Stress field prediction method based on "plate-beam" structure of key stratum of mining overburden rock

Abstract

The present application belongs to the technical field of mine exploitation, and particularly relates to a stress field prediction method based on a "plate-beam" structure of a key stratum of a mining overburden rock. The present application simplifies a key stratum of a bending subsidence zone and a key stratum of a solid coal side fissure zone into a multi-layer superimposed infinite long elastic foundation plate and a semi-infinite long elastic foundation plate respectively, simplifies a broken key stratum of a goaf side fissure zone into a multi-layer superimposed "masonry beam", establishes a stress field prediction model based on a "plate-beam" structure of a key stratum of a mining overburden rock, constructs a prediction equation of a mining stress and a stope support pressure under a key stratum of different horizons, clarifies a quantitative relationship between a broken movement of a key stratum of different horizons and a stress field, and proposes a stress field three-dimensional space evolution prediction method considering an occurrence of a key stratum of an overburden rock and a broken movement characteristic, a shape and a size of a goaf, and the like, thereby avoiding a problem of an insufficient consideration of an occurrence of a key stratum of an overburden rock in a prior art.

Description

Technical Field

[0001] This invention belongs to the field of mining technology, specifically relating to a method for predicting the stress field based on the "plate-beam" structure of the key overburden layer in mining operations. Background Technology

[0002] Coal mining disrupts the initial stress balance, causing a redistribution of stress in the surrounding and overlying strata, thus creating a stress field in the mining-affected overlying strata. Accurately predicting the spatial distribution of this stress field is crucial for guiding the early warning and prevention of disasters such as coal and gas outbursts, rock bursts, and roadway deformation and instability.

[0003] Existing research indicates that the occurrence conditions and fracture movement characteristics of key overburden strata determine the distribution of the stress field. However, current theoretical prediction methods for mining-induced overburden stress fields focus on predicting stope bearing pressure, while coal seam bearing pressure is only a small part of the mining-induced overburden stress field. These methods still cannot predict the stress distribution of key overburden strata at different strata under mining conditions. Furthermore, existing stope bearing pressure prediction methods, such as those based on limit equilibrium theory, those based on the comprehensive movement angle originating at the edge of the bearing pressure distribution, and those based on Winkler elastic foundation beams, do not consider the characteristics of key overburden strata at different strata or simply simplify them into beams. In reality, simplifying unbroken key strata such as curved subsidence zones and solid coal sides into "plates" is more accurate. Existing stress field prediction methods are not applicable to mining conditions where there are typical thick and hard key layers in the overburden. This often leads to a significant discrepancy between the prediction results and the actual field measurements. A quantitative relationship between the fracture movement of key layers at different strata and the stress field of the overburden under mining has not yet been established. There is still a lack of stress field prediction methods that take into account factors such as the occurrence and fracture movement characteristics of key layers at different strata in the overburden, as well as the shape and size of the goaf. Summary of the Invention

[0004] To address the shortcomings of existing stress field prediction methods, this invention proposes a stress field prediction method based on the "plate-beam" structure of key layers in mining-induced overburden, enabling quantitative prediction of the distribution of key layers in different overburden strata and the support pressure in the mining area.

[0005] Specifically, the prediction method of the present invention includes the following steps:

[0006] S1, the mining area is divided along the strata profile, with the x-axis defined along the mining direction of the working face, the y-axis along the length of the cut, and the origin of the coordinate system at the starting position of the cut. The rectangular goaf area is defined as Ω2, and the solid coal side area as Ω1, wherein the limit equilibrium zone of the solid coal side is Ω. p The elastic zone range of the solid coal side is Ω. eThe four endpoints of the goaf are B1, B2, B3, and B4, respectively, starting from the origin of the coordinate system and moving counterclockwise; the four endpoints of the solid coal side area are A1, A2, A3, and A4, respectively, and A1 corresponds to B1.

[0007] S2. Using the critical layer theory controlled by rock strata, the distribution of critical layers in the overlying strata is determined, and the ranges of caving zones, fracture zones, and bending subsidence zones are identified. The critical layers are defined from bottom to top as critical layer i, 1≤i≤n, i∈N. + Among them, the key layers in the fracture zone are key layer 1 to key layer m-1 from bottom to top, and the key layers in the bending and subsidence zone are key layer m to key layer n from bottom to top.

[0008] S3, for different key layers i on the solid coal side, 1≤i≤n, i∈N + The key strata i at different levels of the goaf lateral bending and subsidence zone, m≤i≤n, i∈N + Simplified to a multi-layered composite elastic foundation thin plate, the key fracture layer i at different strata of the side fracture zone in the goaf, 1≤i≤m-1,i∈N + The beam is simplified to a multi-layer composite masonry beam, and a stress field prediction model is established.

[0009] S4. Establish the partial differential equations for the deflection of the multi-layer composite elastic foundation thin plate with different key layers on the solid coal side and different key layers on the goaf side bending subsidence zone, as shown in equations (1) and (2), respectively.

[0010]

[0011]

[0012] In the formula, w i (x,y) represents the deflection of key stratum i at different levels on the solid coal side, m; w c i (x,y) represents the deflection of key layer i at different strata in the goaf lateral bending subsidence zone, m; k i The subgrade coefficient for key layer i at different strata, in N / m. 3 ;k c m The subgrade coefficient for the key stratum m on the goaf side is given in N / m. 3 ;q i For the self-weight of the key layer i and its load layer at different strata, Pa; D i Let be the bending stiffness of key layer i at different strata, in N·m;

[0013] S5, determine the boundary conditions (3) and (5), and determine the continuity condition (4).

[0014]

[0015]

[0016]

[0017] In the formula, θ xi (x,y) and θ yi (x, y) represent the rotation angles along the x and y directions of key strata i at different levels in the bent subsidence zone of the solid coal seam; θ c xi (x,y) and θ c yi (x, y) represent the rotation angles of key strata i at different levels along the x and y directions in the goaf lateral bending subsidence zone, respectively; M xi (x,y) and M yi (x, y) represent the bending moments along the x and y directions of key strata i at different levels on the solid coal side, respectively; M c xi (x,y) and M c yi (x, y) represent the bending moments along the x and y directions of key strata i at different levels in the goaf lateral bending subsidence zone; Q xi (x,y) and Q yi (x, y) represent the shear forces along the x and y directions of key strata i at different levels on the solid coal side, respectively; Q c xi (x,y) and Q c yi (x, y) represent the shear forces along the x and y directions of the key stratum i at different levels in the goaf lateral bending subsidence zone; l0 is the unit width of the fractured block of the key stratum in the fracture zone, in meters; l i , in meters, represents the length of the fractured block of the key stratum i at different strata in the side fracture zone of the goaf.

[0018] S6. Based on the relationship between the deflection, rotation angle, bending moment and shear force of the Winkler elastic substrate in equation (6), and using the boundary conditions of equations (3) and (5) and the continuity condition of equation (4), equations (1) and (2) are solved to calculate the deflection curve equation w of the key layer i at different strata on the coal side of the mining overburden body. i The deflection curve equations w of (x,y) and different key layers i in the goaf lateral bending and subsidence zone c i (x,y)

[0019]

[0020] In the formula, θ x (x,y), θ y (x, y) are the rotation angles along the x and y directions, respectively; M x (x,y),My (x, y) represent the bending moments along the x and y directions, respectively; Q x (x,y), Q y (x, y) represent the shear forces along the x and y directions, respectively;

[0021] S7. Based on the relationship between the deflection, load and subgrade coefficient of the Winkler elastic foundation thin plate, the stress plane distribution equations for mining stress under different key layers i on the coal side of the mining-induced overburden body and different key layers i in the bending subsidence zone on the goaf side are determined, as shown in equations (8) and (9) respectively.

[0022]

[0023]

[0024] In the formula, σ i (x, y) represent the plane distribution equations of mining-induced stress under different key strata i on the solid coal side, respectively, Pa; σ c i (x,y) is the plane distribution equation of mining-induced stress under key layer i at different levels in the goaf side bending subsidence zone, Pa;

[0025] S8, determine the plane distribution equation of mining-induced stress under the critical fracture layer i at different strata in the fracture zone of the 1 / 4 equally divided goaf area, 1≤i≤m-1,i∈N + Equation (10); by utilizing symmetry, the plane distribution of mining-induced stress under the key fracture layer i at different strata in the Ω2 fracture zone of the entire goaf can be obtained.

[0026]

[0027] In the formula, σ c i (x,y) is the plane distribution equation of mining-induced stress under the critical fracture layer i at different strata in the goaf side fracture zone, Pa;

[0028] S9, based on equation (12), calculate the plane distribution of the support pressure in the mining area.

[0029]

[0030] In the formula, σ1(x,y) is the plane distribution equation of mining-induced stress under the key stratum 1 on the solid coal side, in Pa; σ c 1(x,y) is the plane distribution equation of mining-induced stress under the key stratum 1 on the goaf side, Pa; q0 is the self-weight of the rock strata between the coal seam and the key stratum 1, Pa; M is the mining height, m; denoted as the internal friction angle (°); f is the friction coefficient; N0 is the coal seam support capacity (Pa); d(x,y) is the minimum distance from any point in the coal body's limit equilibrium zone to the goaf boundary (m).

[0031] Among them, D i Calculate according to formula (13)

[0032]

[0033] In the formula, D i The bending stiffness of key layer i at different strata is given in N·m; E i For the elastic modulus of key layer i at different strata, Pa; h i Let m be the thickness of the key layer i at different strata; μ be the thickness of the key layer i at different strata. i denoted as Poisson's ratio for key layer i at different strata.

[0034] This invention simplifies the key strata of the bending subsidence zone and the key strata of the solid coal side fracture zone into multi-layered, infinitely long elastic ground plates and semi-infinitely long elastic ground plates, respectively. The key strata of the fracture zone on the goaf side are simplified into multi-layered, composite "masonry beams." A stress field prediction model based on the "plate-beam" structure of the mining-induced overburden key strata is established. Prediction equations for the planar distribution of mining-induced stress and stope support pressure under key strata at different strata are constructed. The quantitative relationship between the fracture movement of key strata at different strata and the stress field is clarified. A three-dimensional spatial evolution prediction method for the stress field is proposed, taking into account the occurrence and fracture movement characteristics of the overburden key strata, the shape and size of the goaf, etc. This avoids the problem of insufficient consideration of the occurrence conditions of the overburden key strata in existing methods. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the stress field prediction model of the present invention along the horizontal stratum.

[0036] Figure 2 This is a schematic diagram of the stress field prediction model of the present invention along the vertical cross section of the strata;

[0037] Figure 3 This is a schematic diagram of the stress field prediction model of the present invention along the vertical cross section of the strata in a specific example;

[0038] Figure 4A This is a specific example of the mining stress plane distribution under subcritical layer 1 in this invention;

[0039] Figure 4B This is a specific example of the mining stress plane distribution under subcritical layer 2 in this invention;

[0040] Figure 4C This is a specific example of the mining stress plane distribution under subcritical layer 3 in this invention;

[0041] Figure 4D This is a specific example of the stress distribution under the subcritical layer 4 of this invention.

[0042] Figure 4EThis is the mining stress plane distribution under the main key layer 5 in a specific example of the present invention;

[0043] Figure 5 This is a specific example of the planar distribution of the support pressure in the mining area according to the present invention. Detailed Implementation

[0044] To better understand the technical content of this invention, specific embodiments are described below in conjunction with the accompanying drawings. Various aspects of this invention are described with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of this invention are not limited to those shown in the drawings. It should be understood that this invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in this invention are not limited to any particular implementation. Furthermore, some aspects of this invention can be used alone or in any suitable combination with other aspects disclosed in this invention.

[0045] The stress field prediction method based on the "plate-beam" structure of the key overburden strata in mining-induced rock mass proposed in this invention is as follows:

[0046] like Figure 1 As shown, the mining area is divided along the stratum bedding profile. The x-axis is defined along the mining direction of the working face, and the y-axis is defined along the length of the cut. The starting position of the cut is the origin 0. a and b are the dimensions of the goaf along the x-axis and y-axis, respectively. The goaf is approximately rectangular with a length of a and a width of b. The four endpoints of the goaf are B1, B2, B3, and B4, respectively, starting counterclockwise from the origin. C1, C2, and C3 are the midpoints of B1B2, the center of the goaf, and the midpoint of B1B4, respectively. C1C2C3 represents a quarter-divided area of ​​the goaf. Assuming the stress field to be predicted is a rectangle A1A2A3A4, and defining the goaf-side region B1B2B3B4 as Ω2, then the solid coal-side region Ω1 is the area of ​​rectangle A1A2A3A4 minus the area of ​​rectangle B1B2B3B4. Mining-induced stress concentration causes a portion of the solid coal area near the goaf to be in a state of limit equilibrium (plastic state), corresponding to a rectangle D1D2D3D4. Therefore, the range Ω1 of the limit equilibrium zone (plastic zone) on the solid coal side is... p The range of the elastic zone on the solid coal side is Ω, calculated by subtracting the rectangular regions B1B2B3B4 from the rectangular regions D1D2D3D4. e Subtract the rectangle D1D2D3D4 from the rectangle A1A2A3A4; where A1, D1 correspond to B1, A2, D2 correspond to B2, A3, D3 correspond to B3, and A4, D4 correspond to B4, with the unit being meters.

[0047] like Figure 2The vertical cross-section of the strata shown indicates that coal mining causes fracturing and flexural subsidence of the overlying strata, forming caving zones, fracture zones, and flexural subsidence zones sequentially from bottom to top within the vertical height range of the strata. The critical stratum theory of strata control proposes that when multiple strata exist in the overlying rock mass of a mining area, the stratum that controls all or part of the rock mass movement is called the critical stratum. The stress field changes caused by strata movement after mining are mainly controlled by the fracturing motion of the critical stratum. When the critical stratum fractures, the subsidence and deformation of all or part of the overlying strata are coordinated and consistent; the former is referred to as strata activity. The primary key layer is called the primary key layer, and the latter is called the sub-key layer. Based on the stratigraphic borehole column, the distribution of the key layer controlled by the rock strata is determined using the key layer theory (Xu Jialin, Qian Minggao. Method for determining the location of the key layer of the overlying strata [J]. Journal of China University of Mining and Technology, 2000, 29(5):463-467.). Then, according to the "Regulations for the Retention of Coal Pillars and Coal Mining in Buildings, Water Bodies, Railways and Main Shafts", the height of the caving zone and the fracture zone is calculated to determine the distribution of the key layers of the fracture zone and the bending subsidence zone. The key layers are defined from bottom to top as key layer i (1≤i≤n,i∈N). + Among them, the key layers in the fracture zone are sub-key layer 1 to sub-key layer m-1 from bottom to top, and the key layers in the bending and subsidence zone are sub-key layer m to main key layer n from bottom to top (the uppermost key layer is the main key layer).

[0048] Furthermore, such as Figure 2 The vertical stratigraphic profile shown indicates that the key strata in the fracture zone on the goaf side have undergone fracture movement, while the key strata at different levels on the solid coal side and the key strata in the bending and subsidence zone on the goaf side have not fractured, but have shown flexural subsidence. Assuming that the key strata at different levels of the overburden and their load-bearing strata conform to the Winkler elastic foundation assumption (according to the strata-controlled key strata theory, the load-bearing strata of key strata i are the strata between key strata i and key strata i+1), and that under normal circumstances the ratio of the thickness of the key strata at different levels to the length A1A2 and width A2A3 of the stress field prediction range is less than 1 / 8 to 1 / 5, conforming to the elastic thin plate assumption, then the key strata i at different levels on the solid coal side (1≤i≤n, i∈N) can be considered as... + ) and key strata i (m≤i≤n,i∈N) at different levels in the goaf lateral bending and subsidence zone + Simplified to a multi-layered composite elastic foundation thin plate, the key fracture layer i (1≤i≤m-1,i∈N) at different strata in the fracture zone on the side of the goaf. + The stress field prediction model is simplified to a multi-layered composite "masonry beam" and based on the "plate-beam" structure of the key layer of mining overburden.

[0049] Key strata i (1≤i≤n, i∈N) at different levels on the solid coal side + ) and key strata i (m≤i≤n,i∈N) at different levels in the goaf lateral bending and subsidence zone +No fracture occurred, which conforms to the assumption of an elastic thin plate. All conditions satisfy the Winkler partial differential equation for the deflection of a thin plate on an elastic foundation, as follows:

[0050]

[0051] In the formula, w(x,y) is the deflection of the thin plate, in meters (m); k is the subgrade coefficient, in N / m. 3 q is the load, Pa; D is the bending stiffness of the thin plate, N·m.

[0052] The key strata i (1≤i≤n, i∈N) at different levels on the solid coal side are considered. + ) and key strata i (m≤i≤n,i∈N) at different levels in the goaf lateral bending and subsidence zone + Simplified to a multi-layered composite elastic foundation thin plate, formula (1) is established for key layers i (1≤i≤n,i∈N) at different strata on the solid coal side. + Equation (2) and key strata i at different levels of the goaf lateral bending subsidence zone (m≤i≤n,i∈N) + The partial differential equations for the deflection of thin plates on multilayer composite elastic foundations;

[0053]

[0054]

[0055] In the formula, w i (x,y) represents the deflection of key stratum i at different levels on the solid coal side (1≤i≤n,i∈N). + ), m; w c i (x, y) represents the deflection of the key layer i at different levels in the goaf lateral bending subsidence zone (m ≤ i ≤ n, i ∈ N). + ), m; k i The subgrade coefficients of key layer i at different strata (1≤i≤n, i∈N) + ), N / m 3 ;k c m The subgrade coefficient for the subcritical layer m on the side of the goaf, in N / m. 3 ;q i The self-weight of the key layer i and its load layer at different strata (1≤i≤n,i∈N) + ), Pa; D i The bending stiffness of key layer i at different strata (1≤i≤n,i∈N) + ), N·m.

[0056] On the solid coal side, the overburden flexural deformation gradually decreases with increasing distance from the goaf, until it drops to zero at the boundary; the key strata i (m≤i≤n, i∈N) at different levels of the flexural subsidence zone. +At the boundary, the fixed-support boundary condition is satisfied, and the deflection and rotation angle of any section on the sinking boundary are both 0. That is, the partial differential equations of deflection of the multilayer composite thin plate in equation (1) satisfy the boundary condition of equation (3) below.

[0057]

[0058] Key layers i (m≤i≤n, i∈N) at different strata in the bent subsidence zone + If flexural subsidence occurs and the key stratum satisfies the continuity condition at the boundary between the solid coal side and the goaf side, then the deflection, rotation angle, bending moment, and shear force experienced by the key stratum on the goaf side and its corresponding key stratum on the solid coal side at the boundary are equal, that is, the partial differential equations of deflection of the multilayer composite plate in equations (1) and (2) satisfy the continuity condition in equation (4).

[0059]

[0060] Key strata i (1≤i≤m-1,i∈N) at different levels in the solid coal side fracture zone + At any section at the boundary of the goaf, the shear force is half the self-weight of the key layer fracture block, and the bending moment is 0. Equation (1) of the partial differential equations for the deflection of the multi-layer composite plate satisfies the following boundary conditions (5).

[0061]

[0062] In equations (3), (4) and (5), θ xi (x,y) and θ yi (x, y) represent the rotation angles along the x and y directions of the key stratum i at different levels of the coal seam side bending subsidence zone (m ≤ i ≤ n, i ∈ N). + );θ c xi (x,y) and θ c yi (x, y) represent the rotation angles of key strata i at different levels in the goaf lateral bending subsidence zone along the x and y directions, respectively (m ≤ i ≤ n, i ∈ N). + M xi (x,y) and M yi (x, y) represent the bending moments along the x and y directions of different key strata i on the solid coal side (1 ≤ i ≤ n, i ∈ N). + M c xi (x,y) and M c yi (x, y) represent the bending moments along the x and y directions of the key stratum i at different levels in the goaf lateral bending subsidence zone (m ≤ i ≤ n, i ∈ N). + );Q xi (x,y) and Q yi(x, y) represent the shear forces along the x and y directions of different key strata i on the solid coal side (1 ≤ i ≤ n, i ∈ N). + );Q c xi (x,y) and Q c yi (x, y) represent the shear forces along the x and y directions of the key stratum i at different levels in the goaf lateral bending subsidence zone (m ≤ i ≤ n, i ∈ N). + ); l0 is the unit width of the fractured block in the key layer of the fracture zone, in meters; l i The length of the fractured block of key layer i at different strata in the side fracture zone of the goaf (1≤i≤m-1,i∈N) + ), m.

[0063] Based on the relationship between the deflection, rotation angle, bending moment and shear force of the Winkler elastic substrate in equation (6), and using the boundary conditions of equations (3) and (5) and the continuity condition of equation (4), we can apply equation (1) to the key strata i (1≤i≤n,i∈N) at different levels on the coal side of the mining overburden body. + Equation (2) and key strata i at different levels of the goaf lateral bending subsidence zone (m≤i≤n,i∈N) + The partial differential equations for the deflection of multi-layer composite plates are solved to calculate the deflection curve equations w of key strata i at different levels on the coal side of the mining-induced overburden solid. i (x,y)(1≤i≤n,i∈N + The deflection curve equations w of key strata i at different levels in the goaf lateral bending and subsidence zone. c i (x,y)(m≤i≤n,i∈N + ).

[0064]

[0065] In the formula, θ x (x,y), θ y (x, y) are the rotation angles along the x and y directions, respectively; M x (x,y),M y (x, y) represent the bending moments along the x and y directions, respectively; Q x (x,y), Q y (x, y) represent the shear forces along the x and y directions, respectively.

[0066] Based on the relationship between the deflection, load, and subgrade coefficient of the Winkler elastic foundation thin plate, see the following equation (7).

[0067] σ(x,y)=kw(x,y) (7)

[0068] In the formula, σ(x,y) is the intensity of the reaction force exerted by the foundation on the thin plate, Pa; w(x,y) is the deflection of the thin plate, m; and k is the foundation coefficient, N / m. 3 ;

[0069] It can be determined that the key strata i (1≤i≤n,i∈N) at different levels on the coal side of the overburden body are mined. + ) and key strata i (m≤i≤n,i∈N) at different levels in the goaf lateral bending and subsidence zone + The stress plane distribution equations for mining at the bottom interface of the key layer are given in equations (8) and (9), respectively.

[0070]

[0071]

[0072] In equations (8) and (9), σ i (x, y) represent the plane distribution equations of mining stress under different key strata i on the solid coal side (1 ≤ i ≤ n, i ∈ N). + ), Pa; σ c i (x,y) is the plane distribution equation of mining stress under the key layer i at different levels of the goaf lateral bending subsidence zone (m≤i≤n,i∈N). + ), Pa.

[0073] For the critical fracture strata i (1≤i≤m-1,i∈N) at different strata in the side fracture zone of the goaf, + The stress distribution equation under mining conditions is given. Due to the "OX" fracture of the key stratum in the fracture zone on the goaf side, the fractured blocks of the key stratum form a "masonry beam" load-bearing structure. Assuming that the key stratum i (1≤i≤m-1,i∈N) at different levels in the fracture zone on the goaf side is... + Half of the self-weight of the boundary fracture block is transferred to the coal and rock mass around the mining area, and the other half of the load is transferred to the goaf, with the force on the underlying rock mass being linearly distributed. Simultaneously, considering the force of the key layer of the goaf lateral bending and subsidence zone on the key layer of the underlying fracture zone, the key layers of different fracture levels i (1≤i≤m-1,i∈N) in the goaf lateral fracture zone are considered. + Simplified to a multi-layered composite "masonry beam", the goaf area can be divided into 1 / 4 equal regions. Figure 1 In the rectangular region B1C1C2C3, the key fracture layers at different strata of the fracture zone are i (1≤i≤m-1,i∈N). + The stress plane distribution equation under mining conditions is as follows (10).

[0074]

[0075] In equation (10), σ c i(x,y) is the plane distribution equation of mining stress under the critical fracture layer i at different levels of the side fracture zone in the goaf (1≤i≤m-1,i∈N). + ), Pa.

[0076] Furthermore, by utilizing symmetry, the entire goaf area can be obtained ( Figure 1 In the Ω2 region, the key fracture layers i (1≤i≤m-1,i∈N) at different strata of the fracture zone are broken. + The plane distribution of mining stress under ( ).

[0077] Based on equations (8) and (10), the plane distribution equations of mining-induced stress σ1(x,y) under sub-key stratum 1 on the solid coal side and the plane distribution equations of mining-induced stress σ1(x,y) under sub-key stratum 1 on the goaf side can be obtained respectively. c 1(x,y), plus the self-weight q0 of the rock strata between the coal seam and the subcritical stratum 1, can be used to obtain the distribution of coal body support pressure in the elastic zone of the solid coal side and the stress distribution in the goaf. At the same time, according to the support pressure distribution equation (Equation 11) of the limit equilibrium zone of the coal body in front of the stope in the literature "Mine Pressure and Strata Control" (Qian Minggao et al., China University of Mining and Technology Press, p. 60, 2010), the plane distribution equation of the support pressure in the stope can be obtained (12):

[0078]

[0079] In the formula, σ p (x,y) is the distribution equation of the bearing pressure in the ultimate equilibrium zone of the coal body, Pa; M is the mining height, m; denoted as the internal friction angle (°); f is the friction coefficient; N0 is the coal face support capacity (Pa); d(x,y) is the minimum distance from any point in the coal body's ultimate equilibrium zone to the goaf boundary (m).

[0080]

[0081] In the formula, σ1(x,y) is the plane distribution equation of mining-induced stress under the subcritical stratum 1 on the solid coal side, in Pa; σ c 1(x,y) is the plane distribution equation of mining-induced stress under sub-key stratum 1 on the side of the goaf, Pa; q0 is the self-weight of the rock strata between the coal seam and sub-key stratum 1, Pa.

[0082] Regarding the selection of prediction parameters for this prediction method, D i Calculate according to formula (13)

[0083]

[0084] In the formula, D i The bending stiffness of key layer i at different strata (1≤i≤n,i∈N) + ), N·m; E iThe elastic modulus of key layer i at different strata (1≤i≤n,i∈N) + ), Pa; h i The thickness of key layer i at different strata (1≤i≤n, i∈N) + ), m; μ i Poisson ratios for different key layers i (1≤i≤n, i∈N) + ).

[0085] In the above specific implementation, for E i h i k i k c m q i The value of can be found in the reference "Method to calculate working surface abutment pressure based on key strata theory" (HAN HK, XU JL, WANG XZ, "Advances in Civil Engineering", 2019, Article ID 7678327, 20 pages). i The value of μ can be found in the reference "Mine Pressure and Strata Control" (Qian Minggao et al., China University of Mining and Technology Press, p. 77, 2010). i Determined based on the mechanical properties of key layers at different strata. f and N0 are determined based on the mechanical properties of the coal body, a and b are determined based on the mining dimensions of the goaf, and M is determined based on the mining height of the coal seam.

[0086] Specific calculation examples

[0087] Based on the borehole columnar section of the Mengjin Coal Mine strata, the distribution of key overlying strata was determined using the critical layer theory controlled by strata. Then, according to the "Regulations for the Retention of Coal Pillars and Coal Mining under Pressure in Buildings, Water Bodies, Railways and Main Shafts," the heights of the caving zone and fracture zone were calculated, determining the distribution of key layers in the fracture zone and the bending subsidence zone. A total of 5 key layers exist in the Mengjin Coal Mine strata, with 1 key layer located in the fracture zone and 4 key layers located in the bending subsidence zone. That is, in the stress field prediction model, m is taken as 2 and n as 5. The key layer in the fracture zone is sub-key layer 1, and the key layers in the bending subsidence zone, from bottom to top, are sub-key layer 2, sub-key layer 3, sub-key layer 4, and main key layer 5 (the uppermost key layer is the main key layer). See Table 1 for details. Figure 3 .

[0088] Table 1 Distribution of key overburden strata in Mengjin Coal Mine

[0089]

[0090] If the predicted range A1A2 is 1400m and A2A3 is 950m, the ratio of the critical layer thickness to this size is less than 1 / 8 to 1 / 5, which meets the assumption of elastic thin plate; the subcritical layers 1, 2, 3, 4, and 5 on the solid coal side and the subcritical layers 2, 3, 4, and 5 on the goaf side bending and subsidence zone are simplified into multi-layer composite elastic foundation thin plate, and the deflection partial differential equations of the multi-layer composite elastic foundation thin plate of the solid coal side and the subcritical layers 2, 3, 4, and 5 on the goaf side bending and subsidence zone are established.

[0091]

[0092]

[0093] In the formula, w1(x,y), w2(x,y), w3(x,y), w4(x,y), and w5(x,y) represent the deflections (in meters) of subcritical layers 1, 2, 3, 4, and 5 on the solid coal side, respectively; w c 2(x,y), w c 3(x,y), w c 4(x,y), w c 5(x,y) represents the deflection (m) of subcritical layers 2, 3, 4, and 5 of the goaf lateral bending subsidence zone; k1, k2, k3, k4, and k5 represent the subgrade coefficients (N / m) of subcritical layers 1, 2, 3, 4, and 5 of the goaf lateral bending subsidence zone. 3 ;k c 2 represents the subgrade coefficient of subcritical layer 2 on the side of the goaf, in N / m. 3 ; q1, q2, q3, q4, and q5 are the self-weights of subcritical layer 1, subcritical layer 2, subcritical layer 3, subcritical layer 4, main critical layer 5, and their load layers, respectively, in Pa; D1, D2, D3, D4, and D5 are the bending stiffnesses of subcritical layer 1, subcritical layer 2, subcritical layer 3, subcritical layer 4, and main critical layer 5, respectively, in N·m.

[0094] On the solid coal side, the overburden flexural deformation gradually decreases with increasing distance from the goaf, until it drops to 0 at the boundary; the subcritical layers 2, 3, 4, and 5 of the bending subsidence zone satisfy the fixed boundary condition at the boundary, and the deflection and rotation angle of any section on the subsidence boundary are 0, that is, the multi-layer composite thin plate deflection partial differential equation system of equation (1) satisfies the boundary condition of equation (3) below.

[0095]

[0096] Subcritical layers 2, 3, 4, and 5 of the bending subsidence zone underwent flexural subsidence. The critical layers satisfy the continuity condition at the boundary between the solid coal side and the goaf side. Therefore, the deflection, rotation angle, bending moment, and shear force experienced by the critical layer on the goaf side and its corresponding critical layer on the solid coal side of the bending subsidence zone at the boundary are equal. That is, the partial differential equations of deflection of the multilayer composite plate in equations (1) and (2) satisfy the continuity condition in equation (4).

[0097]

[0098] The shear force on any section of the subcritical layer 1 in the solid coal side fracture zone at the boundary of the goaf is half the self-weight of the fractured block of the critical layer, and the bending moment is 0. The partial differential equations of deflection of the multi-layer composite plate in equation (1) satisfy the following boundary conditions (5).

[0099]

[0100] In equations (3), (4) and (5), θ x2 (x,y), θ x3 (x,y), θ x4 (x,y), θ x5 (x, y) represent the rotation angles along the x-direction of subcritical layers 2, 3, 4, and 5 in the bending and subsidence zone on the side of the solid coal seam; θ y2 (x,y), θ y3 (x,y), θ y4 (x,y), θ y5 (x, y) represent the rotation angles along the y-direction of subcritical layers 2, 3, 4, and 5 in the bending and subsidence zone on the side of the solid coal seam; θ c x2 (x,y), θ c x3 (x,y), θ c x4 (x,y), θ c x5 (x, y) represent the rotation angles along the x-direction of subcritical layers 2, 3, 4, and 5 in the goaf lateral bending and subsidence zone; θ c y2 (x,y), θ c y3 (x,y), θ c y4 (x,y), θ c y5 (x, y) represent the rotation angles along the y-direction of subcritical layers 2, 3, 4, and 5 in the goaf lateral bending and subsidence zone; M x1 (x,y),Mx2 (x,y),M x3 (x,y),M x4 (x,y),M x5 (x, y) represent the bending moments along the x-direction of subcritical strata 1, subcritical strata 2, subcritical strata 3, subcritical strata 4, and main critical strata 5 on the solid coal side; M y1 (x,y),M y2 (x,y),M y3 (x,y),M y4 (x,y),M y5 (x, y) represent the bending moments along the y-direction of subcritical strata 1, subcritical strata 2, subcritical strata 3, subcritical strata 4, and main critical strata 5 on the solid coal side; M c x2 (x,y),M c x3 (x,y),M c x4 (x,y),M c x5 (x, y) represent the bending moments along the x-direction of subcritical layers 2, 3, 4, and 5 in the goaf lateral bending and subsidence zone; M c y2 (x,y),M c y3 (x,y),M c y4 (x,y),M c y5 (x, y) represent the bending moments along the y-direction of subcritical layers 2, 3, 4, and 5 in the goaf lateral bending and subsidence zone; Q x1 (x,y), Q x2 (x,y), Q x3 (x,y), Q x4 (x,y), Q x5 (x, y) represent the shear forces along the x-direction for subcritical layers 1, 2, 3, 4, and 5 on the solid coal side; Q y1 (x,y), Q y2 (x,y), Q y3 (x,y), Q y4 (x,y), Q y5 (x, y) represent the shear forces along the y-direction for subcritical layers 1, 2, 3, 4, and 5 on the solid coal side; Q c x2 (x,y), Q c x3 (x,y), Q c x4 (x,y), Qc x5 (x, y) represent the shear forces along the x-direction of subcritical layers 2, 3, 4, and 5 in the goaf lateral bending and subsidence zone; Q c y2 (x,y), Q c y3 (x,y), Q c y4 (x,y), Q c y5 (x, y) represent the shear forces along the y-direction of subcritical layers 2, 3, 4, and 5 in the goaf side bending and subsidence zone; l0 represents the unit width of the fractured block of the key layer in the fracture zone, in meters; l1 represents the length of the fractured block of subcritical layer 1 in the goaf side fracture zone, in meters.

[0101] Based on the relationship between the deflection, rotation angle, bending moment, and shear force of the Winkler elastic base plate in equation (6), and using the boundary conditions of equations (3) and (5) and the continuity condition of equation (4), the partial differential equations of the deflection of the multi-layer composite plate of sub-critical layers 1, 2, 3, 4, and 5 at different levels of the sub-critical layers 2, 3, 4, and 5 in the goaf side bending and subsidence zone of the mining-induced overburden coal solid side can be solved. The deflection curve equations w1(x,y), w2(x,y), w3(x,y), w4(x,y), and w5(x,y) of the sub-critical layers 1, 2, 3, 4, and 5 in the mining-induced overburden coal solid side, and the deflection curve equations w1(x,y), w2(x,y), w3(x,y), w4(x,y), and w5(x,y) of the sub-critical layers 1, 2, 3, 4, and 5 in the goaf side bending and subsidence zone, and the deflection curve equations w1(x,y), w2(x,y), w3(x,y), w4(x,y), and w5(x,y) of the sub-critical layers 1, 2, 3, 4, and 5 in the mining-induced overburden coal solid side, and the deflection curve equations w1(x,y), w2(x,y), w3(x,y), w4(x,y), and w5(x,y) of the sub-critical layers 2, 3, 4, and 5 in the goaf side bending and subsidence zone can be calculated. c 2(x,y), w c 3(x,y), w c 4(x,y), w c 5(x,y).

[0102] Based on the relationship between the deflection, load, and foundation coefficient of the Winkler elastic foundation thin plate in equation (7), the stress plane distribution equations for mining under the subcritical layers 1, 2, 3, 4, and 5 on the coal side of the mining-affected overburden body and the subcritical layers 2, 3, 4, and 5 on the goaf side bending and subsidence zone can be derived, as shown in equations (8) and (9), respectively.

[0103]

[0104]

[0105] In equations (8) and (9), σ1(x,y), σ2(x,y), σ3(x,y), σ4(x,y), and σ5(x,y) are the plane distribution equations of mining stress under subcritical layers 1, 2, 3, 4, and 5 on the solid coal side, respectively, in Pa; σ c 2(x,y), σ c 3(x,y), σ c 4(x,y), σ c 5(x,y) represents the plane distribution equation of mining-induced stress under subcritical layers 2, 3, 4, and 5 of the goaf lateral bending subsidence zone, respectively, in Pa.

[0106] For the plane distribution equation of mining-induced stress under sub-critical layer 1 of the fracture zone on the goaf side, since the critical layer of the fracture zone on the goaf side has undergone "OX" fracture, the fractured block of the critical layer forms a "masonry beam" bearing structure. Assuming that half of the self-weight of the fractured block of sub-critical layer 1 at the boundary of the fracture zone on the goaf side is transferred to the coal and rock mass around the mining area, and the other half of the load is transferred to the goaf and the force on the lower rock mass is linearly distributed; at the same time, considering the force of the critical layer of the goaf side bending and subsidence zone on the fractured critical layer of the lower fracture zone, the sub-critical layer 1 of the fracture zone on the goaf side is simplified into a multi-layer superimposed "masonry beam". The plane distribution equation of mining-induced stress under sub-critical layer 1 of different layers of fracture zone in the 1 / 4 equally divided area of ​​the goaf can be obtained as follows (10).

[0107]

[0108] In equation (10), σ c 1(x,y) is the plane distribution equation of mining-induced stress under sub-critical layer 1 of the side fracture zone in the goaf, Pa.

[0109] Furthermore, by utilizing symmetry, the entire goaf area can be obtained ( Figure 1 Planar distribution of mining-induced stress under subcritical layer 1 of the fracture zone in the Ω2 region.

[0110] Based on equations (8), (9), and (10), the planar distribution of mining stress under the sub-critical layers 1, 2, 3, 4, and 5 of the mining-induced overburden in Mengjin Coal Mine can be calculated:

[0111] Based on equations (8) and (10), the plane distribution equations of mining-induced stress σ1(x,y) under sub-key stratum 1 on the solid coal side and the plane distribution equations of mining-induced stress σ1(x,y) under sub-key stratum 1 on the goaf side can be obtained respectively. c1(x,y), plus the self-weight q0 of the rock strata between the coal seam and the subcritical stratum 1, can yield the distribution of coal body support pressure in the elastic zone of the solid coal side and the stress distribution in the goaf. At the same time, according to the distribution equation of support pressure in the limit equilibrium zone of the coal body in front of the mining area (Equation 11), the plane distribution equation of the mining area support pressure (12) can be obtained. Based on this, the plane distribution of the mining area support pressure in Mengjin Coal Mine is obtained, see Figure 5 .

[0112] The values ​​of the relevant parameters for the specific examples above are shown in Tables 2-3.

[0113] Table 2 Calculation parameters of key overburden strata in Mengjin Coal Mine

[0114] <![CDATA[MN / m 3 ]]> m GPa / MPa m Primary Key Layer 5 <![CDATA[k5=108.2]]> <![CDATA[h5=46.8]]> <![CDATA[E5=18.24]]> <![CDATA[μ5=0.32]]> <![CDATA[q5=5.20]]> Subcritical layer 4 <![CDATA[k4=84.0]]> <![CDATA[h4=8.62]]> <![CDATA[E4=13.06]]> <![CDATA[μ4=0.25]]> <![CDATA[q4=2.33]]> Subcritical layer 3 <![CDATA[k3=182.5]]> <![CDATA[h3=12.36]]> <![CDATA[E3=18.24]]> <![CDATA[μ3=0.32]]> <![CDATA[q3=3.09]]> Subcritical layer 2 <![CDATA[k2=139.7]]> <![CDATA[h2=8.76]]> <![CDATA[E2=18.24]]> <![CDATA[μ2=0.32]]> <![CDATA[q2=2.67]]> Subcritical layer 1 <![CDATA[k1=169.9]]> <![CDATA[h1=8.54]]> <![CDATA[E1=18.24]]> <![CDATA[μ1=0.32]]> <![CDATA[q1=4.05]]> <![CDATA[l1=28.4]]>

[0115] Table 3 Other relevant calculation parameters for Mengjin Coal Mine

[0116]

Claims

1. A method for predicting the stress field of a "plate-beam" structure in a key layer of mining-induced overburden, characterized in that, Includes the following steps: S1, the mining area is divided along the stratum bedding profile, the x-axis is defined along the mining direction of the working face, the y-axis is defined along the length of the cut, and the starting position of the cut is defined as the origin of the coordinate system; the rectangular goaf area is defined as Ω2, and the solid coal side area is defined as Ω1. S2. Using the critical layer theory controlled by rock strata, the distribution of critical layers in the overlying strata is determined, and the ranges of caving zones, fracture zones, and bending subsidence zones are identified. The critical layers are defined from bottom to top as critical layer i, 1≤i≤n, i∈N. + Among them, the key layers in the fracture zone are key layer 1 to key layer m-1 from bottom to top, and the key layers in the bending and subsidence zone are key layer m to key layer n from bottom to top. S3, for different key layers i on the solid coal side, 1≤i≤n, i∈N + The key strata i at different levels of the goaf lateral bending and subsidence zone, m≤i≤n, i∈N + Simplified to a multi-layered composite elastic foundation thin plate, the key fracture layer i at different strata of the side fracture zone in the goaf, 1≤i≤m-1,i∈N + The beam is simplified to a multi-layer composite masonry beam, and a stress field prediction model is established. S4. Establish the partial differential equations for the deflection of the multi-layer composite elastic foundation thin plate with different key layers on the solid coal side and different key layers on the goaf side bending subsidence zone, as shown in equations (1) and (2), respectively. In the formula, w i (x,y) represents the deflection of key stratum i at different levels on the solid coal side, m; w c i (x,y) represents the deflection of key layer i at different strata in the goaf lateral bending subsidence zone, m; k i The subgrade coefficient for key layer i at different strata, in N / m. 3 ;k c m The subgrade coefficient for the key stratum m on the goaf side is given in N / m. 3 ;q i For the self-weight of the key layer i and its load layer at different strata, Pa; D i Let be the bending stiffness of key layer i at different strata, in N·m; S5, determine the boundary condition equation and the continuity condition equation; S6. Based on the relationship between the deflection, rotation angle, bending moment, and shear force of the Winkler elastic base plate and the boundary and continuity conditions determined in step S5, equations (1) and (2) are solved to calculate the deflection curve equation w of the key layer i at different strata on the coal side of the mining overburden body. i The deflection curve equations w of (x,y) and different key layers i in the goaf lateral bending and subsidence zone c i (x,y); S7. Based on the relationship between the deflection, load and subgrade coefficient of the Winkler elastic foundation thin plate, the stress plane distribution equations for mining stress under different key layers i on the coal side of the mining-induced overburden body and different key layers i in the bending subsidence zone on the goaf side are determined, as shown in equations (8) and (9) respectively. In the formula, σ i (x, y) represent the plane distribution equations of mining-induced stress under different key strata i on the solid coal side, respectively, Pa; σ c i (x,y) is the plane distribution equation of mining-induced stress under key layer i at different levels in the goaf side bending subsidence zone, Pa; S8, determine the plane distribution equation of mining-induced stress under the critical fracture layer i at different strata in the fracture zone of the 1 / 4 equally divided goaf area, 1≤i≤m-1,i∈N + See equation (10); by utilizing symmetry, the plane distribution of mining-induced stress under the key fracture layer i at different strata in the Ω2 fracture zone of the entire goaf can be obtained. In the formula, σ c i (x,y) represents the plane distribution equation of mining-induced stress under the critical fracture stratum i at different strata in the goaf side fracture zone, Pa;l i The length (m) of the fractured block of the key layer i at different strata in the side fracture zone of the goaf.

2. The stress field prediction method according to claim 1, characterized in that, D i Calculate according to the formula In the formula, D i The bending stiffness of key layer i at different strata is given in N·m; E i For the elastic modulus of key layer i at different strata, Pa; h i Let m be the thickness of the key layer i at different strata; μ be the thickness of the key layer i at different strata. i Poisson's ratio for key layer i at different strata.

3. The stress field prediction method according to claim 1 or 2, characterized in that, Assume the four endpoints of the goaf are B1, B2, B3, and B4 respectively, counterclockwise from the origin; the four endpoints of the solid coal side region are A1, A2, A3, and A4 respectively, and A1 corresponds to B1; in step S5, the boundary conditions are equations (3) and (5), and the continuity condition is equation (4). In the formula, θ xi (x,y) and θ yi (x, y) represent the rotation angles along the x and y directions of key strata i at different levels in the bent subsidence zone of the solid coal seam; θ c xi (x,y) and θ c yi (x, y) represent the rotation angles of key strata i at different levels along the x and y directions in the goaf lateral bending subsidence zone, respectively; M xi (x,y) and M yi (x, y) represent the bending moments along the x and y directions of key strata i at different levels on the solid coal side, respectively; M c xi (x,y) and M c yi (x, y) represent the bending moments along the x and y directions of key strata i at different levels in the goaf lateral bending subsidence zone; Q xi (x,y) and Q yi (x, y) represent the shear forces along the x and y directions of key strata i at different levels on the solid coal side, respectively; Q c xi (x,y) and Q c yi (x, y) represent the shear forces along the x and y directions of the key stratum i at different levels in the goaf side bending subsidence zone; l0 is the unit width of the fractured block of the key stratum in the fracture zone, in meters; l i The length (m) of the fractured block of the key layer i at different strata in the side fracture zone of the goaf.

4. The stress field prediction method according to claim 3, characterized in that, Define the limit equilibrium zone on the solid coal side as Ω p The elastic zone range of the solid coal side is Ω. e The planar distribution of support pressure in the mining area can be calculated based on the following formula. In the formula, σ1(x,y) is the plane distribution equation of mining-induced stress under the key stratum 1 on the solid coal side, in Pa; σ c 1(x,y) is the plane distribution equation of mining-induced stress under the key stratum 1 on the goaf side, Pa; q0 is the self-weight of the rock strata between the coal seam and the key stratum 1, Pa; M is the mining height, m; denoted as the internal friction angle (°); f is the friction coefficient; N0 is the coal seam support capacity (Pa); d(x,y) is the minimum distance from any point in the coal body's limit equilibrium zone to the goaf boundary (m).

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