taken as a reference. Because the dynamic process deformation that the surface building may suffer is greater than the final static deformation. For example, when the working face reaches the stage of over-sufficient mining, a flat bottom appears in the surface subsidence basin, and the final surface movement and deformation in the flat bottom area are very small. The mining damage in this area is mainly caused by the dynamic process deformation during the active stage of the surface. Therefore, constructing a dynamic prediction method for surface subsidence with spatio-temporal element coupling has important practical significance for coal mine production, surface building protection, ecological restoration, etc.

[0003] Regarding the dynamic prediction method of surface subsidence process, it is generally constructed by combining the final static subsidence prediction method of the surface with a time function. The final static subsidence prediction method of the surface mostly adopts the relatively mature probability integral method. The time function usually uses the "S" curve function to fit the subsidence process, and the Knothe time function model and its optimized models are widely used. The classical dynamic prediction method is generally constructed by directly multiplying the final static subsidence state of the surface by the time function describing the surface subsidence process. However, there are the following problems in the construction of the above methods: The spatial and time factors in the dynamic process of surface subsidence are independently modeled, ignoring the influence of the mining duration on the mining space. It can be seen from the above analysis of the surface subsidence process that the spatio-temporal elements are coupled with each other. As the working face advances continuously in time, the mining space increases continuously, and the degree of mining damage also increases continuously. In the classical method, the time function only considers the time lag effect of surface subsidence and ignores the influence of time on the mining space. Therefore, in view of the above problems, constructing a dynamic prediction method of surface subsidence process considering the coupling of spatio-temporal elements can further improve the construction system of the dynamic prediction method of surface subsidence process and improve the actual prediction accuracy. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides the following technical solutions:

[0005] A dynamic prediction method of surface subsidence with spatio-temporal coupling includes the following steps:

[0006] (1) Collect geological and mining information of the mining area;

[0007] (2) Divide the working face based on the periodic caving step distance, and construct the time function of each mining unit;

[0008] (3) Construct the relationship between the degree of surface subsidence sufficiency and the degree of mining damage of the working face;

[0009] (4) Integrate the time function, the surface subsidence sufficiency function, and the probability integral function;

[0010] (5) Predict the dynamic surface subsidence.

[0011] In the above dynamic prediction method of surface subsidence with spatio-temporal coupling, in step (1): it includes the surface static subsidence prediction parameters and the surface dynamic prediction parameters;

[0012] The surface static subsidence prediction parameters include: subsidence coefficient q, average mining depth H of the working face, average coal seam thickness m of the working face, coal seam dip angle α, and mining size; and the surface subsidence value W obtained by the static subsidence method;

[0013] W is calculated according to the probability integral method:

[0014]

[0015] In formula (1), m is the average thickness of the coal seam in the working face, q is the subsidence coefficient, α is the dip angle of the coal seam, r is the mining influence radius, (x, y) is the coordinate of the ground point, and η and ζ are the length and width of the goaf respectively;

[0016] The dynamic prediction parameters of the ground surface include: the average mining speed v of the working face, the initial caving step distance L of the roof c and the periodic caving step distance L z , the time influence function parameters c and k, and the ground surface subsidence sufficiency function parameters x 0 and p. The time influence function parameters and the ground surface subsidence sufficiency function parameters are obtained by least square fitting according to the on-site ground surface subsidence monitoring and the mining situation of the working face.

[0017] For the above dynamic prediction method of ground surface subsidence with spatio-temporal coupling, in step (2), each mining unit is divided based on the periodic caving step distance, and the working face is divided into n mining units. Then, the time function of each mining unit is constructed:

[0018]

[0019] In formula (2), c is the time influence parameter, k is the shape adjustment parameter, and t is the mining time of each mining unit;

[0020] According to the average mining speed v of the working face and the mining time t, the mining length of the working face at time t is determined, that is, mining length = v × t.

[0021] For the above dynamic prediction method of ground surface subsidence with spatio-temporal coupling, in step (3), the ground surface subsidence sufficiency at time t is obtained by the following formula:

[0022]

[0023] In formula (3), n 1 , n 3 are the ground surface subsidence sufficiencies in the strike and dip directions of the working face at time t respectively.

[0024] For the above dynamic prediction method of ground surface subsidence with spatio-temporal coupling, when calculating the mining degree of the working face, it is calculated according to the mining unit division and the overlying strata fracture situation. Then, the calculation length in the strike direction of the working face is:

[0025]

[0026] In formula (4), represents rounding down, H is the average mining depth of the working face, L c is the initial caving step distance of the roof, and L z is the periodic caving step distance.

[0027] The above method for dynamically predicting surface subsidence with spatio-temporal coupling constructs the relationship between the degree of surface subsidence adequacy and the degree of mining disturbance of the working face: the degree of surface subsidence adequacy and the degree of mining disturbance of the working face show an "S" relationship, which is expressed using the Logistic function. The relationship between the adequacy of strike surface subsidence and the degree of mining disturbance of the working face is as shown in Equation (5):

[0028]

[0029] The relationship between the adequacy of dip surface subsidence and the degree of mining disturbance of the working face is calculated by Equation (6).

[0030]

[0031] In Equations (5) and (6), L’ is the calculated length of the working face along the strike, D is the mining width of the working face, H is the average mining depth of the working face, x 0 and p are influencing parameters.

[0032] In the above method for dynamically predicting surface subsidence with spatio-temporal coupling, in step (4), the time function of the mining unit in step (2), the surface subsidence adequacy function in step (3), and the probability integral function of the subsidence value by the static subsidence method in step (1) are integrated. Then, the subsidence value at any point on the surface at time t is calculated by Equation (7):

[0033]

[0034] In Equation (7), W i (x, y, n, t) is the subsidence value at time t after mining the i-th unit, which is calculated by the following formula:

[0035]

[0036] In Equation (8), is the time function, t 1 is the time after the first unit; Δt represents the time required for periodic caving; D 1 is the mining width of the working face of the first unit; n(t) refers to the surface subsidence adequacy calculated from the mining adequacy determined according to the advancing dimension of the working face at time t by Equation (3).

[0037] The technical solution of the present invention has achieved the following beneficial technical effects:

[0038] The present invention realizes the coupling of mining time and mining space elements by introducing the time influence function of the mining degree, and improves the prediction accuracy of surface subsidence dynamics. By using the method of the present invention, the mining degree of the working face can be calculated according to the mining time and the advancing speed of the working face, and the influence of the surface subsidence lag effect can be obtained according to the time influence parameter. By combining the mining degree, the time lag effect and the prediction method of the final surface subsidence, the surface subsidence value at any time can be obtained. Compared with the static prediction model, the relative mean square error of the dynamic prediction result of this application is about 10%, and the prediction result is better than the static prediction model, which proves the reliability of the prediction model of this application.

[0039] This prediction method has rigorous theory and wide applicability, and provides a scientific basis for the prediction of surface subsidence in mining areas and the identification of damage to buildings and structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a schematic flow chart of the method of the present invention;

[0041] Figure 2 The probability integral method is used to predict the surface subsidence shape;

[0042] Figure 3 Time influence function curve;

[0043] Figure 4 Surface subsidence sufficiency curve;

[0044] Figure 5 is the spatial relationship between the working face and the surface observation station in the implementation of the present invention;

[0045] Figure 6 is a comparison chart of the prediction result of the present invention and the measured surface result. DETAILED DESCRIPTION OF THE INVENTION

[0046] As Figure 1 shown, a dynamic prediction method for surface subsidence with spatio-temporal coupling includes the following steps:

[0047] Example:

[0048] Taking the actual situation of surface subsidence in a certain mine as an example:

[0049] a. Collect geological and mining information of the mining area to determine the prediction parameters.

[0050] Surface static subsidence prediction parameters: The average mining thickness m of the coal seam in the working face is 2.8 m, the average mining depth H of the working face is 780 m, the coal seam dip angle α is 20°, the strike length L is 672 m, and the dip length D is 135 m;

[0051] The surface subsidence value W is obtained by using the static subsidence method: W is calculated by formula (1) according to the probability integral method:

[0052]

[0053] The prediction parameters of the probability integral method are obtained from reference materials or can also be obtained by fitting the surface movement observation station. The subsidence coefficient q = 0.75, and the tangent of the main influence angle tgβ = 1.5. The mining influence radius coefficient r = H / tgβ. Then, according to the probability integral method, the final surface subsidence form is predicted as Figure 2 shown below.

[0054] Surface dynamic prediction parameters: The average mining speed of the working face v = 1.5 m / d, and the initial caving step distance of the roof L c = 102 m, and the periodic caving step distance L z = 40 m; the parameters c and k of the time influence function, and the parameters x 0 and p of the surface subsidence sufficiency function.

[0055] The parameters of the surface subsidence sufficiency influence and the time influence function can be obtained by least squares fitting through on-site surface subsidence monitoring and the mining situation of the working face. The parameters of the surface subsidence sufficiency influence are x 0 = 0.3196 and p = 3.41887, and the parameters of the time influence function are c = 0.006 and k = 6.0296.

[0056] b. Construct the time function of each mining unit, as shown in Equation (2):

[0057]

[0058] In Equation (2), c is the time influence parameter, k is the shape adjustment parameter, t is the mining time of each mining unit, and the shape of the time function is as Figure 3 shown below. Each mining unit is divided based on the periodic caving step distance, and the working face is divided into n mining units. According to the average mining speed v of the working face and the mining time t, the mining length of the working face at time t can be determined, that is, mining length = v × t.

[0059] c. The surface subsidence sufficiency at time t, as shown in Equation (3):

[0060]

[0061] In the formula, n 1 , n 3 are the surface subsidence sufficiencies in the strike and dip directions of the working face, respectively.

[0062] The surface subsidence sufficiency in the strike direction is related to the calculated length of the working face in the strike direction. Due to the lag effect of the overburden conduction time, when calculating the mining degree of the working face, it is necessary to calculate according to the mining unit division and the overburden fracture situation. Then, the calculated length of the working face in the strike direction is:

[0063]

[0064] In formula (4), represents rounding downwards, H is the mining depth, and L c is the initial caving step distance, and L z is the periodic caving step distance.

[0065] According to the literature, it is known that the degree of surface subsidence sufficiency has an "S" relationship with the degree of mining in the working face. Using the Logistic function to represent it, the relationship between the degree of surface subsidence sufficiency along the strike and the degree of mining in the working face is shown in formula (5):

[0066]

[0067] In the formula, L' is the calculated length of the working face along the strike, H is the mining depth, and x 0 and p are influencing parameters.

[0068] The relationship between the degree of surface subsidence sufficiency along the dip and the degree of mining in the working face can be calculated by formula (6)

[0069]

[0070] In the formula, D is the mining width of the working face.

[0071] Substitute the geological mining conditions and predicted parameters collected in step (a) into the surface subsidence sufficiency formula (3) in the calculation model to obtain:

[0072]

[0073] Then the curve of the surface subsidence sufficiency changing with the mining time is as Figure 4 shown.

[0074] This example is for a single working face. Therefore, for the dip sufficiency n 3 the calculation only considers the dip width of the mining working face. If there are adjacent gob areas in the dip direction of the working face, the width of the existing gob area needs to be considered. After adding the width of the existing gob area and the dip width of the mining working face, substitute it into the formula to calculate n 3 .

[0075] d. The subsidence value of any point on the surface at time t can be calculated by formula (7):

[0076]

[0077] In the formula, W i (x, y, n, t) is the subsidence at time t after mining the i-th unit.

[0078] W i (x, y, n, t) is calculated by the following formula:

[0079]

[0080] In formula (8), is a function of time, t 1 is the time after the first unit; Δt represents the time required for periodic caving; D 1 is the mining width of the working face of the first unit; n(t) refers to the surface subsidence adequacy calculated from the mining adequacy determined according to the advance dimension of the working face at time t by formula (3).

[0081] Select the 212th day, 577th day, 730th day, and 852nd day after mining to predict the surface subsidence value and compare it with the measured surface value.

[0082] As Figure 5 shown is the spatial relationship between the working face and the surface observation station. Figure 6 is a comparison chart of the 4 dynamic prediction results with the static prediction results and the measured results. It can be seen that the dynamic prediction subsidence and the measured subsidence curves fit well, and the dynamic prediction accuracy is higher than the static prediction.

[0083] In order to quantify the overall accuracy of the prediction, the mean square error and the relative mean square error are used as the evaluation criteria. The calculation formula is as follows:

[0084]

[0085] In the formula, RMSE represents the prediction mean square error, △ is the difference between the predicted subsidence and the measured subsidence value at each point, n is the number of measured times, and W max is the maximum subsidence value in each observation.

[0086] The calculation results of the accuracy index are shown in Table 1. The relative mean square error of the dynamic prediction result is about 10%, and the prediction result is better than the static prediction model, which proves the reliability of this model.

[0087] Table 1 Prediction error calculation

[0088]

[0089] Obviously, the above embodiments are only examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the claims of this patent application.

Claims

1. A spatiotemporal coupled method for predicting dynamic surface subsidence, characterized in that: The steps include: (1) Collect geological and mining information of the mining area; (2) Based on the periodic collapse step distance, the working face is divided and the time function of each mining unit is constructed; (3) Construct the relationship between the degree of surface subsidence and the degree of mining at the working face; (4) Integrate the time function, surface subsidence sufficiency function and probability integral function; (5) Prediction of dynamic surface subsidence.

2. A time-space coupled surface subsidence dynamic prediction method according to claim 1, characterized in that: In step (1): including surface static subsidence prediction parameters and surface dynamic prediction parameters; The predicted parameters of static ground subsidence include: subsidence coefficient q, average mining depth H of working face, average thickness m of coal seam at working face, coal seam inclination α and mining size; and the ground subsidence value W obtained by static subsidence method; W is calculated according to the probability integral method: In formula (1), m is the average thickness of the coal seam at the working face, q is the subsidence coefficient, α is the coal seam inclination, r is the mining influence radius, (x, y) is the coordinates of the surface point, η and ζ are the length and width of the goaf respectively; Surface dynamic prediction parameters include: average mining speed v of the working face, initial roof collapse step L c and periodic collapse step length L z , time influence function parameters c and k, surface subsidence sufficiency function parameters x0 and p, and the time influence function parameters and surface subsidence sufficiency function parameters are obtained by least squares fitting according to on-site surface subsidence monitoring and working face mining conditions.

3. The method for dynamic prediction of surface subsidence coupled with time and space according to claim 1, characterized in that: In step (2), each mining unit is divided based on the periodic collapse step distance, the working face is divided into n mining units, and then the time function of each mining unit is constructed: In formula (2), c is the time influencing parameter, k is the morphological adjustment parameter, and t is the recovery time of each mining unit; According to the average mining speed v and mining time t of the working face, the mining length of the working face in time t is determined, that is, mining length = v×t.

4. The method for dynamic prediction of surface subsidence coupled with time and space according to claim 3 is characterized in that: In step (3), the surface subsidence sufficiency at time t is obtained using the following formula: In formula (3), n1 and n3 are the surface subsidence sufficiency of the working face strike and dip at time t, respectively.

5. The method for dynamic prediction of surface subsidence coupled with time and space according to claim 4, characterized in that: When calculating the degree of mining at the working face, the calculation is carried out according to the division of mining units and the breaking of the overburden rock. The calculated length of the working face is: In formula (4), It means rounding down, H is the average mining depth of the working face, L c is the initial collapse step distance of the roof, L z is the periodic collapse step distance.

6. A time-space coupled surface subsidence dynamic prediction method according to claim 5, characterized in that: Construct the relationship between the surface subsidence sufficiency and the mining degree of the working face: The surface subsidence sufficiency and the mining degree of the working face are in an "S" relationship. Using the Logistic function to express it, the relationship between the surface subsidence sufficiency and the mining degree of the working face is shown in formula (5): The relationship between the surface subsidence degree and the mining degree of the working face is calculated by formula (6): In formula (5) and formula (6), L' is the calculated length of the working face, D is the mining width of the working face, H is the average mining depth of the working face, and x0 and p are influencing parameters.

7. A time-space coupled surface subsidence dynamic prediction method according to claim 6, characterized in that: In step (4), the mining unit time function in step (2), the surface subsidence sufficiency function in step (3) and the probability integral function of the subsidence value of the static subsidence method in step (1) are integrated, and the subsidence value of any point on the surface at time t is calculated by formula (7): In formula (7), W i (x, y, n, t) is the subsidence value at time t after mining the i-th unit, which is calculated by the following formula: In formula (8), is a time function, t1 is the time after the first unit; Δt represents the time required for periodic collapse; D1 is the mining width of the working face of the first unit; n(t) refers to the surface subsidence sufficiency calculated by formula (3) based on the mining sufficiency determined by the advancement size of the working face at time t.

Images