Coal rock mass pressure relief effect prediction method based on underlying key layer structure of upper protective layer

Abstract

The present application belongs to the technical field of mine exploitation, and particularly relates to a coal rock mass pressure relief effect prediction method based on a key layer structure underlying a protective layer. The present application simplifies the key layer underlying different layer positions of the protective layer mining into a multi-layer superimposed elastic foundation plate, considers the influence of the number, layer height, thickness, stiffness value and interlayer rock combination conditions of the underlying key layer on the pressure relief effect of the coal rock mass of the floor, establishes a coal rock mass pressure relief effect prediction method based on the key layer structure underlying the protective layer mining, and constructs a coal rock mass stress and deformation prediction equation. The present application solves the problem that the existing prediction method excessively simplifies the underlying coal rock mass of the protective layer mining, and does not consider the lithological heterogeneity variation characteristics of the underlying coal rock mass and the influence of the key layer on the pressure relief effect of the coal rock mass of the floor.

Description

Technical Field

[0001] This invention belongs to the field of mining technology, specifically relating to a method for predicting the pressure relief effect of coal and rock masses based on the structure of the underlying key strata of the upper protective layer. Background Technology

[0002] Mining of the upper protective layer not only causes changes in stress around the stope and in the roof, but also redistributes stress in the floor coal and rock mass. Accurately predicting the stress-relieving effect of upper protective layer mining on the floor coal and rock mass is crucial for rationally determining the upper protective layer mining height and guiding the efficient extraction of depressurized gas.

[0003] Existing research indicates that the underlying strata conditions during the mining of the upper protective layer affect the stress relief effect on the bottom coal and rock mass. However, current theoretical prediction methods for the stress relief effect of the bottom coal and rock mass during the mining of the upper protective layer mainly employ soil mechanics theory, treating the bottom coal and rock mass as a homogeneous elastic body to calculate the stress relief effect. However, this method does not consider the lithological changes of the underlying strata during the mining of the protective layer, nor the influence of key strata on the stress relief effect of the bottom coal and rock mass. Therefore, a prediction method for the stress relief effect of the bottom coal and rock mass that considers the conditions of the key strata beneath the upper protective layer is still lacking. Summary of the Invention

[0004] To address the shortcomings of existing methods for predicting the stress relief effect of coal and rock mass under upper protective layer mining, this invention, based on the key layer theory and Winkler's elastic stratum theory, simplifies the underlying key layers at different strata during upper protective layer mining into multiple layers of composite thin plates. Considering the structure of the underlying key layers during upper protective layer mining, the stress and deformation of the coal and rock mass under the upper protective layer are predicted. Specifically, this invention proposes a method for predicting the stress relief effect of coal and rock mass based on the structure of the underlying key layers under the upper protective layer, comprising the following steps:

[0005] S1, a planar cross-section along the working face of the protective layer, defines the mining direction along the working face of the protective layer as the x-axis, the length direction of the cut as the y-axis, the starting position of the cut as the origin of the coordinate system, and the range of the coal and rock mass to be predicted as a rectangle ABCD;

[0006] S2, determine the distribution of key layers in the underlying strata, and define key layers i from top to bottom, 1≤i≤n, i∈N. + ;

[0007] S3, simplify the key layer into a multi-layered composite elastic foundation thin plate, and establish a prediction model for the pressure relief effect of coal and rock mass considering the structure of the upper protective layer and the underlying key layer;

[0008] S4. Establish a set of partial differential equations for the deflection of multilayer composite thin plates with different underlying key layers i, as shown in equation (1).

[0009]

[0010] In the formula, w i (x,y) represents the deflection curve equations of key strata i at different underlying strata, where m and k are the values ​​of x and y respectively. i The subgrade coefficient (N / m) represents the subgrade coefficient of key stratum i at different underlying strata. 3 ;q i Let Pa be the self-weight of the underlying key stratum i and its load layer at different strata. When i = 1, q1 is the self-weight of the underlying key stratum 1 and the coal and rock strata between it and the upper protective layer; D i σi represents the bending stiffness of the underlying key stratum i at different strata, in N·m; σ0(x,y) represents the plane distribution equation of the support pressure in the upper protective stratum mining area, in Pa;

[0011] S5, determine the boundary conditions, see equation (2).

[0012]

[0013] In the formula, θ xi (x,y) and θ yi (x, y) represent the rotation angles of the underlying key layer i along the x and y directions, respectively;

[0014] S6. Based on the relationship between the deflection and rotation angle of the Winkler elastic substrate in equation (3), and using the boundary conditions of equation (2), equation (1) is solved to calculate the deflection curve equation w for different underlying key layers i under the upper protective layer mining. i (x,y) is subtracted from the initial compression of the strata caused by the initial vertical ground stress before mining. The deflection curve equations of the underlying key strata i caused by the mining of the upper protective layer are obtained, as shown in equation (4).

[0015]

[0016] d i (x,y)=w i (x,y)-T i (1≤i≤n,i∈N + (4)

[0017] In the formula, θ x (x,y), θ y (x, y) are the rotation angles along the x and y directions, respectively; d i (x,y) represents the deflection curve equation of the underlying key stratum i at different strata caused by the mining of the upper protective layer, m; T i Let m be the initial compression of the underlying key stratum i caused by the initial vertical ground stress, which is equal to (q0 + Q). i ) / k i to (q0+Q) n ) / k n sum; Qi from q1 to q i , which represents the dead weight of key layer i at different underlying horizons and the coal and rock mass between the key layer i and the upper protective layer, in Pa; q0 is the initial vertical in-situ stress of the upper protective layer, in Pa;

[0018] S7, according to the relationship among deflection, load and foundation coefficient of Winkler elastic foundation thin plate, determine the plane distribution equation of mining stress under key layer i at different underlying horizons after upper protective layer mining, as shown in equation (6)

[0019]

[0020] where, σ i (x,y) is the plane distribution equation of mining stress under key layer i at different underlying horizons, in Pa;

[0021] S8, determine the plane distribution equation of expansion deformation of floor coal and rock mass, as shown in equation (7)

[0022]

[0023] where, F i (x,y) is the plane distribution equation of expansion deformation of coal and rock mass between key layer i-1 and key layer i, in ‰; when i=1, F i (x,y) represents the plane distribution equation of expansion deformation of coal and rock mass between the upper protective layer and key layer 1, in ‰; k0 is the foundation coefficient of coal and rock mass between the upper protective layer and key layer 1, in N / m 3 ; d i-1 (x,y), d i (x,y) are respectively the deflection curve equations of key layer i-1 and key layer i caused by upper protective layer mining, in m; H0 is the interval between the upper protective layer and key layer 1, in m; H i-1 is the interval between key layer i-1 and key layer i, in m;

[0024] S9, assuming that the protected layer is located between key layer m and key layer m+1, m<n, then the plane distribution equation of mining stress and the plane distribution equation of expansion deformation of the protected layer are shown in equation (8) and (9) respectively

[0025] σ F (x,y)=σ m (x,y)+q F (8)

[0026]

[0027] where, σ F (x,y) is the plane distribution equation of mining stress of the protected layer, in Pa; σ m(x,y) represents the plane distribution equation of mining stress under the key layer m, Pa; q F The weight of the rock strata between the protected layer and the key layer m is Pa; F(x,y) is the plane distribution equation of the expansion deformation of the protected layer, ‰; d m (x,y),d m+1 (x, y) are the deflection curve equations of key layer m and key layer m+1 caused by the mining of the protective layer, respectively, where m; H m Let m be the interlayer spacing between key layer m and key layer m+1.

[0028] Among them, D i Calculate according to formula (10)

[0029]

[0030] In the formula, D i The bending stiffness (N·m) of the underlying key stratum i at different subsurface levels; E i The elastic modulus of the underlying key layer i at different subsurface depths is given in Pa; h. i Let m be the thickness of the underlying key layer i at different strata; μ be the thickness of the underlying key layer i. i denoted as Poisson's ratio for key layer i at different underlying strata.

[0031] Beneficial Effects: This invention simplifies the underlying key strata at different levels during the mining of the upper protective layer into a multi-layered composite elastic substrate. Considering the influence of the number, elevation, thickness, stiffness, and interlayer rock combination conditions of the underlying key strata on the stress relief effect of the underlying coal and rock mass, a method for predicting the stress relief effect of the underlying coal and rock mass based on the structure of the underlying key strata during the mining of the upper protective layer is established. Prediction equations for the stress and deformation of the underlying coal and rock mass are constructed. This avoids the shortcomings of existing prediction methods that oversimplify the underlying coal and rock mass during the mining of the upper protective layer, treating it as a homogeneous elastic body to predict the stress relief effect of the underlying coal and rock mass. It also prevents the problem that existing prediction methods do not consider the lithological variation characteristics of the underlying coal and rock mass during the mining of the protective layer and the influence of the key strata on the stress relief effect of the underlying coal and rock mass. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the strata distribution at the bottom of the coal and rock mass decompression effect prediction model of the present invention;

[0033] Figure 2 This is a schematic diagram of the vertical cross-section of the coal and rock mass decompression effect prediction model of the present invention along the strata;

[0034] Figure 3 This is a schematic diagram of the strata distribution at the bottom of the coal and rock mass decompression effect prediction model, which is a specific example of this invention.

[0035] Figure 4A This is the planar distribution of mining stress under key layer 1 in a specific example of the present invention;

[0036] Figure 4B This is the planar distribution of mining stress under the key layer 2 in a specific example of the present invention;

[0037] Figure 4C This is the planar distribution of mining stress under the key layer 3 in a specific example of the present invention;

[0038] Figure 5 This is a specific example of the stress distribution in the protected layer in the planar distribution of the present invention.

[0039] Figure 6A This is a specific example of the planar distribution of coal and rock mass expansion deformation between the protective layer and the key layer 1 in this invention.

[0040] Figure 6B This is a specific example of the planar distribution of coal and rock mass expansion deformation between key layer 1 and key layer 2 in this invention.

[0041] Figure 6C This is a specific example of the planar distribution of coal and rock mass expansion deformation between key layer 2 and key layer 3 in this invention.

[0042] Figure 6D This is a specific example of the present invention showing the planar distribution of the expansion deformation of the protected layer. Detailed Implementation

[0043] 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.

[0044] The method for predicting the pressure relief effect of coal and rock masses based on the structure of the underlying key strata under the upper protective layer proposed in this invention is as follows:

[0045] like Figure 1 As shown, in the planar cross-section of the protective layer working face, the direction of mining along the protective layer working face is defined as the x-axis, the direction of the cut length is defined as the y-axis, and the starting position of the cut is the origin 0. In this specific embodiment, the protective layer is a coal seam; a and b are the dimensions of the goaf along the x-axis and y-axis, respectively, that is, the goaf (protective layer working face) is approximately rectangular with a length of a and a width of b; it is assumed that the range of the coal and rock mass to be predicted is a rectangle ABCD, with the unit being m.

[0046] like Figure 2The vertical cross-section of the strata shown indicates that the mining of the upper protective layer caused flexural deformation of the underlying strata. Based on the strata borehole column, and using the key layer theory of strata control (Xu Jialin, Qian Minggao. Method for determining the location of key layers in overburden [J]. Journal of China University of Mining and Technology, 2000, 29(5):463-467.), the distribution of sub-key layers (hereinafter referred to as key layers in this patent) in the underlying strata is determined. The key layers in the underlying strata are defined from top to bottom as key layer i (1≤i≤n,i∈N). + ).

[0047] Furthermore, such as Figure 2 The vertical stratigraphic profile shown assumes that the underlying key layers and their load-bearing strata conform to the Winkler elastic foundation assumption (according to the strata-controlled key layer theory, the load layer of key layer i is the stratum between key layer i-1 and key layer i, where the load layer of key layer 1 is the stratum between key layer 1 and the upper protective layer). Furthermore, the ratio of the thickness of the underlying key layers to the predicted length AB and width BC is typically less than 1 / 8 to 1 / 5, conforming to the elastic thin plate assumption. Therefore, the underlying key layers i (1≤i≤n, i∈N) are considered as different layers below the upper protective layer. + The structure is simplified to a multi-layered composite elastic foundation thin plate, and a prediction model for the pressure relief effect of coal and rock mass based on the structure of the upper protective layer and the underlying key layer is established.

[0048] Mining of the upper protective layer reveals different underlying key layers i (1≤i≤n,i∈N) + It conforms to the elastic thin plate assumption and satisfies the Winkler partial differential equation for the deflection of a thin plate on an elastic foundation, as follows:

[0049]

[0050] 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.

[0051] The upper protective layer will be mined, and the underlying key layers i (1≤i≤n, i∈N) will be mined. + Simplified to a multi-layered composite elastic foundation thin plate, key layers i (1≤i≤n, i∈N) are established beneath different underlying strata. + The partial differential equations for the deflection of a thin plate on a multilayer composite elastic foundation are given in equation (1).

[0052]

[0053] In the formula, w i (x,y) represents the deflection curve equations of different underlying key layers i (1≤i≤n,i∈N). + ), m; k iThe subgrade coefficients of key strata i under different underlying strata (1≤i≤n, i∈N) + ), N / m 3 ;q i The self-weight of the underlying key layer i and its load layer at different subsurface levels (2≤i≤n,i∈N) + ), Pa, when i=1, q1 is the self-weight of the underlying key layer 1 and the coal and rock strata between it and the upper protective layer, Pa; D i The bending stiffness of the underlying key layer i at different subsurface levels (1≤i≤n,i∈N) + ), N·m; σ0(x,y) is the plane distribution equation of the support pressure in the upper protective layer mining area, Pa.

[0054] Under the support pressure of the upper protective layer stope, the underlying key strata at different levels undergo flexural deformation. The amount of flexural deformation gradually decreases with increasing distance from the goaf, eventually reaching zero at the boundary. The underlying key strata at different levels i (1≤i≤n, i∈N) + The boundary condition is satisfied at the boundary, where the deflection and rotation angle of any section on the 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 in equation (2) below.

[0055]

[0056] In the formula, θ xi (x,y) and θ yi (x, y) represent the turning angles of the underlying key layer i along the x and y directions, respectively (1 ≤ i ≤ n, i ∈ N). + );

[0057] Based on the relationship between the deflection and rotation angle of the Winkler elastic substrate in equation (3), and using the boundary conditions in equation (2), the key layers i (1≤i≤n,i∈N) under different underlying strata can be mined from the protective layer in equation (1). + The partial differential equations of deflection of multi-layer composite plates are solved to calculate the deflection curve equations w of key layers i at different underlying strata under the upper protective layer. i (x,y)(1≤i≤n,i∈N + ).

[0058]

[0059] In the formula, θ x (x,y), θ y (x, y) are the rotation angles along the x and y directions, respectively, and D is the bending stiffness of the plate.

[0060] The deflection curve equations w of different underlying key strata i after the upper protective layer is mined are calculated. i(x,y), respectively, minus the initial compression of the strata caused by the initial vertical ground stress before mining, the deflection curve equations of the underlying key strata i at different strata caused by the mining of the upper protective layer are shown in equation (4).

[0061] d i (x,y)=w i (x,y)-T i (1≤i≤n,i∈N + (4)

[0062] In the formula, d i (x,y) represents the deflection curve equation of the underlying key stratum i at different strata caused by the mining of the upper protective layer, m; T i Let m be the initial compression of the underlying key stratum i caused by the initial vertical ground stress, which is equal to (q0 + Q). i ) / k i to (q0+Q) n ) / k n sum; Q i For q1 to q i The sum of these values ​​represents the self-weight of the underlying key stratum i and the coal and rock strata between it and the upper protective stratum, in Pa; Q. n For q1 to q n The sum represents the self-weight of the underlying key stratum n and the coal and rock strata between it and the upper protective stratum, in Pa; k. n The subgrade coefficient representing the underlying key stratum n, in N / m 3 ; q0 is the initial vertical ground stress of the upper protective layer, in Pa.

[0063] Based on the relationship between the deflection, load, and subgrade coefficient of the Winkler elastic foundation thin plate, see the following equation (5).

[0064] σ(x,y)=kw(x,y) (5)

[0065] 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 ;

[0066] The plane distribution equation of mining-induced stress under different underlying key strata i can be derived (1≤i≤n,i∈N). + See equation (6).

[0067]

[0068] In the formula, σ i (x,y) is the plane distribution equation of mining stress under different underlying key strata i when the upper protective layer is mined (1≤i≤n,i∈N). + ), Pa.

[0069] Determine the plane distribution equation of the expansion and deformation amount of the floor coal and rock mass, as shown in Equation (7)

[0070]

[0071] In the formula, F i (x,y) is the plane distribution equation of the expansion and deformation amount of coal and rock mass between key layer i-1 and key layer i, ‰; when i=1, F i (x,y) represents the plane distribution equation of the expansion and deformation amount of coal and rock mass between the upper protective layer and key layer 1, ‰; k0 is the foundation coefficient of coal and rock mass between the upper protective layer and key layer 1, N / m 3 ; d i-1 (x,y), d i (x,y) are respectively the deflection curve equations of key layer i-1 and key layer i caused by the mining of the upper protective layer, m; H0 is the interlayer spacing between the upper protective layer and key layer 1, m; H i-1 is the interlayer spacing between key layer i-1 and key layer i, m;

[0072] Assume that the protected layer is located between the underlying key layer m and key layer m+1, and m<n, then the plane distribution equation of mining stress and the plane distribution equation of expansion deformation of the protected layer are shown in Equation (8) and Equation (9) respectively

[0073] σ F (x,y)=σ m (x,y)+q F (8)

[0074]

[0075] In Equations (8) and (9), σ F (x,y) is the plane distribution equation of mining stress of the protected layer, Pa; σ m (x,y) is the plane distribution equation of mining stress of key layer m, Pa; q F is the self-weight of rock strata between the protected layer and key layer m, Pa; F(x,y) is the plane distribution equation of the expansion and deformation amount of the protected layer, ‰; d m (x,y), d m+1 (x,y) are respectively the deflection curve equations of key layer m and key layer m+1 caused by protective layer mining, m; H m is the interlayer spacing between key layer m and key layer m+1, m.

[0076] For the selection of prediction parameters in this prediction method, D i is calculated according to Equation (10)

[0077]

[0078] In the formula, Di The bending stiffness of the underlying key layer i at different subsurface levels (1≤i≤n,i∈N) + ), N·m; E i The elastic modulus of the underlying key layer i at different subsurface levels (1≤i≤n, i∈N) + ), Pa; h i The thickness of the underlying key layer i at different subsurface levels (1≤i≤n, i∈N) + ), m; μ i The Poisson ratio of the underlying key layer i at different subsurface levels (1≤i≤n,i∈N) + ).

[0079] In the above specific implementation, for σ0(x,y), E i h i k i q i The values ​​of k0 and μ can be found in the reference "Han Hongkai. Theoretical study on the influence law of key layer on bearing pressure distribution [D]. Xuzhou: China University of Mining and Technology, 2019." i Determined based on the mechanical properties of key strata at different levels, a and b are determined according to the mining dimensions of the goaf, q0, H0, q F H m H i-1 Determined based on stratigraphic occurrence conditions.

[0080] Specific calculation examples

[0081] Based on the borehole columnar data near the working face of the upper protective layer in Mengjin Coal Mine, the distribution of the underlying key layers was determined using the key layer discrimination method. There are a total of three key layers beneath the upper protective layer. Therefore, in the prediction model of the pressure relief effect of the underlying coal and rock mass during upper protective layer mining, the number of underlying key layers (n) is taken as 3, from top to bottom: Key Layer 1, Key Layer 2, and Key Layer 3. The protected layer is located between Key Layer 1 and Key Layer 2. See Table 1 for details. Figure 3 .

[0082] Table 1 Distribution of underlying key strata and protected strata during the mining of the upper protective layer in Mengjin Coal Mine

[0083] 1 17.86 Large sandstone Key Layer 1 2 5.93 coal seam Protected layer 3 5.41 fine-grained sandstone Key Layer 2 4 6.80 limestone Key Layer 3

[0084] If the predicted range length AD is 1400m and the width AB is 950m, the ratio of the thickness of the underlying key layer at different strata to this size is less than 1 / 8 to 1 / 5, which meets the assumption of an elastic thin plate; the key layers 1, 2, and 3 are simplified into multi-layer composite elastic foundation thin plates, and the partial differential equations of deflection of the multi-layer composite elastic foundation thin plates of key layers 1, 2, and 3 are established.

[0085]

[0086] In the formula, w1(x,y), w2(x,y), and w3(x,y) are the deflection curve equations of underlying key layers 1, 2, and 3, respectively, in meters (m); k1, k2, and k3 are the subgrade coefficients of underlying key layers 1, 2, and 3, respectively, in N / m. 3 ; q1 is the self-weight of the underlying key layer 1 and the coal and rock strata between it and the upper protective layer; q2 and q3 are the self-weights of the underlying key layers 2 and 3 and their load layers, respectively, in Pa; D1, D2, and D3 are the bending stiffnesses of the underlying key layers 1, 2, and 3, respectively, in N·m; σ0(x,y) is the plane distribution equation of the support pressure in the upper protective layer mining area, in Pa.

[0087] Under the support pressure of the upper protective layer mining area, the key layers of different layers of the bottom plate undergo flexural deformation. As the distance from the goaf increases, the amount of flexural deformation gradually decreases until it drops to 0 at the boundary. The underlying key layers 1, 2 and 3 satisfy the fixed support boundary conditions at the boundary. The deflection and rotation angle of any section on this boundary are 0. That is, the multi-layer composite thin plate deflection partial differential equation set of equation (1) satisfies the boundary conditions of equation (2) below.

[0088]

[0089] In the formula, θ x1 (x,y), θ x2 (x,y), θ x3 (x, y) represent the rotation angles along the x-direction of the underlying key layers 1, 2, and 3, respectively; θ y1 (x,y), θ y2 (x,y), θ y3 (x, y) represent the rotation angles of the underlying key layers 1, 2, and 3 along the y-direction.

[0090] Based on the relationship between the deflection and rotation angle of the Winkler elastic substrate in equation (3), and using the boundary conditions in equation (2), the partial differential equations of the deflection of the multilayer composite plate under the upper protective layer mining, namely key layer 1, key layer 2, and key layer 3 in equation (1) can be solved, and the deflection curve equations w1(x,y), w2(x,y), and w3(x,y) under the upper protective layer mining, namely key layer 1, key layer 2, and key layer 3 can be calculated.

[0091]

[0092] In the formula, θ x (x,y), θ y (x, y) are the rotation angles along the x and y directions, respectively, and D is the bending stiffness of the plate.

[0093] The deflection curve equations w1(x,y), w2(x,y), and w3(x,y) of the underlying key layers 1, 2, and 3 caused by the mining of the upper protective layer are calculated. The initial compression of the strata caused by the initial vertical ground stress before mining is subtracted from each equation. The deflection curve equations of the underlying key layers 1, 2, and 3 caused by the mining of the upper protective layer are shown in equation (4).

[0094]

[0095] In the formula, q0 is the initial vertical ground stress of the upper protective layer, Pa; d1(x,y), d2(x,y), and d3(x,y) are the deflection curve equations of the underlying key layers 1, 2, and 3 caused by the mining of the upper protective layer, respectively, m.

[0096] Based on Winkler's elastic foundation assumption (Equation 5), the plane distribution equation of mining stress under key strata at different levels of the foundation is shown in Equation (6).

[0097]

[0098] In the formula, σ1(x,y), σ2(x,y), and σ3(x,y) are the stress plane distribution equations for mining under the underlying key layers 1, 2, and 3, respectively, in Pa.

[0099] The plane distribution equations for the expansion deformation of coal and rock mass between the upper protective layer and key layer 1, between key layer 1 and key layer 2, and between key layer 2 and key layer 3 are as follows:

[0100]

[0101] In the formula, F1(x,y), F2(x,y), and F3(x,y) are the plane distribution equations of the expansion deformation of the coal and rock mass between the upper protective layer and key layer 1, key layer 1 and key layer 2, and key layer 2 and key layer 3, respectively, in‰; k0 is the subgrade coefficient of the coal and rock mass between the upper protective layer and key layer 1, in N / m. 3 H0, H1, and H2 are the interlayer spacings between the upper protective layer and key layer 1, key layer 1 and key layer 2, and key layer 2 and key layer 3, respectively, in meters.

[0102] If the protected layer is located between key layer 1 and key layer 2, then the plane distribution equations for the mining-induced stress and the plane distribution equations for the expansion deformation of the protected layer are as follows:

[0103] σ F (x,y)=σ1(x,y)+q F (8)

[0104]

[0105] In the formula, σF (x,y) is the plane distribution equation of mining stress in the protected layer, Pa; σ1(x,y) is the plane distribution equation of mining stress under key layer 1, Pa; q F Let be the self-weight of the rock strata between the protected layer and the key layer 1, Pa; F(x,y) is the plane distribution equation of the expansion deformation of the protected layer, ‰.

[0106] The mining dimensions of the goaf are a = 600m and b = 150m. Based on equations (1), (2), (3), (4), and (6), the plane distribution of mining stress under the underlying key layers 1, 2, and 3 of the upper protective layer in Mengjin Coal Mine can be calculated, as shown in Figure 4. Based on equation (8), the plane distribution of mining stress under the underlying protected layer of the upper protective layer in Mengjin Coal Mine can be calculated, as shown in Figure 4. Figure 5 According to equations (7) and (9), the planar distribution of expansion deformation between the upper protective layer and key layer 1, between key layer 1 and key layer 2, between key layer 2 and key layer 3, and between the protected layer in Mengjin Coal Mine can be calculated, as shown in Figure 6. The values ​​of relevant parameters for the above specific calculation examples are shown in Table 2.

[0107] Table 2 Calculation parameters of pressure relief effect of underlying coal and rock mass in Mengjin Coal Mine

[0108] Subcritical layer 1 <![CDATA[k1=104.23]]> <![CDATA[h1=17.86]]> <![CDATA[D1=4.54×10 7 ]]> <![CDATA[q1=0.51]]> Subcritical layer 2 <![CDATA[k2=75.57]]> <![CDATA[h2=5.41]]> <![CDATA[D2=3.13×10 7 ]]> <![CDATA[q2=0.38]]> Subcritical layer 3 <![CDATA[k3=56.44]]> <![CDATA[h3=6.80]]> <![CDATA[D3=2.77×10 7 ]]> <![CDATA[q3=0.57]]> 0.15 18.64 230.77 2.47 5.93 10.80

Claims

1. A method for predicting the pressure relief effect of coal and rock mass based on the structure of the underlying key strata beneath the upper protective layer, characterized in that, Comprising the following steps: S1, along the plane section of the protective layer working face, defining the mining direction along the working face of the protective layer as the x-axis, the direction along the length of the cut as the y-axis, and setting the starting position of the open cut as the coordinate origin; S2, determining the distribution of key layers of underlying rock, defining the key layers from top to bottom as key layer i, 1≤i≤n, i∈N + ; S3, simplifying the key strata into multi-layer laminated elastic foundation thin plates, and establishing a prediction model for the pressure relief effect of coal and rock mass considering the structure of the key strata underlying the upper protective layer; S4, establishing a system of partial differential equations for deflection of multi-layer laminated thin plates of key strata i at different underlying horizons, as shown in formula (1) In the formula, w i (x, y) is the deflection curve equation of the underlying different horizon key layer i, m; k i is the foundation coefficient of the underlying different horizon key layer i, N / m 3 ; q i Let Pa be the self-weight of the underlying key stratum i and its load layer at different strata. When i = 1, q1 is the self-weight of the underlying key stratum 1 and the coal and rock strata between it and the upper protective layer; D i σi represents the bending stiffness of the underlying key stratum i at different strata, in N·m; σ0(x,y) represents the plane distribution equation of the support pressure in the upper protective stratum mining area, in Pa; S5, determining boundary conditions; S6. Based on the relationship between the deflection and rotation angle of the Winkler elastic substrate, the boundary conditions are used to solve equation (1) to calculate the deflection curve equation w for the key layer i at different underlying layers. i (x,y) is subtracted from the initial compression of the strata caused by the initial vertical ground stress before mining. The deflection curve equations of the underlying key strata i caused by the mining of the upper protective layer are obtained, as shown in equation (4). d i (x,y) = w i (x,y) - T i (1≤i≤n,i∈N + ) (4) In the formula, d i (x, y) is the deflection curve equation of the key layer i of the underlying different layer position caused by the upper protective layer mining, m; T i Let m be the initial compression of the underlying key stratum i caused by the initial vertical ground stress, which is equal to (q0 + Q). i ) / k i to (q0+Q) n ) / k n sum; Q i For q1 to q i The sum of these values ​​represents the self-weight of the underlying key layer i and the coal and rock strata between it and the upper protective layer, in Pa; q0 is the initial vertical in-situ stress of the upper protective layer, in Pa. S7, determining the plane distribution equation of mining stress under key strata i at different underlying horizons after upper protective layer mining according to the relationship among deflection, load and foundation coefficient of Winkler elastic foundation thin plates, as shown in formula (6) In the formula, σ i (x, y) is the mining stress plane distribution equation of underlying different layer key layer i, Pa.

2. The method for predicting the pressure relief effect of coal and rock mass according to claim 1, characterized in that, further comprising the following steps: S8, determining the plane distribution equation of expansion deformation of floor coal and rock mass, as shown in formula (7) In the formula, F i (x, y) is the plane distribution equation of the swelling deformation of the coal and rock mass between the key layer i-1 and the key layer i, ‰; When i = 1, F i (x,y) represents the planar distribution equation of the expansion deformation of the coal-rock mass between the upper protective layer and the key layer 1, in ‰; k0 is the subgrade coefficient of the coal-rock mass between the upper protective layer and the key layer 1, in N / m. 3 ; d i-1 (x,y),d i (x, y) represent the deflection curve equations of key layer i-1 and key layer i caused by the mining of the upper protective layer, respectively, in meters; H0 is the interlayer spacing between the upper protective layer and key layer 1, in meters; H i-1 Let m be the interlayer spacing between key layer i-1 and key layer i.

3. The method for predicting the pressure relief effect of coal and rock mass according to claim 2, characterized in that, further comprising the following steps: S9, assuming that the protected layer is located between key stratum m and key stratum m+1, where m < n, then the plane distribution equation of mining stress and the plane distribution equation of expansion deformation of the protected layer are shown in formula (8) and formula (9) respectively s F (x,y)=σ m (x,y)+q F (8) In the formula, σ F (x,y) is the plane distribution equation of the mining stress of the protected layer, Pa; σ m (x,y) represents the plane distribution equation of mining stress under the key layer m, Pa; q F The weight of the rock strata between the protected layer and the key layer m is Pa; F(x,y) is the plane distribution equation of the expansion deformation of the protected layer, ‰; d m (x,y),d m+1 (x, y) are the deflection curve equations of key layer m and key layer m+1 caused by the mining of the protective layer, respectively, where m; H m Let m be the interlayer spacing between key layer m and key layer m+1.

4. The method for predicting the pressure relief effect of coal and rock mass according to any one of claims 1-3, characterized in that, D i Calculate according to the formula In the formula, D i The bending stiffness (N·m) of the underlying key stratum i at different subsurface levels; E i The elastic modulus of the underlying key layer i at different subsurface depths is given in Pa; h. i Let m be the thickness of the underlying key layer i at different strata; μ be the thickness of the underlying key layer i. i denoted as Poisson's ratio for key layer i at different underlying strata.

5. The method for predicting the pressure relief effect of coal and rock mass according to any one of claims 1-3, characterized in that, In step S5, the boundary conditions are shown in formula (2) In the formula, θ xi (x,y) and θ yi (x, y) represent the rotation angles of the underlying key layer i along the x and y directions, respectively.

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