Rock hardness grading method based on three-dimensional arch shell space structure and application thereof

Abstract

The application discloses a rock hardness grading method based on a three-dimensional arch shell space structure and application thereof, and the rock hardness grading method comprises the following steps: (1) dividing according to whether working face mining is sufficient, calculating an arch shell structure trajectory equation corresponding to different mining stages of coal, and calculating a volume formed by closing the arch shell structure; (2) arranging an observation line on a main section of the working face and regularly observing, and drawing a surface subsidence basin function according to a probability integral method; dividing the surface subsidence basin into multiple sections, and calculating a surface subsidence basin volume based on a differential thought; (3) calculating a damage volume ratio; (4) giving a damage volume ratio critical value, and determining a hardness grading of an overlying rock mass of a goaf. The damage volume ratio is used to calculate a surface residual subsidence coefficient. The application can solve the problem that the existing determination of the hardness of the overlying rock mass does not consider the comprehensive effect after rock strata combination, and thus the accuracy of the surface residual subsidence coefficient of a mining area is low.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of comprehensive lithology judgment. Specifically, it is a rock hardness grading method based on three-dimensional arch space structure and its application. BACKGROUND

[0002] Coal, as the main consumer energy in China at present, plays an important role in the rapid development of the national economy. By the end of 2021, the national coal production has reached 4.13 billion tons. At the same time, the energy distribution characteristics of China determine that the primary energy status of coal will be difficult to change in the short term. Coal mining will cause surface subsidence, which lasts for a long time, and the surface will have residual subsidence deformation for a long time, which will have an adverse effect on the mine surface buildings. Therefore, understanding and mastering the laws of residual subsidence of the mine surface is of great significance to the construction and utilization of the mining subsidence area, the safety analysis of buildings, and the treatment of goaf.

[0003] Currently, the main method to determine the surface residual subsidence coefficient is to use the empirical formula given in the "three-under" coal mining regulations. However, this formula requires the determination of an empirical coefficient by humans, which is ambiguous, and does not take into account the lithology of the overburden rock, resulting in inaccurate calculation results and making it impossible to safely carry out construction projects. Therefore, when determining the surface residual subsidence coefficient, the relationship between the surface residual subsidence coefficient and the lithology of the overburden rock should be considered. Research has shown that the process and results of surface residual subsidence are greatly affected by the lithology of the overburden rock, so it is particularly important to determine the comprehensive lithology of the overburden rock in the mining area.

[0004] Existing research shows that the harder the overburden rock is, the smaller the surface subsidence coefficient is, and the larger the surface residual subsidence coefficient is. The softer the overburden rock is, the larger the subsidence coefficient is, and the smaller the surface residual subsidence coefficient is. Therefore, it is particularly important to accurately determine the overburden rock firmness coefficient. The overburden rock firmness coefficient is generally obtained through physical experiments after drilling and sampling, but the cost of drilling is too high, and the coefficient obtained cannot represent the entire mining area, lacking universality. At the same time, the stratum is composed of many rock layers, with hard and soft lithology, and the effect of only one rock layer cannot be considered, the comprehensive effect of the rock layer combination should be considered, so it has a certain restriction on the goaf engineering project.

[0005] Patent document CN111577268B discloses a method for determining rock lithology by using drill tool vibration parameters. The method uses extracted drill tool vibration data to analyze rock lithology according to acceleration root mean square, stress-strain relationship and mechanical specific energy. However, due to multiple rock layers in the formation, the determination of rock lithology by using drill tool vibration data can only be applied to one or several layers, and cannot determine the comprehensive lithology of the mine area (predicted area). Moreover, it is time-consuming and labor-intensive. Patent document CN102720489B discloses a method for analyzing formation lithology while drilling in gas drilling. The method can quickly and accurately analyze the cuttings returned from gas drilling, determine the cuttings arrival time, obtain the cuttings, and analyze the lithology by X-ray diffraction analysis on site. This method can accurately determine the lithology on site during drilling, but cannot determine the comprehensive lithology of the entire mine area (predicted area).

[0006] Therefore, it is necessary to explore a method for determining the comprehensive lithology after considering the combination of rock layers, so as to reasonably determine the surface residual subsidence coefficient of the mine area and provide accurate guidance for the utilization of land resources. SUMMARY

[0007] Therefore, the technical problem to be solved by the present application is to provide a rock mass hardness grading method based on a three-dimensional arch shell spatial structure and an application thereof, so as to solve the problem that the determination of overburden lithology in the prior art does not consider the comprehensive effect after the combination of rock layers, thereby affecting the accuracy of the determination of the surface residual subsidence coefficient of the mine area.

[0008] To solve the above technical problems, the present application provides the following technical solutions:

[0009] The rock mass hardness grading method based on a three-dimensional arch shell spatial structure comprises the following steps:

[0010] Step (1): dividing according to whether the working face is fully mined, calculating the arch shell structure trajectory equation corresponding to different mining stages of coal, and calculating the volume V g formed by the closure of the arch shell structure.

[0011] Step (2): arranging observation lines on the main section of the working face and observing regularly, determining the surface movement and deformation prediction parameters according to the measured data obtained by observation, and drawing the surface subsidence basin function by using the probability integral method according to the surface movement and deformation prediction parameters; dividing the surface subsidence basin into multiple sections, and calculating the volume V d of the surface subsidence basin based on the differential thought.

[0012] Step (3): calculating the damage volume ratio a.

[0013] Step (4): giving the critical value of the damage volume ratio to determine the classification of the overburden rock mass hardness of the mine area.

[0014] The rock hardness grading method based on the three-dimensional arch shell space structure has the following steps (1) in the above method:

[0015] When the working face is in a non-sufficient mining state, i.e., L c , at this time, D c or D c The calculation method of the arch shell structure trajectory equation is as follows:

[0016] First, determine the semi-ellipsoidal equation of the spatial arch shell structure as follows:

[0017]

[0018] In formula (1): C = h;

[0019] Substitute the calculation formulas of A, B and C into formula (1) to obtain the arch shell structure trajectory equation:

[0020]

[0021] When the working face is in a sufficient mining state, i.e., L c , at this time, D c or D c The arch shell structure is a flat semi-ellipsoidal surface, and the arch shell structure trajectory equation is as follows in the following two intervals:

[0022] ① When , the trajectory equation of the arch shell structure is as follows:

[0023]

[0024] ② When , the trajectory equation of the arch shell structure is as follows:

[0025]

[0026] In formula (2), formula (3) and formula (4): L c is the critical advancing distance of the working face, m; L c = (1.2-1.4)H; D c is the critical inclination length of the working face, m; D c = (1.2-1.4)H; H is the mining depth, m; L is the advancing distance of the working face, m; S L is the distance from the inside of the strike shell base to the coal wall, m; D is the inclination length of the working face, m; S D is the distance from the inside of the inclination shell base to the coal wall, m; h is the height of the arch shell structure, m; h c is the height of the bedrock, i.e., the height of the arch shell structure reaches the maximum value of the geological mining conditions, m.

[0027] In step (1), the distance S from the coal wall to the inside of the shell base along the working face direction is calculated L The calculation formula of the height h of the arch shell structure is

[0028]

[0029] The calculation formula of the height h of the arch shell structure is

[0030]

[0031] In formula (5) and formula (6), M is the thickness of the coal seam, m; and K is an empirical coefficient, and the value is 0.05-1.

[0032] In step (1), the volume V of the arch shell structure closed is calculated g When:

[0033] ① When the working face direction is in a non-sufficient mining state, i.e., L c , the arch shell structure is a semi-ellipsoidal surface, and the volume V of the arch shell structure closed in this stage is g

[0034]

[0035] ② When the working face direction is in a sufficient mining state, i.e., L≥L c , the arch shell structure is a flat semi-ellipsoidal surface, and the volume V of the arch shell structure closed in this stage is g

[0036]

[0037] In formula (7) and formula (8), L c is the critical advancing distance of the working face, m; L c =(1.2-1.4)H; D c is the critical length of the working face in the direction of inclination, m; D c =(1.2-1.4)H, m; H is the mining depth, m; L is the advancing distance of the working face, m; D is the length of the working face in the direction of inclination, m; h c is the height of the base rock, m; M is the thickness of the coal seam, m; and K is an empirical coefficient, and the value is 0.05-1.

[0038] In step (2), the surface movement and deformation prediction parameters include the subsidence coefficient, the horizontal movement coefficient, the mining influence propagation angle, the tangent of the main influence angle, and the inflection point offset distance. The surface movement and deformation prediction parameters are calculated as follows:

[0039] ​​Subsidence coefficient = maximum subsidence value / (coal thickness * cosine of coal seam dip angle);

[0040] Horizontal movement coefficient = maximum horizontal movement value / maximum subsidence value;

[0041] Main influence propagation angle = mining depth / main influence radius;

[0042] Mining influence propagation angle = 90 - coal seam dip angle * empirical coefficient;

[0043] The determination of the inflection point offset distance is to find the point of half of the maximum subsidence value on the subsidence curve, and measure the horizontal distance from the point to the working face recovery boundary line.

[0044] The rock hardness classification method based on the three-dimensional arch shell spatial structure, in step (2), the surface subsidence basin function drawn according to the probability integral method is denoted as:

[0045] z = f (x, y) (9);

[0046] Then the surface subsidence basin volume V d calculated based on the differential idea is:

[0047]

[0048] In formula (9) and formula (10), z is the surface subsidence value, mm; x is the horizontal distance of the surface strike observation line, m; r x is the surface subsidence basin range strike direction distance, m; y is the horizontal distance of the surface dip observation line, m; r y is the surface subsidence basin range dip direction distance, m; Δx is the length of the surface subsidence basin strike flat bottom part, m; Δy is the length of the surface subsidence basin dip flat bottom part, m; W max is the maximum surface subsidence value, mm;

[0049] L c is the working face critical advance distance, m; L c = (1.2 ~ 1.4) H, H is the mining depth, m; D c is the working face critical dip length, m; D c = (1.2 ~ 1.4) H; H is the mining depth, m; L is the working face advance distance, m; D is the working face dip length, m.

[0050] The rock hardness classification method based on the three-dimensional arch shell spatial structure, in step (3), the calculation formula of the damage volume ratio α is:

[0051]

[0052] V c = LDM (12);

[0053] In formula (11) and formula (12): V c is the goaf volume, L is the working face advancing distance, m; D is the working face tendency length, m; M is the coal seam thickness, m.

[0054] In the rock hardness classification method based on the three-dimensional arch shell spatial structure, when the value of the damage volume ratio a is less than or equal to 0.30 in step (4), the overlying rock hardness of the goaf is classified as soft rock; when the value of the damage volume ratio a is greater than 0.30 and less than or equal to 0.65, the overlying rock hardness of the goaf is classified as medium-hard rock; and when the value of the damage volume ratio a is greater than 0.65 and less than or equal to 1.00, the overlying rock hardness of the goaf is classified as hard rock.

[0055] In the rock hardness classification method based on the three-dimensional arch shell spatial structure, the volume V g closed by the arch shell structure is calculated in step (1).

[0056] ① When the working face strike is in a non-sufficient mining state, that is, L c , the arch shell structure is a semi-ellipsoidal surface, and the volume V g closed by the arch shell structure in this stage is:

[0057]

[0058] ② When the working face strike is in a sufficient mining state, that is, L c , the arch shell structure is a flat semi-ellipsoidal surface, and the volume V g closed by the arch shell structure in this stage is:

[0059]

[0060] In step (2), the ground movement and deformation prediction parameters include the subsidence coefficient, the horizontal movement coefficient, the mining influence propagation angle, the tangent of the main influence angle, and the inflection point offset distance; the ground subsidence basin function drawn according to the probability integral method is denoted as:

[0061] z=f(x,y) (9);

[0062] The volume V d of the ground subsidence basin calculated based on the differential idea is:

[0063]

[0064] In formula (9) and formula (10), z is the ground subsidence value, mm; x is the horizontal distance of the ground strike observation line, m; r xis the distance of the surface subsidence basin range in the strike direction, m; y is the horizontal distance of the surface subsidence basin range in the dip direction, m; r y is the distance of the surface subsidence basin range in the dip direction, m; Δx is the length of the flat bottom part of the surface subsidence basin in the strike direction, m; Δy is the length of the flat bottom part of the surface subsidence basin in the dip direction, m; W max is the maximum surface subsidence value, mm;

[0065] In step (3), the calculation formula of the damage volume ratio a is:

[0066]

[0067] V c = LDM (12) ;

[0068] In formula (11) and formula (12), V c is the goaf volume;

[0069] In step (4), when the value of the damage volume ratio a is less than or equal to 0.30, the hardness classification of the overlying rock mass of the goaf is soft and weak rock; when the value of the damage volume ratio a is greater than 0.30 and less than or equal to 0.65, the hardness classification of the overlying rock mass of the goaf is medium-hard rock; when the value of the damage volume ratio a is greater than 0.65 and less than or equal to 1.00, the hardness classification of the overlying rock mass of the goaf is hard rock.

[0070] An application of a rock hardness classification method based on a three-dimensional arch shell spatial structure, which utilizes the above-mentioned rock hardness classification method based on a three-dimensional arch shell spatial structure to calculate a surface residual subsidence coefficient q c ; the calculation formula of the surface residual subsidence coefficient q c is:

[0071]

[0072] In formula (13), q is the surface subsidence coefficient corresponding to the end of working face mining, which is measured

[0073] ; a is the damage volume ratio; t is the time from the end of mining, a.

[0074] The technical scheme of the present application has the following beneficial technical effects:

[0075] 1. The rock hardness grading method based on three-dimensional arch shell space structure of the application determines the comprehensive rock hardness grade by calculating the arch shell structure volume in the coal mining process, the surface subsidence basin volume, the damage volume ratio, and giving a critical value to achieve the goal of determining the comprehensive rock hardness grade, and reasonably determining the surface residual subsidence coefficient. The application can effectively solve the problem that the rock properties determined by physical experiments in the prior art cannot represent the entire mining area and the comprehensive effect after the rock combination is not considered, and provides an economic and reliable, reasonable and feasible solution for reasonably determining the surface residual subsidence coefficient and providing guidance for land resource utilization.

[0076] 2. The application associates the damage volume ratio with the rock hardness grading and the residual subsidence coefficient, can accurately and efficiently determine the comprehensive rock hardness grade of the entire mining area, and is beneficial to determining the surface residual subsidence coefficient. The existing method often takes points to represent the surface or only considers the effect of a certain rock layer, and the application determines the comprehensive rock hardness grade based on the development process of the arch shell structure through the damage volume ratio, which is more universal. Compared with the drilling sampling to determine the rock properties (multiple drill holes are arranged in the entire mining area or the expected area, and the sampling comparison determines the comprehensive rock properties), the cost is greatly reduced, the maximum economic benefit can be obtained, the comprehensive rock properties can be accurately determined, and the surface residual subsidence coefficient can be more accurately determined. BRIEF DESCRIPTION OF DRAWINGS

[0077] Figure 1 The arch shell structure evolution schematic diagram (L c ) in the embodiment of the application;

[0078] Figure 2 The arch shell structure evolution schematic diagram (L c ) in the embodiment of the application;

[0079] Figure 3 The strike section schematic diagram (L c ) in the embodiment of the application;

[0080] Figure 4 The dip section schematic diagram (L c ) in the embodiment of the application;

[0081] Figure 5 The strike section schematic diagram (L c ) in the embodiment of the application;

[0082] Figure 6 The surface subsidence basin form diagram (bowl shape) of different mining sufficiency in the embodiment of the application;

[0083] Figure 7 The surface subsidence basin form diagram (trough shape) of different mining sufficiency in the embodiment of the application;

[0084] Figure 8Morphological diagrams (disc-shaped) of surface subsidence basins with different levels of exploitation adequacy in embodiments of the present invention. Detailed Implementation

[0085] The rock mass hardness grading method based on a three-dimensional arched shell spatial structure in this embodiment mainly includes the following steps:

[0086] Step (1): Divide the mining face into different stages based on whether the mining is sufficient, calculate the trajectory equation of the arch shell structure corresponding to different stages of coal mining, and calculate the volume V formed by the closure of the arch shell structure. g ;

[0087] As the working face advances, the overlying strata in the mining area will collapse under their own control, forming an "arch" structure. This structure provides macroscopic support for the overall overlying strata, such as... Figures 1 to 5 As shown.

[0088] The X-axis represents the strike direction of the working face, the Y-axis represents the dip direction, and the Z-axis is vertically upward. The XOY plane represents the plane of the coal seam being mined. When the working face advances by ΔL, the origin of the coordinate system advances by ΔL / 2 along the positive X-axis. Considering that the dip length of the working face is generally determined when it is laid out, different mining stages are divided based on the strike length. When L < L c At that time, the mechanical model of the arch shell is as follows: Figure 1 As shown. When L = L c At that time, the height of the arch shell structure reaches its maximum value under the geological and mining conditions. As the working face continues to advance, the height of the arch shell structure no longer changes, such as... Figure 2 As shown.

[0089] (I) When the working face is not fully mined, i.e., L < L c At this point, the tendency is towards full or insufficient exploitation, i.e., D < D0. c or D≥D c The calculation method for the trajectory equation of the arch shell structure is as follows:

[0090] The equation of the semi-ellipsoid of the spatial arch shell structure is determined as follows:

[0091]

[0092] As can be seen from the above equation, the equation for the arch shell structure can be determined simply by determining the values ​​of coefficients A, B, and C; as shown in the figure, in equation (1): C = h;

[0093] Substituting the calculation formulas for A, B, and C into equation (1) yields the trajectory equation of the arch shell structure:

[0094]

[0095] In this embodiment: L cLcrit is the critical advancing distance of working face, m; L c = (1.2-1.4)H; D c Dcrit is the critical tendency length of working face, m; D c = (1.2-1.4)H; H is the mining depth, m; L is the advancing distance of working face, m; S L is the distance from the inner side of the shell base to the coal wall along the strike, m; D is the tendency length of working face, m; S D is the distance from the inner side of the shell base to the coal wall along the tendency, m; h is the height of the arch shell structure, m.

[0096] (II) When the working face strike is in the fully mined state, i.e. L≥L c , the arch shell structure is a flat semi-ellipsoidal surface, and the tendency is fully mined or insufficiently mined, i.e. D<D c or D≥D c ; the trajectory equation of the arch shell structure is respectively: and two intervals:

[0097] ① When , the trajectory equation of the arch shell structure is:

[0098]

[0099] ② When , the trajectory equation of the arch shell structure is:

[0100]

[0101] In this embodiment: h c is the height of the bedrock, i.e. the height of the arch shell structure reaches the maximum value of the geological mining conditions, m.

[0102] As the working face continuously advances, the height h c of the arch shell structure no longer changes, and the profile along the tendency is basically constant (as shown in Figure 4 ), only the profile along the strike is elongated, and the profile along the strike evolves from an arch shape to a flat arch (as shown in Figure 5 ), wherein the flat part c(Lc-L) increases with the increase of the advancing distance of the working face, and a stable periodic compression phenomenon occurs, the flat arch along the strike no longer has a bearing effect, and the arch along the tendency has a bearing effect.

[0103] (III) Calculate the volume of the arch shell structure

[0104] Since the shell base will gradually move to the deep part of the coal wall during the advancing of the working face, i.e. S L and S D will increase with the increase of the advancing distance L of the working face, according to the two-zone constraint theory of A.H. Wilson, the distance SL The height h of the arch shell structure can be expressed as:

[0105]

[0106] The height h of the arch shell structure can be expressed as:

[0107]

[0108] In formula (5) and formula (6), M is the thickness of the coal seam, m; K is an empirical coefficient, and the value is 0.05-1.

[0109] ① When L < L c , the arch shell shape is a half ellipsoid, and according to the ellipsoid volume formula, the volume V of the arch shell structure at this stage is: g

[0110]

[0111] ② When L ≥ L c , the arch shell structure is a flat half ellipsoid, and the volume V g of the arch shell structure closed at this stage is:

[0112]

[0113] Step (2): arranging an observation line on the main section of the working face and observing regularly, determining the surface movement and deformation prediction parameters according to the measured data obtained by observation, and drawing the surface subsidence basin function by using the probability integral method according to the surface movement and deformation prediction parameters; dividing the surface subsidence basin into multiple sections, and calculating the volume V d of the surface subsidence basin based on the differential thought.

[0114] The surface movement and deformation prediction parameters include the subsidence coefficient, the horizontal movement coefficient, the mining influence propagation angle, the tangent of the main influence angle, and the inflection point offset distance. The calculation process of the surface movement and deformation prediction parameters is as follows:

[0115] The subsidence coefficient = the maximum subsidence value / (the coal thickness * the cosine value of the coal seam inclination);

[0116] The horizontal movement coefficient = the maximum horizontal movement value / the maximum subsidence value;

[0117] The main influence propagation angle = the mining depth / the main influence radius;

[0118] The mining influence propagation angle = 90 - the coal seam inclination * the empirical coefficient;

[0119] The determination of the inflection point offset distance is to find the point of half of the maximum subsidence value on the subsidence curve, and to measure the horizontal distance from the point to the working face recovery boundary line. ​

[0120] Based on the different mining stages, i.e., the adequacy of mining, surface subsidence basins can be divided into three types: two-way inadequacy ("bowl-shaped"), one-way inadequacy ("trough-shaped"), and two-way adequacy ("disc-shaped"). Figures 6 to 8 As shown. Based on the measured data, the fitted surface subsidence basin function is as follows:

[0121] z = f(x,y) (9);

[0122] The volume V of the surface subsidence basin calculated based on the concept of differential calculus. d for:

[0123]

[0124] In formulas (9) and (10), z is the surface subsidence value in mm; x is the horizontal distance of the surface strike observation line in m; r x y represents the strike direction distance of the surface subsidence basin, in meters; y represents the horizontal distance of the surface dip observation line, in meters; r y Δx represents the dip direction distance of the surface subsidence basin, in meters; Δx represents the length of the strike-sloping flat bottom portion of the surface subsidence basin, in meters; Δy represents the length of the dip-sloping flat bottom portion of the surface subsidence basin, in meters; W max The maximum subsidence value is expressed in mm.

[0125] Step (3): Calculate the damage volume ratio α. The calculation formula is:

[0126]

[0127] V c =LDM (12);

[0128] In formulas (11) and (12): V c This represents the volume of the goaf.

[0129] Step (4): Give the critical value of the damage volume ratio and determine the hardness classification of the overlying rock mass in the goaf of the mining area;

[0130] When the damage volume ratio α is less than or equal to 0.30, the hardness of the overlying rock mass in the goaf is classified as weak lithology; when the damage volume ratio α is greater than 0.30 and less than or equal to 0.65, the hardness of the overlying rock mass in the goaf is classified as medium-hard lithology; when the damage volume ratio α is greater than 0.65 and less than or equal to 1.00, the hardness of the overlying rock mass in the goaf is classified as hard lithology.

[0131] In this embodiment, after determining the hardness classification of the overlying rock mass in the mining area's goaf, the residual surface subsidence coefficient q is calculated using its damage volume ratio α. c The calculation formula is:

[0132]

[0133] In formula (13), q is a surface subsidence coefficient corresponding to the end of working face mining, which is obtained by measurement; t is the time from the end of mining, a (years).

[0134] Obviously, the above embodiments are merely exemplary but not as a limitation to the embodiments. Based on the above description, one of ordinary skill in the art can further make other different forms of changes or modifications. Here, all the embodiments are not required to be enumerated. The obvious changes or modifications derived from the above are still within the protection scope of the patent application claims.

Claims

1. A rock mass hardness classification method based on three-dimensional arch shell spatial structure, characterized in that, Comprising the following steps: Step (1): dividing according to whether the working face is fully mined, calculating the trajectory equation of the arch structure corresponding to different mining stages of coal, and calculating the volume formed by the closure of the arch structure V g ; Step (2): laying observation lines on the main section of the working face and observing periodically, determining the surface movement and deformation prediction parameters according to the measured data obtained by observation, and drawing the surface subsidence basin function by using the probability integral method according to the surface movement and deformation prediction parameters; dividing the surface subsidence basin into multiple sections, and calculating the volume of the surface subsidence basin based on the differential thought V d ; Step (3): Calculate the damage volume ratio α; Step (4): Give the damage volume ratio critical value, determine the hardness classification of overburden rock mass above the mined-out area of the mine; In step (1): When the working face is in a non-full mining state, that is, at this time, or , the calculation method of the arch shell structure trajectory equation is: First determine the half-ellipsoidal surface equation of the spatial arch shell structure as: （1）； In formula (1): , , ; The calculation formula of A , B , C is substituted into equation (1) to obtain the trajectory equation of the arch shell structure: （2）； When the working face is in a fully mined state, i.e. At this time, Or The arch shell structure is a flat semi-ellipsoidal surface, and the trajectory equation of the arch shell structure is respectively in the following two intervals: When the trajectory equation of the arch shell structure is: （3）； When the trajectory equation of the arch shell structure is: （4）； In formula (2), formula (3) and formula (4): L c is the critical advancing distance of the working face, m; L c = (1.2~1.4) H ; D c is the critical inclination length of the working face, m; D c = (1.2~1.4) H ; H m is the depth of exploitation; L m is the distance of working face advancing; S L m is the distance from the coal wall to the inside of the strike base; D m is the length of the working face inclination; S D m is the distance from the coal wall to the inside of the inclination base; h m is the height of the arch structure; h c m is the height of the base rock, that is, the height of the arch structure reaches the maximum value of the geological mining conditions. In step (1), the distance from the inner side of the advancing shell to the coal wall S L The calculation formula is: （5）； Height of the arch shell structure h The calculation formula is: （6）； In formula (5) and formula (6): M is the thickness of the coal seam, m; K is an empirical coefficient, and the value is 0.05-1; In step (1), the volume enclosed by the vault structure is calculated V g Time: ①When the working face is in the non-sufficient mining state, that is , the arch shell structure is a semi-ellipsoid, and the volume formed by the closed arch shell structure in this stage is V g : （7）； When the working face is in the fully-mined state, i.e. , the arch shell structure is a flat semi-ellipsoidal surface, and the volume formed by the closed arch shell structure at this stage is V g : （8）； In formula (7) and formula (8): L c For the critical advancing distance of the working face, m; L c = (1.2~1.4) H ; H For the mining depth, m; L For the advancing distance of the working face, m; D For the length of the working face inclination, m; h c For the height of the bedrock, m; M For the thickness of the coal seam, m; K For the empirical coefficient, the value is 0.05~1; In step (2), the surface movement deformation prediction parameters include the subsidence coefficient, the horizontal movement coefficient, the mining influence propagation angle, the tangent of the main influence angle and the inflection point offset distance; In step (2), the surface subsidence basin function drawn according to the probability integral method is denoted as: （9）； Then the volume of the surface subsidence basin is calculated based on the differential idea V d is: （10）； In formula (9) and formula (10), z is the surface subsidence value, mm; x is the horizontal distance of the surface to the observation line, m; r x is the horizontal distance of the surface subsidence basin range to the observation line, m; y is the horizontal distance of the surface to the observation line, m; r y is the horizontal distance of the surface subsidence basin range to the observation line, m; △ x m for the length of the flat bottom part of the surface subsidence basin, m; △ y m for the length of the flat bottom portion of the surface subsidence basin, m; W max Maximum ground settlement, mm; L c is a critical advancing distance of the working face, L c = (1.2 ~ 1.4) H , H is a mining depth, m; D c is a critical tendency length of the working face, D c = (1.2 ~ 1.4) H , m; L is an advancing distance of the working face, m; D is a tendency length of the working face, m; In step (3), the calculation formula of the damage volume ratio α is: （11）； （12）； In formula (11) and formula (12): V c is the volume of the goaf, L is the working face advancing distance, m; D is the working face length, m; M for coal seam thickness, m; In step (4), when the value of the damage volume ratio α is less than or equal to 0.30, the hardness classification of the overburden rock mass above the mined-out area is soft and weak rock; when the value of the damage volume ratio α is greater than 0.30 and less than or equal to 0.65, the hardness classification of the overburden rock mass above the mined-out area is medium-hard rock; when the value of the damage volume ratio α is greater than 0.65 and less than or equal to 1.00, the hardness classification of the overburden rock mass above the mined-out area is hard rock.

2. Application of a rock mass hardness classification method based on three-dimensional arch shell spatial structure, characterized in that, The ground residual subsidence coefficient is calculated by using the rock hardness grading method based on the three-dimensional arch shell space structure in claim 1 q c ; the ground residual subsidence coefficient q c The calculation formula is: （13）； In formula (13), q is the surface subsidence coefficient corresponding to the end of working face mining, obtained by actual measurement; a is the damage volume ratio; t is the time from the end of mining, a.

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