A method for constructing a rock stratum movement main section "collapse-fracture-bend" vector field model

Abstract

The application discloses a construction method of a rock stratum movement main section "collapse-crack-bend" vector field model, which comprises the following steps: dividing the whole area on the overlying rock stratum movement main section into a rock block pile pressure area, a staggered end beam area, a broken rock stratum area and a curved rock stratum area; establishing a collapse accumulation block movement model for the rock block pile pressure area structure, establishing a "staggered end beam" movement model for the staggered end beam area structure, establishing a rock stratum movement model for the broken rock stratum area structure, and establishing a movement model of the upper and lower layers of the curved rock stratum and a movement model of the surface soil layer; establishing boundary conditions of each movement partition, and giving a rock stratum and surface movement full section vector field model with coordination constraints; and establishing a calculation model of the position, depth and width of the normal cracks of the rock stratum and the surface. The application can make up for the deficiency of the existing mining subsidence calculation means.

Description

Technical Field

[0001] This invention relates to the field of mining subsidence calculation technology, specifically a method for constructing a "collapse-crack-bend" vector field model of the main cross-section of rock strata movement, used to calculate and describe the movement deformation, collapse, and cracking of the main cross-section of rock strata movement. Background Technology

[0002] Calculating the movement of rock strata and the surface caused by underground coal mining involves multiple disciplines such as geology, mining, surveying, and mechanics. Furthermore, rock strata movement and deformation take many forms, including collapse, cracking, and bending, which are difficult to accurately describe using a single mechanical model. 1) Previous numerical simulation methods, including the finite element method, discrete element method, boundary element method, and finite difference method, cannot comprehensively reflect the various damage and movement scenarios of rock strata, and their calculation accuracy is affected by model bias and parameter value deviations. 2) Commonly used formulas for calculating the height of the "two zones" of rock strata movement describe the outlines of the collapse and crack zones, and are empirical formulas that cannot describe the movement of individual rock strata. 3) Models such as the probability integral method are used to describe continuous surface movement and deformation, but cannot describe discontinuous deformation phenomena such as rock strata fracture and surface cracks. Summary of the Invention

[0003] To address this, the present invention provides a classification method for the combined equilibrium structure of mining-induced rock masses, offering a method for constructing a "collapse-crack-bending" vector field model of the main cross-section of rock strata movement to calculate and describe the movement deformation, collapse, and cracking of the main cross-section. This method aims to solve the problem that existing mining subsidence studies do not provide a comprehensive quantitative description of rock strata movement and to compensate for the deficiencies in existing mining subsidence calculation methods. The model constructed using this method can achieve a quantitative description of continuous and discontinuous surface deformation and internal rock strata movement, providing a scientific basis for controlling mining-induced rock strata, evaluating the degree of mining damage, optimizing mining design, and protecting the ecological environment of mining areas.

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0005] A method for constructing a vector field model of the main cross-section of rock strata movement, characterized by "collapse-fracture-bending", includes the following steps:

[0006] Step (1): Divide the entire area on the main cross section of the overlying strata movement into four movement zones: rock block accumulation zone, misaligned beam zone, fractured strata zone, and bent strata zone.

[0007] Step (2): Establish a moving model of collapsed and accumulated blocks for the structure of the rock block accumulation zone, establish a moving model of "misaligned beams" for the structure of the misaligned beam zone, establish a moving model of rock strata with full thickness fracture and layered arrangement for the structure of the fractured rock strata zone, and establish a moving model of the upper and lower layers of the curved rock strata and the moving model of the topsoil layer for the structure of the curved rock strata zone.

[0008] Step (3): Based on the basic laws of mining subsidence, establish the boundary conditions of each moving zone and derive the full-section vector field model of rock strata and surface movement with coordinated constraints.

[0009] Step (4): Based on the medium characteristics of the rock strata and the tensile deformation of the rock strata, establish a calculation model for the location, depth and width of the normal cracks in the rock strata; based on the characteristics of the surface soil and rock and the tensile deformation of the surface, establish a calculation model for the location, depth and width of the surface cracks.

[0010] In the above-mentioned method for constructing the "collapse-crack-bend" vector field model of the main cross section of rock strata movement, in step (1), when dividing the overlying rock strata movement structure into zones: according to the classification method of the combined equilibrium structure of mining rock mass, the mining rock mass is divided into three types of equilibrium structures. Taking the second type of equilibrium structure, namely "secondary rock arch-compression body + bending compression body-secondary rock arch", as an example, the entire area of ​​overlying rock strata movement is divided into zones based on the rock strata fracture mechanics criteria and the rock strata movement angle parameters.

[0011] The above-mentioned method for constructing the "collapse-crack-bend" vector field model of the main cross-section of rock strata movement uses the Thiessen polygon optimization subdivision algorithm and affine transformation to establish the movement model of the collapsed accumulation block. The specific method is as follows:

[0012] First, the Thiessen polygon optimization subdivision algorithm is used to subdivide the collapsed rock layers in the rock block accumulation area without overlap or omission, resulting in subdivided polygonal blocks.

[0013] Determine the minimum bounding rectangle P0P1P2P3 of the natural block, and determine the minimum bounding rectangle Q0Q1Q2Q3 of the corresponding subdivided polygon block; transform rectangle P0P1P2P3 into rectangle Q0Q1Q2Q3 using affine transformation, and record the affine transformation matrix.

[0014] By performing an affine transformation on the natural block according to the affine transformation matrix, the natural block can be transformed into the rectangle Q0Q1Q2Q3;

[0015] Next, the natural block after affine transformation is taken as the clipping object, the polygon block is divided into clipping polygons, and the Weiler-Atherton polygon clipping algorithm is used for clipping.

[0016] The above operations can be performed on each subdivided polygon block to generate a model of the collapsing stacked block movement.

[0017] The above-mentioned method for constructing the "collapse-crack-bending" vector field model of the main cross-section of rock strata movement is based on the stress-deformation relationship of mining-induced stress on a single-end fixed-support upper-pressure lower-support beam, establishing a "misaligned-end stacked beam" movement model:

[0018] Through the rock strata movement boundary and the collapse angle αK Determine the boundaries between the misaligned beam stacking zone and the rock block compression zone; the differential equation for the bending deformation of the stacked beams in the misaligned beam stacking zone is expressed as:

[0019]

[0020] In equation (1): E is the elastic modulus of a certain stacked beam, I is the flexural stiffness of a certain stacked beam, and w is the deflection of a certain stacked beam. (4) denoted as the fourth derivative of the deflection; x represents the distance from the point of maximum compressive stress on a certain stacked beam, positive to the right and negative to the left. The maximum support stress; q i0 =γ s h s +∑γ k h k γ s h is the bulk density of the loose layer. s γ represents the thickness of the loose layer. k Let h be the unit weight of the k-th rock layer. k h is the thickness of the k-th rock layer; i α represents the thickness of the stacked beams or rock strata, in meters (m); K For the collapse angle; k w The subgrade coefficient of the coal and rock mass is MN / m. 3 L i1 L is the distance from the intersection of the lower beam of a given stacked beam and the boundary line of rock strata movement to the point of maximum compressive stress; i2 It is the distance from the fracture boundary of the lower beam of a certain stacked beam to the point of maximum compressive stress;

[0021] k w The formula for calculation is:

[0022] In equation (2), the rock strata numbered from the coal seam to the staggered beam at the end of the strata are 1, 2, 3, ..., m; E1, E2, E3, ... E m These are the elastic moduli of rock layers 1, 2, 3, ..., m, respectively, in MN / m. 2 h1, h2, h3, ... h m The thicknesses, in meters, represent the thicknesses of the 1st, 2nd, 3rd, ..., mth rock layers.

[0023] The above-mentioned method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement uses a "masonry beam" structure to establish a rock strata movement model in which the rock strata are broken in full thickness and arranged in layers in the fractured rock strata zone; the subsidence curve equation of the "masonry beam" structure in the fractured rock strata zone is:

[0024]

[0025] In equation (3), W(x) is the displacement of the "masonry beam" in meters; x is the distance from the mining boundary, negative on the coal side and positive on the goaf side in meters; W qt Δd is the maximum settlement value of the masonry beam, in meters; Δd is the length of the masonry beam block, in meters; a qt =0.25Δd; L qt W represents the length of the masonry beam above the goaf, in meters. qt =m c -Σh·(K p -1), m c The thickness of the coal seam is given in meters (m); Σh is the distance from the masonry beam to the coal seam roof in meters (m); K p L is the residual breccia coefficient of the collapsed rock strata. qt =L-2h / tan(α) K L is the mining length, in meters; h is the height of the "masonry beam" structure from the coal seam roof, i.e., the thickness of the "staggered beam" structure, in meters; α K The collapse angle;

[0026] The displacement equation for the masonry beam portion above the "staggered beam" zone on the cut-eye side is:

[0027]

[0028] In equation (4), w1(x) is the displacement of the masonry beam portion above the "staggered beam" area on the cut-off side, in meters; x is the distance from the mining boundary, negative on the coal body side and positive on the goaf side, in meters; k qt The subgrade coefficient is the same as the subgrade coefficient k of the coal and rock mass. w The calculation method is the same, E qt I qt q represents the flexural stiffness of the "masonry beam" structure. qt For the load above the "masonry beam";

[0029] The coefficients A1 and A2 are respectively:

[0030]

[0031] Based on the displacement equation of the "masonry beam", the masonry beam structure is divided into three categories, and filled with dots, horizontal lines and crosses respectively. After the three types of "masonry beam" structures are drawn, the rock strata movement model of the fractured rock strata with full thickness fracture and layered arrangement is completed.

[0032] The above-mentioned method for constructing the "collapse-crack-bend" vector field model of the main cross section of rock strata movement uses Boltzmann functions to establish movement models of the upper and lower layers of the bent rock strata and the topsoil layer.

[0033] The subsidence curve function of the main cross-section of the surface movement basin during limited mining is as follows:

[0034]

[0035] In equation (6), W 0 (x) represents the surface subsidence of the main cross-section under limited mining conditions, in meters; x is the distance from the mining boundary, negative on the coal body side and positive on the goaf side, in meters; R is the radius of severe influence; L is the strike length of the working face, i.e., the mining length, in meters; s3 and s4 are the offset distances of the left and right inflection points, respectively; W0 is the maximum surface subsidence, in meters.

[0036] The predicted subsidence curve function on the main cross-section of the surface movement basin under limited mining conditions is as follows:

[0037]

[0038] In equation (7), W 0 W(y) represents the surface subsidence of the main face under finite mining conditions, in meters; W(y) represents the surface subsidence of the main face under semi-infinite mining conditions, in meters; W(yD) represents the surface subsidence of the main face under semi-infinite mining conditions considering the working face dip length D, in meters; y represents the coordinates on the main face, in meters; D represents the working face dip length; s1 and s2 represent the offset distances of the downhill and uphill inflection points, respectively; H1 represents the downhill mining depth; α represents the coal seam dip angle; θ0 represents the mining influence propagation angle; R1 and R2 represent the severe influence radius of the downhill and uphill areas, respectively; W0 represents the maximum surface subsidence, in meters.

[0039] The function for the horizontally shifted projected curve is:

[0040]

[0041] In equation (8), b is the horizontal movement coefficient, which is between 0.2 and 0.4; W0 is the maximum subsidence value of the ground surface, in m; x is the coordinate on the main cross section of the strike; R is the radius of severe influence; L is the strike length of the working face, i.e. the mining length, in m; s3 and s4 are the offset distances of the left and right inflection points, respectively.

[0042] The above-mentioned method for constructing the "collapse-crack-bend" vector field model of the main cross section of rock strata movement determines the range of rock strata movement based on the coal seam dip angle, average mining depth, mining length, downhill boundary angle, uphill boundary angle, loose layer movement angle, and loose layer thickness.

[0043] The number of collapsed rock strata is determined based on the coal seam thickness, the distance between the collapsed rock strata and the coal seam, and the fragmentation characteristics of the rock strata. The overlying rock strata are defined from bottom to top as layer 1, layer 2, ... layer n. When the first to the (n-1)th rock strata collapse and accumulate in the goaf, the distance between the collapsed rock strata and the uncollapsed rock strata is:

[0044]

[0045] In equation (9), M is the thickness, h i K represents the thickness of the i-th rock layer. i Represents the coefficient of fragmentation of the i-th rock stratum; when Δ n-1,n When the distance is less than or equal to 0, the distance between the (n-1)th rock layer and the nth rock layer is less than or equal to 0, that is, the nth rock layer no longer collapses, and a total of n-1 layers collapse, that is, the number of collapsed rock layers is n-1.

[0046] Based on the number of collapse layers and the collapse angle α K Determine the boundaries between the rock block accumulation zone and the staggered beam zone;

[0047] The rock block accretion zone is represented by the collapse accumulation block movement model established in step (2);

[0048] The bending deformation of the "staggered beam" structure is described using the "staggered beam" moving model established in step (2), thus completing the expression of the staggered beam area;

[0049] The rock strata movement model with full-thickness fracture and layered arrangement established in step (2) is used to complete the expression of the fractured rock strata zone (masonry beam);

[0050] The movement models of the upper and lower layers of the curved rock strata and the topsoil layer established in step (2) are used to complete the representation of the curved rock strata area.

[0051] The above-mentioned method for constructing the "collapse-crack-bend" vector field model of the main cross section of rock strata movement takes into account the deformation coordination between different layers when using the movement models of the upper and lower layers of the bent rock strata and the movement model of the topsoil layer established in step (2) to complete the expression of the bent rock strata region. Specifically, in formula (6):

[0052] The formula for calculating the radius of influence R of the Boltzmann function at different layers is as follows:

[0053]

[0054] In equation (10), R(z) i ) represents the radius of severe influence of the stratigraphic level to be determined; H0 represents the mining depth; Z represents the radius of severe influence of the stratigraphic level to be determined; i R0 is the height of the stratum to be determined from the top of the coal seam, and R0 is the radius of severe influence on the surface.

[0055] Maximum sinking W in Boltzmann functions at different levels 岩 The formula for calculating W is 岩 =Mq 岩 cosα; where M is the coal seam thickness, α is the coal seam dip angle, and q 岩 The subsidence coefficient within the overlying strata is calculated using the following formula:

[0056]

[0057] In equation (11), q is the surface subsidence coefficient, H0 is the mining depth, and Z is the depth of mining. i The desired stratum is the height of the stratum above the coal seam roof; the surface subsidence coefficient q is calculated using the following formula:

[0058]

[0059] q 砌 =W 砌 / M;W 砌 =M-Σh·(K p -1); where: H0 is the mining depth, Z is the depth of mining. i Let q be the height of the desired seam from the roof of the coal seam. 砌 W represents the subsidence coefficient of the overlying strata at the masonry beam structure above the "collapse zone"; 砌 The maximum settlement value of the masonry beam structure above the "collapse zone" is given by M, where M is the coal seam thickness and h is the overburden layer thickness; K p The coefficient of stratification and swelling of the overlying strata;

[0060] Since the surface subsidence coefficient q is calculated after full mining has been achieved, the subsidence rate ρ is introduced into the calculation of surface subsidence during the mining process; the calculation of the subsidence rate ρ is as follows:

[0061]

[0062] In equation (13), k L The width-to-depth ratio is represented by A1, A2, A3, and A4, which are coefficients: A1 = 0, A2 = 1; when the overlying rock strata are hard, A3 = 0.620, A4 = 0.099; when the overlying rock strata are medium-hard, A3 = 0.394, A4 = 0.063; when the overlying rock strata are soft, A3 = 0.282, A4 = 0.045.

[0063] The formulas for calculating the offset distances s3 and s4 at the left and right inflection points are as follows:

[0064]

[0065] In equation (14), S(k) L ) represents the offset distance of the left turning point s3 or the offset distance of the right turning point s4, where s is the offset distance of the surface turning point under fully exploited conditions, and k L The aspect ratio is B1, B2, and B3 are coefficients.

[0066] When the overlying rock strata are hard, B1 = 0.8827, B2 = 0.620, B3 = 0.099; when the overlying rock strata are medium-hard, B1 = 1.3886, B2 = 0.394, B3 = 0.063; when the overlying rock strata are soft, B1 = 1.9420, B2 = 0.282, B3 = 0.045.

[0067] By calculating the subsidence rate and subsidence coefficient of the overlying rock or the surface, the inflection point offset distances s3 and s4 of different layers and the radius of severe influence R, the movement curves of the curved rock layer and the topsoil layer can be calculated by Equation (6), thus completing the expression of the curved rock layer area.

[0068] In the above method for constructing the "collapse-crack-bend" vector field model of the main cross-section of rock strata movement, step (4) involves establishing the calculation model for the location, depth, and width of the normal cracks in the rock strata.

[0069] Using 9 mm / m as the critical value for tensile deformation of the rock mass, region A is determined in the lower middle part and upper ends of the rock beam. A 10 mm / m contour line is drawn in region A; this contour line and the rock beam boundary form the area where cracks occur. The rock beam with span l and width h is divided into m rows and n columns of grid. Each grid has a length of l / n and a width of h / m, and is numbered (i,j), 1≤i≤m, 1≤j≤n. The horizontal deformation value ε(i,j) of each grid is calculated using the following formula:

[0070]

[0071] In equation (15), ε x Let x be the horizontal deformation of the curved rock strata, y be the coordinate along the direction of the curved rock strata, l be the span of the rock strata, h be the thickness of the rock strata, q be the load on the rock strata, E be the elastic modulus of the rock strata, and μ be Poisson's ratio.

[0072] Mark the grids with a horizontal deformation value of 10 mm / m, formulate a search strategy to determine the grid number of the grid with a horizontal deformation value of 10 mm / m, determine the position of the grid relative to the rock beam based on the grid number, and determine the location, depth and width of the crack based on the relative position and grid size (l / n, h / m);

[0073] The shape of the crack is determined using normal vectors: Assume that region A is a quadrilateral ABCD with coordinates A(x1,y1), B(x2,y2), C(x3,y3), and D(x4,y4). Then the outward normal vector of vector AB is n1 = (y2–y1,x1–x2), and the outward normal vector of vector CD is n3 = (y4–y3,x3–x4). The shape of the crack is determined using normal vectors n1 and n3.

[0074] Assuming the crack is A1P1B1, the normal vector Q1P1 pointing from vector A1B1 into the rock layer is determined, and the coordinates of point P1 are determined based on the crack depth. Point P1 is inserted between points A1 and B1 to update the coordinate sequence of the two polylines and obtain the deformation state of the rock layer after cracking. This completes the description of the normal crack in the rock layer and establishes a calculation model for the location, depth, and width of the normal crack in the rock layer.

[0075] In the above method for constructing the "collapse-crack-bend" vector field model of the main cross-section of rock strata movement, step (4) involves establishing the calculation model for the location, depth, and width of the normal cracks in the rock strata.

[0076] The depth of surface fissure development is denoted as H. z Areas M1P1P2M2 are surface fissures formed due to mining activities, d l Let ρ be the distance between adjacent surface cracks, and ρ be the radius of curvature of the surface. Then the crack width is... for:

[0077]

[0078] In equation (16), tanβ is the tangent of the main influence angle, H0 is the average sampling depth, and W m H represents the maximum surface subsidence. z This represents the crack depth. The critical horizontal deformation value of the average surface crack is calculated by the following formula:

[0079]

[0080] In equation (17), E is the tensile strength of the soil, and c is the cohesion. It is the internal friction angle;

[0081] Mining-induced surface fissure depth H z The calculation formula is:

[0082]

[0083] In equation (18), σ xm where c is the tensile strength of the soil and c is the cohesion. γ is the internal friction angle, and γ is the unit weight of the soil.

[0084] Location of surface cracks:

[0085] In the formula: x1 and x2 are the abscissas of the surface cracks, respectively; L is the mining length, and R is the main influence radius.

[0086] The technical solution of the present invention achieves the following beneficial technical effects:

[0087] This invention provides a method for constructing a "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement. Given relevant overburden and mining parameters, this method can calculate the movement and deformation of rock strata and the surface under the influence of mining, and construct a "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement. This accurately and dynamically reflects the state of rock strata movement and deformation. This invention is suitable for calculating and representing the "collapse, fracture, and bending" state of rock strata under the influence of coal seam mining with a dip angle less than or equal to 35°, providing a scientific basis for accurate assessment of mining damage. Attached Figure Description

[0088] Figure 1 A schematic diagram of the "collapse-crack-bend" vector field model of the main cross-section of rock strata movement in this embodiment of the invention;

[0089] Figure 2 Layered cross-section diagram of collapsed rock strata in an embodiment of the present invention;

[0090] Figures 3a to 3c This is a schematic diagram illustrating the generation of natural blocks in an embodiment of the present invention;

[0091] Figure 4 Schematic diagram of the collapsed block accumulation in an embodiment of the present invention;

[0092] Figure 5 A schematic diagram of the "staggered beam" structure in an embodiment of the present invention;

[0093] Figure 6a Schematic diagram of the stress-deformation principle of staggered beams in this embodiment of the invention;

[0094] Figure 6b A schematic diagram illustrating the calculation of the movement and deformation of the i-th layer of rock under the upper pressure and lower cushion in this embodiment of the invention;

[0095] Figure 7 A schematic diagram illustrating the establishment of the displacement equation for the "masonry beam" in an embodiment of the present invention;

[0096] Figure 8 A schematic diagram of the drawing process for masonry beam structures in this embodiment of the invention;

[0097] Figure 9 Diagram showing the range of rock strata movement in an embodiment of the present invention;

[0098] Figure 10 Contour maps of horizontal deformation of rock strata in embodiments of the present invention;

[0099] Figure 11 A schematic diagram illustrating the determination of crack properties in an embodiment of the present invention;

[0100] Figure 12a and Figure 12b This is a schematic diagram of the geometric representation of rock fractures in an embodiment of the present invention;

[0101] Figure 13a A schematic diagram illustrating the depth of surface cracks and the solution for that depth, as shown in this embodiment of the invention.

[0102] Figure 13b This is an embodiment of the present invention. Figure 13a A magnified view of the solution for surface fractures in the middle section;

[0103] Figure 14a A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=0°,

[0104] L=50m);

[0105] Figure 14b A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=0°,

[0106] L=100m);

[0107] Figure 14c A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=0°,

[0108] L=200m);

[0109] Figure 14d A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=0°,

[0110] L=300m);

[0111] Figure 14e A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=5°,

[0112] L=200m);

[0113] Figure 14f A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=10°,

[0114] L=200m);

[0115] Figure 14g A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=15°, L=200m);

[0116] Figure 14h A schematic diagram of the dynamic visualization of the vector field of the main cross-section of rock strata movement in this embodiment of the invention (α=20°,L=200m);

[0117] Figure 15 Schematic diagram of the Class II equilibrium structure of the mining-induced rock mass in this embodiment of the invention (secondary rock arch - accretion mass +

[0118] (Bending compression body - secondary rock arch). Detailed Implementation

[0119] The method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement in this embodiment includes the following steps:

[0120] Step 1: Based on the classification method of mining-induced rock mass combination equilibrium structure, rock stratum fracture mechanics criteria, and rock stratum movement angle parameters, determine the four zones of the overlying rock stratum movement structure.

[0121] This embodiment considers three states of the overlying strata under the influence of mining: collapse, cracking, and bending. Based on the classification method of the combined equilibrium structure of the mining-induced rock mass, the mining-induced rock mass is divided into three types of equilibrium structures. Considering the Class II equilibrium structure of the mining-induced rock mass ("secondary rock arch - accretionary body + bending accretionary body - secondary rock arch"), the movement structure zones of the overlying strata are further determined. The main structural zones include: accretionary rock block zone (i.e., collapse zone), staggered beam zone, fractured strata zone (masonry beam), and bent strata zone (with or without cracks), such as... Figure 1 .

[0122] Step 2: Using the Thiessen polygon optimization subdivision algorithm and affine transformation, a model of the collapsing accumulation block movement is generated; based on the stress-deformation relationship of the single-end fixed support upper pressure lower pad beam, a "staggered beam" movement model is established; using the "masonry beam" structure, a model of the movement of rock strata with full thickness fracture and layered arrangement is established; Boltzmann functions are used to establish movement models of the upper and lower layers of the curved rock strata and the topsoil layer.

[0123] The Thiessen polygon optimization subdivision algorithm is used to achieve non-overlapping and complete subdivision of collapsed rock strata, such as... Figure 2 .Sure Figure 3a Located in ηO loc The minimum bounding rectangle P0P1P2P3 of the natural block in the ζ-coordinate system is determined. Figure 3b Located in XO glo The minimum bounding rectangle Q0Q1Q2Q3 of the partitioned block in the Y coordinate system is used to transform ηO. loc The rectangle P0P1P2P3 in the ζ coordinate system is transformed into XO glo Rectangles Q0Q1Q2Q3 in the Y-coordinate system record the affine transformation matrix. By performing an affine transformation on the natural block according to this matrix, the natural block can be transformed to... Figure 3b Within the rectangle Q0Q1Q2Q3, the natural block after affine transformation is used as the clipping object, and the subdivided block is used as the clipping polygon. The Weiler-Atherton polygon clipping algorithm is used for clipping, as follows: Figure 3c By performing the above operations on each of the resulting polygons, a model of the collapsing, stacked blocks can be generated, such as... Figure 4 As shown.

[0124] like Figure 1 and Figure 15 Along the dip direction of the coal seam (or along the strike direction if it is a horizontal coal seam), the strata collapse area can be divided into a left-side "misaligned beam" zone (downhill direction), a rock block accumulation zone, and a right-side "misaligned beam" zone (uphill direction). The boundaries of these three zones can be determined by the strata movement boundary and the collapse angle α. K Sure.

[0125] according to Figure 6a and Figure 6b Under the influence of overlying support pressure and underlying rock strata, the differential equation for the bending deformation of a certain beam in a staggered-end stacked beam structure can be expressed in piecewise form:

[0126]

[0127] In equation (1): E is the elastic modulus of a certain stacked beam, I is the flexural stiffness of a certain stacked beam, and w is the deflection of a certain stacked beam. (4) denoted as the fourth derivative of the deflection; x represents the distance from the point of maximum compressive stress on a certain stacked beam, positive to the right and negative to the left. The maximum support stress; q i0 =γ s h s +∑γ k h k γ s h is the bulk density of the loose layer. s γ represents the thickness of the loose layer. k Let h be the unit weight of the k-th rock layer. k h is the thickness of the k-th rock layer; i α represents the thickness of the stacked beams or rock strata, in meters (m); K For the collapse angle; k w The subgrade coefficient of the coal and rock mass is MN / m. 3 L i1 L is the distance from the intersection of the lower beam of a given stacked beam and the boundary line of rock strata movement to the point of maximum compressive stress; i2 It is the distance from the fracture boundary of the lower beam of a certain stacked beam to the point of maximum compressive stress;

[0128] k w The formula for calculation is:

[0129] In equation (2), the rock strata numbered from the coal seam to the staggered beam at the end of the strata are 1, 2, 3, ..., m; E1, E2, E3, ... E m These are the elastic moduli of rock layers 1, 2, 3, ..., m, respectively, in MN / m. 2 h1, h2, h3, ... h m The thicknesses, in meters, represent the thicknesses of the 1st, 2nd, 3rd, ..., mth rock layers.

[0130] Considering the stress-deformation relationship of the single-end fixed support upper pressure lower pad beam, the equation (1) is numerically solved according to the values ​​of each parameter in equation (1) to obtain the moving model of the "misaligned stacked beam".

[0131] In areas of rock slab accumulation (i.e., caving zones) and overlapping beam zones, the rock strata above will fracture in their entirety and be arranged in layers, forming fractured rock strata zones (masonry beams). For example... Figure 7 As shown, the equation for the settlement curve of the "masonry beam" structure within the goaf is:

[0132]

[0133] In equation (3), W(x) is the displacement of the "masonry beam" in meters; x is the distance from the mining boundary, negative on the coal side and positive on the goaf side in meters; W qt Δd is the maximum settlement value of the masonry beam, in meters; Δd is the length of the masonry beam block, in meters; a qt =0.25Δd; L qt W represents the length of the masonry beam above the goaf, in meters. qt =m c -Σh·(K p -1), m c The thickness of the coal seam is given in meters (m); Σh is the distance from the masonry beam to the coal seam roof in meters (m); K p L is the residual breccia coefficient of the collapsed rock strata. qt =L-2h / tan(α) K L is the mining length, in meters; h is the height of the "masonry beam" structure from the coal seam roof, i.e., the thickness of the "staggered beam" structure, in meters; α K The collapse angle;

[0134] Considering the masonry beam portion above the staggered beam section on the cut-off side, and taking into account the support of the staggered beam structure and the coal seam being mined on the masonry beam, the displacement equation for the masonry beam portion above the staggered beam section on the cut-off side can be obtained as follows:

[0135]

[0136] In equation (4), w1(x) is the displacement of the masonry beam portion above the "staggered beam" area on the cut-off side, in meters; x is the distance from the mining boundary, negative on the coal body side and positive on the goaf side, in meters; k qt The subgrade coefficient is the same as the subgrade coefficient k of the coal and rock mass. w The calculation method is the same, E qt I qt q represents the flexural stiffness of the "masonry beam" structure. qt For the load above the "masonry beam";

[0137] The coefficients A1 and A2 are respectively:

[0138]

[0139] Once the displacement equation of the "masonry beam" is determined, the structure of the "masonry beam" is expressed. For example... Figure 8 The masonry beam structure is divided into three categories, represented by point filling, horizontal filling, and cross filling, respectively. First, the masonry beam block with point filling (A) is drawn. 1_ 1A2A3A 4_1 B1B 2_1 B 3_1 First, draw the masonry beam blocks filled with horizontal lines (A2C2C3C4, D1B1D3D4), and then draw the masonry beam blocks filled with cross lines (E1E2E3C3, F1F2F3E3, G1G2G3F3, H1H2H3G3). Once these three types of masonry beam structures are drawn, the fractured rock strata zone (masonry beams) is represented.

[0140] The Boltzmann function was used to establish movement models for the upper and lower bedding planes of the curved rock strata and for the topsoil layer. Considering the subsidence curve function of the main cross-section of the surface movement basin under limited mining conditions, as shown in equation (6):

[0141]

[0142] In equation (6), W 0 (x) represents the surface subsidence of the main cross-section under limited mining conditions, in meters; x is the distance from the mining boundary, negative on the coal body side and positive on the goaf side, in meters; R is the radius of severe influence; L is the strike length of the working face, i.e., the mining length, in meters; s3 and s4 are the offset distances of the left and right inflection points, respectively; W0 is the maximum surface subsidence, in meters.

[0143] The predicted subsidence curve function on the main cross-section of the surface movement basin under limited mining conditions is as follows:

[0144]

[0145] In equation (7), W 0 W(y) represents the surface subsidence of the main face under finite mining conditions, in meters; W(y) represents the surface subsidence of the main face under semi-infinite mining conditions, in meters; W(yD) represents the surface subsidence of the main face under semi-infinite mining conditions considering the working face dip length D, in meters; y represents the coordinates on the main face, in meters; D represents the working face dip length; s1 and s2 represent the offset distances of the downhill and uphill inflection points, respectively; H1 represents the downhill mining depth; α represents the coal seam dip angle; θ0 represents the mining influence propagation angle; R1 and R2 represent the severe influence radius of the downhill and uphill areas, respectively; W0 represents the maximum surface subsidence, in meters.

[0146] The function for the horizontally shifted projected curve is:

[0147]

[0148] In equation (8), b is the horizontal movement coefficient, which is between 0.2 and 0.4; W0 is the maximum subsidence value of the ground surface, in m; x is the coordinate on the main cross section of the strike; R is the radius of severe influence; L is the strike length of the working face, i.e. the mining length, in m; s3 and s4 are the offset distances of the left and right inflection points, respectively.

[0149] Equations (6) to (8) are used to describe the movement and deformation of curved rock strata and topsoil.

[0150] Step 3: Based on the basic laws of mining subsidence, the boundary conditions of each adjacent rock stratum movement zone were established, and a full-section vector field model of rock strata and surface movement with coordinated constraints was derived.

[0151] like Figure 9 Given the coal seam dip angle α, average mining depth H0, mining length L, downhill boundary angle β0, uphill boundary angle γ0 (if the coal seam is horizontal, then downhill boundary angle β0 = uphill boundary angle γ0 = strike boundary angle δ0), and loose layer movement angle. Loose layer thickness H s Based on these parameters, the range of rock strata movement, P1P2P3P4, is determined.

[0152] The number of collapsed rock strata is determined by considering the coal seam thickness, the distance between the collapsed strata and the coal seam, and the fragmentation characteristics of the strata. During the working face advance, the overlying strata are designated as layer 1, layer 2, ..., layer n from bottom to top. When strata 1 to (n-1)th collapse and accumulate in the goaf, the distance between the collapsed strata and the uncollapsed strata is:

[0153]

[0154] In equation (9), M is the thickness, h i K represents the thickness of the i-th rock layer. i Represents the coefficient of fragmentation of the i-th rock stratum;

[0155] When Δ n-1,n When the distance is less than or equal to 0, the distance between the (n-1)th rock layer and the nth rock layer is less than or equal to 0, meaning the nth rock layer will not collapse. A total of n-1 layers collapsed, therefore the number of collapsed rock layers is n-1. Based on the determined number of collapsed layers and the collapse angle α... K Identify the rock mass accumulation zone (i.e., the caving zone) and the staggered beam zone, such as... Figure 5 .

[0156] The rock block accretion zone was represented by the collapse accumulation block movement model established in step (2).

[0157] The bending deformation of the "misaligned beam" structure is described using the "misaligned beam" moving model established in step (2), as shown by the red solid line in the rock collapse area in Figure 14, which represents the bending deformation of the "misaligned beam", thus completing the expression of the misaligned beam area.

[0158] Using the rock strata movement model established in step (2) based on the "masonry beam" structure, which shows the rock strata breaking in full thickness and arranged in layers, the expression of the broken rock strata zone (masonry beam) is completed.

[0159] The moving models of the upper and lower layers of the curved rock strata and the moving model of the topsoil layer established in step (2) are used to represent the curved rock strata region. However, for the representation of the curved rock strata region, the deformation coordination between each layer needs to be considered. Specifically, in formula (6):

[0160] The formula for calculating the radius of influence R of the Boltzmann function at different layers is as follows:

[0161]

[0162] In equation (10), R(z) i ) represents the radius of severe influence of the stratigraphic level to be determined; H0 represents the mining depth; Z represents the radius of severe influence of the stratigraphic level to be determined; i R0 is the height of the stratum to be determined from the top of the coal seam, and R0 is the radius of severe influence on the surface.

[0163] Maximum sinking W in Boltzmann functions at different levels 岩 The formula for calculating W is 岩 =Mq 岩 cosα; where M is the coal seam thickness, α is the coal seam dip angle, and q 岩 The subsidence coefficient within the overlying strata is calculated using the following formula:

[0164]

[0165] In equation (11), q is the surface subsidence coefficient, H0 is the mining depth, and Z is the depth of mining. i The desired stratum is the height of the stratum above the coal seam roof; the surface subsidence coefficient q is calculated using the following formula:

[0166]

[0167] q 砌 =W 砌 / M;W 砌 =M-Σh·(K p -1); where: H0 is the mining depth, Z is the depth of mining. i Let q be the height of the desired seam from the roof of the coal seam. 砌 W represents the subsidence coefficient of the overlying strata at the masonry beam structure above the "collapse zone"; 砌The maximum settlement value of the masonry beam structure above the "collapse zone" is given by M, where M is the coal seam thickness and h is the overburden layer thickness; K p The coefficient of stratification and swelling of the overlying strata;

[0168] After the surface subsidence coefficient q is calculated, the overburden subsidence coefficient q is calculated according to equation (11). 岩 .

[0169] Since the surface subsidence coefficient q is calculated after full mining, the subsidence rate ρ needs to be introduced for calculating surface subsidence during the mining process. The calculation is performed using equation (13):

[0170]

[0171] In the formula, k L The aspect ratio is represented by A1, A2, A3, and A4, which are coefficients; A1 = 0, A2 = 1.

[0172] For overlying strata of different lithologies, the coefficients A3 and A4 are respectively:

[0173]

[0174] Based on the lithology of the overlying strata, appropriate coefficients are selected, and then the width-to-depth ratio is obtained through the mining depth and mining width, thereby calculating the surface subsidence rate.

[0175] In equation (6), the inflection point offsets s3 and s4 in the Boltzmann functions of different strata can be obtained by multiplying the inflection point offset coefficient by the height of the stratum to be determined from the roof of the coal seam. Similar to the surface subsidence rate ρ, the inflection point offset s i It is also related to the adequacy of mining, the offset distance S(k) of the overlying strata inflection point L Calculation formula:

[0176]

[0177] In equation (14), S(k) L ) represents the offset distance of the left turning point s3 or the offset distance of the right turning point s4, where s is the offset distance of the surface turning point under fully exploited conditions, and k L The aspect ratio is B1, B2, and B3 are coefficients.

[0178] For overlying strata of different lithologies, the coefficients B1, B2, and B3 are respectively:

[0179]

[0180] When the subsidence rate (subsidence coefficient) of the overlying rock or the surface is known, the inflection point offset distances s3 and s4 of different layers and the radius of severe influence R have been calculated, the movement curves of the curved rock layer and the topsoil layer are calculated by formula (6) to complete the expression of the curved rock layer area.

[0181] Step 4: Based on the characteristics of the rock strata and the magnitude of the tensile deformation, establish a calculation model for the location, depth, and width of the normal cracks in the rock strata; based on the characteristics of the surface soil and rock and the magnitude of the surface tensile deformation, establish a calculation model for the location, depth, and width of the surface cracks.

[0182] When rock strata located in a curved stratum region crack, normal fractures will form. The horizontal deformation field of the curved strata is calculated according to equation (15), resulting in a contour map of the horizontal deformation of the curved strata, as shown below. Figure 10 .

[0183]

[0184] In equation (15), ε x Let x be the horizontal deformation of the curved rock strata, y be the coordinate along the direction of the curved rock strata, l be the span of the rock strata, h be the thickness of the rock strata, q be the load on the rock strata, E be the elastic modulus of the rock strata, and μ be Poisson's ratio.

[0185] 9 mm / m (0.009) is taken as the critical value for tensile deformation of the rock mass, that is, the area in the rock strata where the horizontal deformation value exceeds 0.009. According to... Figure 10 It can be determined that the cracks originated in the lower middle and upper ends of the rock beam; the specific locations of these areas need to be determined. Figure 10 Abstraction and induction are used to obtain Figure 11 .

[0186] Figure 11 In the diagram, three smooth curves represent the 10 mm / m contour lines, which, together with the rock beam boundary, form the area where cracks occur. The rock beam with span l and width h is divided into m rows and n columns of grid. Each grid has a length of l / n and a width of h / m, and is numbered (i,j), 1≤i≤m, 1≤j≤n. The horizontal deformation value ε(i,j) of each grid is calculated according to the formula. The horizontal deformation value of the gray grid in the diagram is 10 mm / m. A search strategy is developed to determine the grid number of the grid with a horizontal deformation value of 10 mm / m. Based on the grid number, the position of that grid relative to the rock beam is determined. Based on the relative position and the grid size (l / n, h / m), the location, depth, and width of the crack can be determined.

[0187] Figure 12a The mathematical expressions for the external normals of each side of quadrilateral ABCD are described. The external normal vector of vector AB is n1 = (y2–y1, x1–x2); the external normal vector of vector CD is n3 = (y4–y3, x3–x4). The shape of the crack is determined by using the normal vectors n1 and n3.

[0188] consider Figure 12bCracks A1P1B1, A2P2B2, and C1P3D1 are identified. Based on vectors A1B1, A2B2, and C1D1, their respective normal vectors pointing into the rock stratum are determined: Q1P1, Q2P2, and Q3P3. Then, the coordinates of points P1, P2, and P3 are determined based on the crack depth. Point P1 is inserted between points A1 and B1, point P2 between points A2 and B2, and point P3 between points C1 and D1. The coordinate sequences of the two polylines are updated to obtain the deformation state of the rock stratum after cracking. This completes the description of the normal cracks in the rock stratum and establishes a calculation model for the location, depth, and width of the normal cracks.

[0189] Due to the influence of rock strata bending deformation, mining-induced cracks will occur in loose soil at the surface. Based on the Mohr-Coulomb criterion, calculation formulas are given for the critical horizontal deformation value, crack development depth, and crack development width, and a calculation model for surface crack location, crack depth, and crack width is established.

[0190] like Figure 13a and Figure 13b As shown, the depth of surface fissure development is denoted as H. z Regions M1P1P2M2 represent surface fissures formed by mining activities, α is the ultimate fissure angle, and d l Let ρ be the distance between adjacent surface cracks, and ρ be the radius of curvature of the surface. Then the crack width is... for:

[0191]

[0192] In equation (16), tanβ is the tangent of the main influence angle, H0 is the average sampling depth, and W m H represents the maximum surface subsidence. z This represents the crack depth. The critical horizontal deformation value of the average surface crack is calculated by the following formula:

[0193]

[0194] In equation (17), E is the tensile strength of the soil, and c is the cohesion. It is the internal friction angle;

[0195] Mining-induced surface fissure depth H z The calculation formula is:

[0196]

[0197] In equation (18), σ xm where c is the tensile strength of the soil and c is the cohesion. γ is the internal friction angle, and γ is the unit weight of the soil.

[0198] The location of the surface cracks is The model is defined as follows: x1 and x2 represent the abscissas of the surface fissures, L represents the mining length, and R represents the main influence radius. This completes the establishment of the calculation model for surface fissure location, fissure depth, and fissure width.

[0199] The "collapse-crack-bend" vector field model of the main cross section of rock strata movement constructed using the method described above in this embodiment is used to quantitatively express and describe the rock strata movement during coal seam mining at different dip angles.

[0200] When mining horizontal coal seams (α=0°), the strike boundary angle δ0=60°, the strike fully mined angle ψ3=58°, and the loose layer movement angle… Considering the rock strata movement at mining lengths L of 50m (before the initial roof collapse), 100m (partial mining), 200m (fully mined), and 300m (excessively fully mined), the data is plotted on [date missing]. Figures 14a to 14d .

[0201] When mining gently inclined coal seams (α = 5°, 10°, 15°, 20°), given the uphill boundary angle γ0 = 70°, the downhill boundary angle β0 = 54°, the uphill full mining angle ψ2 = 58°, the downhill full mining angle ψ1 = 54°, and the loose layer movement angle... Considering the rock strata movement when the mining length L is 200m, the following plot is drawn. Figures 14e to 14h .

[0202] The method of this invention is not applicable to situations with a dip angle greater than 35°. This is because when the coal seam dip angle α is greater than 35°, the overburden is subjected to tangential forces, and the overburden experiences shearing along the bedding planes. In this case, the damage to the overburden and its post-damage morphology under inclined coal seam mining conditions will change significantly and require further analysis.

[0203] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of the claims of this patent application.

Claims

1. A method for constructing a vector field model of a main cross-section of rock strata movement, characterized in that, Includes the following steps: Step (1): Divide the entire area on the main cross section of the overlying strata movement into four movement zones: rock block accumulation zone, misaligned beam zone, fractured strata zone, and bent strata zone. Step (2): Establish a moving model of collapsed and accumulated blocks for the structure of the rock block accumulation zone, establish a moving model of "staggered beams" for the structure of the staggered beam zone, establish a moving model of rock strata with full thickness fracture and layered arrangement for the structure of the fractured rock strata zone, and establish a moving model of the upper and lower layers of the curved rock strata and the moving model of the topsoil layer for the structure of the curved rock strata zone. A model of the movement of collapsed stacked blocks is established using the Thiessen polygon optimization subdivision algorithm and affine transformation. The specific method is as follows: First, the Thiessen polygon optimization subdivision algorithm is used to subdivide the collapsed rock layers in the rock block accumulation area without overlap or omission, resulting in subdivided polygonal blocks. Determine the minimum bounding rectangle of a natural block. P 0 P 1 P 2 P 3. Determine the minimum bounding rectangle of the subdivided polygonal block corresponding to the natural block. Q 0 Q 1 Q 2 Q 3; Use affine transformation to transform the rectangle P 0 P 1 P 2 P 3. Transform into a rectangle Q 0 Q 1 Q 2 Q 3. Record the affine transformation matrix; By performing an affine transformation on the natural block using the affine transformation matrix, the natural block can be transformed into a rectangle. Q 0 Q 1 Q 2 Q Within 3; Next, the natural block after affine transformation is taken as the clipping object, the polygon block is divided into clipping polygons, and the Weiler-Atherton polygon clipping algorithm is used for clipping. By performing the above operations on each subdivided polygonal block, a model of the collapsing stacked block movement can be generated. Based on the stress-deformation relationship of a single-end fixed-support upper-pressure lower-support beam, a moving model of "misaligned stacked beams" is established: Through rock strata movement boundaries and collapse angles α K Determine the boundaries between the misaligned beam stacking zone and the rock block compression zone; the differential equation for the bending deformation of the stacked beams in the misaligned beam stacking zone is expressed as: （1）； In formula (1): E Let be the elastic modulus of a certain stacked beam. I Let be the bending stiffness of a certain stacked beam. w Let the deflection of a certain stacked beam be... w (4) The fourth derivative of the deflection; x This represents the distance from the point of maximum compressive stress on a certain stacked beam, with positive values ​​to the right and negative values ​​to the left. φ im This represents the maximum support stress. , γ s The bulk density of the loose layer h s The thickness of the loose layer, γ k For the first k The unit weight of the rock strata h k For the first k The thickness of the rock strata; h i The thickness of the stacked beams or rock strata is in meters (m). α K The collapse angle; k w The subgrade coefficient of the coal and rock mass is MN / m. 3 ; L i1 It is the distance from the intersection of the lower beam of a certain stacked beam and the boundary line of rock stratum movement to the point of maximum compressive stress; L i2 It is the distance from the fracture boundary of the lower beam of a certain stacked beam to the point of maximum compressive stress; k w The formula for calculation is: （2）； In equation (2), the rock strata from the coal seam to the staggered beam at the end of the strata are numbered 1, 2, 3, …, m, respectively; E 1, E 2, E 3, … E m MN / m represents the elastic modulus of rock layers 1, 2, 3, ..., m. 2 ; h 1, h 2, h 3, … h m The thicknesses, in meters, represent the thicknesses of the 1st, 2nd, 3rd, ..., mth rock layers. A rock strata movement model is established in the fractured rock strata zone using a "masonry beam" structure, where the rock strata are fully fractured and arranged in layers. The settlement curve equation of the "masonry beam" structure in the fractured rock strata zone is as follows: （3）； In equation (3), W ( x () represents the displacement of the "masonry beam", in meters. x The distance from the mining boundary is represented by negative values ​​on the coal seam side and positive values ​​on the goaf side, in meters (m). W qt The maximum settlement value of the "masonry beam" is in meters (m); Δ d The length of the masonry beam block is in meters (m). a qt =0.25Δ d ; L qt The length of the "masonry beam" above the goaf, in meters; W qt = m c −Σ h ·( K p -1), m c For the thickness of the ore, m; Σ h The distance from the "masonry beam" to the top of the coal seam, in meters (m). K p The residual fragmentation coefficient of the collapsed rock strata; L qt = L -2 h / tan( α K ), L The length of the quarry is in meters (m). h The height of the "masonry beam" structure from the top of the coal seam is the same as the thickness of the "staggered beam" structure, in meters. α K The collapse angle; The displacement equation for the masonry beam portion above the "staggered beam" zone on the cut-eye side is: （4）； In equation (4), w 1 ( x ) represents the displacement of the "masonry beam" portion above the "staggered beam" area on the side of the cut-in eye, in meters; x The distance from the mining boundary is represented by negative values ​​on the coal seam side and positive values ​​on the goaf side, in meters (m). , k qt The subgrade coefficient of the cushion layer and the subgrade coefficient of the coal and rock mass. k w The calculation method is the same. E qt I qt The bending stiffness of the "masonry beam" structure; q qt For the load above the "masonry beam"; coefficient A 1 and A 2 are respectively: ； （5）； Based on the displacement equation of the "masonry beam", the masonry beam structure is divided into three categories, and filled with dots, horizontal lines and crosses respectively. Once the three types of "masonry beam" structures are drawn, the rock strata movement model of the rock strata in the fractured rock strata area with full thickness fracture and layered arrangement is completed. Boltzmann functions were used to establish movement models of the upper and lower layers of curved rock strata and the topsoil layer. The subsidence curve function of the main cross-section of the surface movement basin during limited mining is as follows: （6）； In equation (6), W 0 ( x (m) represents the surface subsidence along the main cross-section under limited mining conditions. x The distance from the mining boundary is represented by negative values ​​on the coal seam side and positive values ​​on the goaf side, in meters (m). R This significantly affects the radius; L The working face length, i.e., the mining length, is in meters (m). s 3 and s 4 represents the offset distance between the left and right inflection points; W 0 represents the maximum surface subsidence, in meters (m). The predicted subsidence curve function on the main cross-section of the surface movement basin under limited mining conditions is as follows: （7）； In equation (7), W 0 ( y (m) represents the surface subsidence along the main cross-section under limited mining conditions. W ( y ) represents the surface subsidence of the inclined main cross section under semi-unlimited mining conditions, in meters; W ( yD ) represents the surface subsidence of the dip main section under semi-infinite mining conditions considering the dip length D of the working face, in meters; y represents the coordinates on the dip main section, in meters. D For the working face dip length, s 1 and s 2 represents the offset distance between the turning points on the downhill and uphill sides, respectively. H 1 represents the downhill mining depth, and α represents the coal seam dip angle. θ 0 represents the angle of propagation of the impact of mining. R 1 and R 2 represents the radius of severe impact when going downhill and the radius of severe impact when going uphill, respectively; W 0 represents the maximum surface subsidence, in meters (m). The function for the horizontally shifted projected curve is: （8）； In equation (8), b This is the horizontal shift factor, with a value between 0.2 and 0.

4. W 0 represents the maximum surface subsidence, in meters (m). x To find the coordinates on the main cross-section, R This significantly affects the radius; L The working face length, i.e., the mining length, is in meters (m). s 3 and s 4 represents the offset distance between the left and right inflection points; Step (3): Based on the basic laws of mining subsidence, establish the boundary conditions of each moving zone and derive the full-section vector field model of rock strata and surface movement with coordinated constraints. The range of rock strata movement is determined based on the coal seam dip angle, average mining depth, mining length, downhill boundary angle, uphill boundary angle, loose layer movement angle, and loose layer thickness. The number of collapsed rock strata is determined based on the coal seam thickness, the distance between the collapsed rock strata and the coal seam, and the fragmentation characteristics of the rock strata; the overlying rock strata are defined from bottom to top as layer 1, layer 2, ... layer n; when the first rock strata reach the nth layer... n -1 rock strata collapsed and accumulated in the goaf. At this time, the distance between the collapsed rock strata and the uncollapsed rock strata is: （9）； In equation (9), M To obtain thick, h i Indicates the first i The thickness of each rock layer K i Indicates the first i The coefficient of fragmentation of each rock stratum; when Δ n-1,n When the distance is less than or equal to 0, the distance between the (n-1)th rock layer and the nth rock layer is less than or equal to 0, that is, the distance between the (n-1)th rock layer and the nth rock layer is less than or equal to 0. n No more rock layers collapsed, and a total of n-1 layers collapsed, meaning the number of collapsed rock layers is (the total number of layers is 1). n -1; Based on the number of collapse layers and the collapse angle α K Determine the boundaries of the rock block accumulation zone and the staggered beam zone; The rock block accretion zone is represented by the collapse accumulation block movement model established in step (2); The bending deformation of the "staggered beam" structure is described using the "staggered beam" moving model established in step (2), thus completing the expression of the staggered beam area; The rock strata movement model with full-thickness fracture and layered arrangement established in step (2) is used to complete the expression of the fractured rock strata zone (masonry beam); The movement models of the upper and lower layers of the curved rock strata and the topsoil layer established in step (2) are used to complete the representation of the curved rock strata area; Step (4): Based on the medium characteristics of the rock strata and the tensile deformation of the rock strata, establish a calculation model for the location, depth and width of the normal cracks in the rock strata; based on the characteristics of the surface soil and rock and the tensile deformation of the surface, establish a calculation model for the location, depth and width of the surface cracks.

2. The method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement according to claim 1, characterized in that, In step (1), when dividing the overlying strata movement structure into zones: according to the classification method of mining rock mass combination equilibrium structure, for the third type of equilibrium structure, namely "secondary rock arch - accretion body + bending pressure body - secondary rock arch", the entire area of ​​overlying strata movement is divided into zones based on the rock fracture mechanics criteria and rock strata movement angle parameters.

3. The method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement according to claim 2, characterized in that, When using the moving models of the upper and lower layers of the curved rock strata and the moving model of the topsoil layer established in step (2) to complete the representation of the curved rock strata region, the deformation coordination between each layer is considered. Specifically, in formula (6): Radius of influence in Boltzmann functions at different levels R The formula for calculation is: （10）； In equation (10), R ( z i () represents the radius of severe influence of the layer to be determined; H 0 represents the mining depth; Z i The height of the desired stratum from the top of the coal seam. R 0 represents the radius of severe impact on the Earth's surface; Maximum sinking in Boltzmann functions at different levels W 岩 The calculation formula is W 岩 = Mq 岩 cosα; where M Where α is the coal seam thickness and α is the coal seam dip angle. q 岩 The subsidence coefficient within the overlying strata is calculated using the following formula: （11）； In equation (11), q This is the surface subsidence coefficient. H 0 represents the mining depth. Z i The height of the desired stratum from the top of the coal seam; Surface subsidence coefficient q Calculate using the following formula: （12）； q 砌 =W 砌 / M W 砌 = M −Σ h ·( K p -1); where: H 0 represents the mining depth. Z i The height of the desired stratum from the top of the coal seam. q 砌 W represents the subsidence coefficient of the overlying strata at the "masonry beam" structure above the "collapse zone"; 砌 This represents the maximum settlement value of the masonry beam structure above the "collapse zone". M For coal seam thickness, h The thickness of the overlying rock layers; K p The coefficient of stratification and swelling of the overlying strata; Due to the surface subsidence coefficient q This calculation is based on the results obtained after full mining has been achieved. The subsidence rate is introduced into the calculation of surface subsidence during the mining process. ρ ; Subsidence rate ρ Calculation: （13）； In equation (13), k L Aspect ratio, A 1. A 2. A 3 and A 4 is the coefficient. A 1=0, A 2=1; when the overlying rock layer is a hard rock layer, A 3 = 0.620 A 4 = 0.099; when the overlying strata are medium-hard strata, A 3 = 0.394 A 4 = 0.063; when the overlying rock layer is a weak rock layer, A 3 = 0.282, A 4 = 0.045; Left and right turning point offset distance s 3 and s The formula for calculating 4 is: （14）； In equation (14), S ( k L () represents the offset distance of the left turning point. s 3 or right turning point offset distance s 4, s The offset distance of the surface inflection point under fully exploited conditions. k L Aspect ratio, B 1. B 2 and B 3 is the coefficient; When the overlying rock strata are hard rock strata B I = 0.8827 B 2 = 0.620, B 3 = 0.099; When the overlying strata are medium-hard strata B 1 = 1.3886 B 2 = 0.394, B 3 = 0.063; when the overlying rock layer is a weak rock layer, B 1 = 1.9420 B 2 = 0.282, B 3 = 0.045; By calculating the subsidence rate and subsidence coefficient of the overlying strata or the surface respectively, the inflection point offset distance of different layers was determined. s 3 and s 4 and severely affect the radius R The movement curves of the curved rock layer and the topsoil layer can be calculated by formula (6), thus completing the expression of the curved rock layer area.

4. The method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement according to claim 3, characterized in that, In step (4): the calculation model for the location, depth, and width of the rock strata normal fracture is established: Using 9 mm / m as the critical value for tensile deformation of the rock mass, region A is determined in the lower middle part and upper ends of the rock beam. Contour lines of 10 mm / m are drawn in region A; these 10 mm / m contour lines and the rock beam boundary form the area where cracks occur. m OK n The grid pairs of columns have a span of l Width is h The rock beams are divided into grids, each grid being [length missing]. l / n Width is h / m Each grid is numbered ( i , j ), 1≤ i ≤ m , 1≤ j ≤ n ; Calculate the horizontal deformation value for each grid. ε ( i , j The calculation formula is: （15）； In equation (15), ε x This represents the horizontal deformation of the bent rock strata. x The coordinates are along the direction of the curved rock strata. y The coordinates are perpendicular to the direction of the curved rock strata; l The span of the rock strata, h For the thickness of the rock strata, q The load on the rock strata. E The elastic modulus of the rock strata. μ Poisson's ratio; Mark the grids with a horizontal deformation value of 10 mm / m, formulate a search strategy to determine the grid number of the grid with a horizontal deformation value of 10 mm / m, determine the position of the grid relative to the rock beam based on the grid number, and then determine the relative position and grid size ( l / n , h / m Determine the location, depth, and width of the crack; Using normal vectors to determine the crack shape: Assume region A is a quadrilateral ABCD, with coordinates A(x1,y1), B(x2,y2), C(x3,y3), and D(x4,y4). Then the vectors... AB Outer normal vector n 1=( y 2– y 1, x 1– x 2), Vector CD Outer normal vector n 3=( y 4– y 3, x 3– x 4) Using the normal vector n 1 and n 3. Determine the morphology of the crack; Assuming the crack is A1P1B1, the normal vector pointing from A1B1 to the interior of the rock stratum... Q 1 P 1. Then, determine the coordinates of point P1 based on the crack depth, insert point P1 between point A1 and point B1, update the coordinates of the point sequence of the two polylines to obtain the deformation state after the rock layer cracks, thereby completing the description of the rock layer normal crack and establishing a calculation model for the location, depth and width of the rock layer normal crack.

5. The method for constructing the "collapse-fracture-bending" vector field model of the main cross-section of rock strata movement according to claim 4, characterized in that, In step (4): the calculation model for the location, depth, and width of the rock strata normal fracture is established: The depth of surface fissure development is denoted as . H z Areas M1P1P2M2 are surface fissures formed due to mining activities. d l Let ρ be the distance between adjacent surface cracks, and ρ be the radius of curvature of the surface. Then the crack width is... for: （16）； In equation (16), tan β The tangent value is the main influencing factor. H 0 represents the average mining depth. W m This represents the maximum surface subsidence value. H z This represents the crack depth. The critical horizontal deformation value of the average surface crack is calculated by the following formula: （17）； In equation (17), E The tensile strength of the soil. c The cohesive force is φ, and the internal friction angle is φ. Mining-induced surface fissure depth H z The calculation formula is: （18）； In equation (18), σ xm The tensile strength of the soil. c φ is the cohesive force, φ is the internal friction angle, and γ is the unit weight of the soil. Location of surface cracks: ， ； In the formula: x 1 and x 2 represents the x-coordinate of the surface cracks; L For the length of the mine, R The radius of influence is the primary factor.

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