Method for calculating vertical stress of interlayer rock stratum in column type goaf

Abstract

The invention belongs to the field of mine pressure numerical calculation, and particularly relates to a method for calculating vertical stress of an interlayer rock stratum in a column type goaf. The method includes: assuming that a lower coal seam is not mined, calculating the sum of vertical stresses transmitted from all coal pillars in an upper coal seam pillar type goaf to interlayer rock strata; assuming that the upper coal seam is not mined, calculating the stress generated when the working face of the lower coal seam is pushed to the interlayer rock stratum above the goaf at the L position and the advanced bearing pressure generated by the interlayer rock stratum above the coal body to be mined; respectively endowing correction parameters for the vertical stress transmitted by the coal pillar and the vertical stress formed by the recovery of the lower coal seam, and then summing; and determining an optimal correction parameter to obtain the vertical stress of the interlayer rock stratum in the upper coal seam column type goaf. According to the method, the upper coal seam column type goaf residual coal pillars and the lower coal seam working face mining disturbance influence factors are considered, the accuracy of interlayer rock stratum vertical stress calculation is greatly improved, and a theoretical basis is provided for accurate calculation of the upper coal seam column type goaf lower advance bearing pressure and the working face caving step pitch.

Description

Technical Field

[0001] The present invention belongs to the field of numerical calculation of mine pressure, and particularly relates to a method for calculating the vertical stress of the interlayer rock stratum in the lower layer of a pillar goaf. Background Art

[0002] Coal is the main energy source, and the economic development has a great demand for coal energy. Therefore, many coal mines have entered the stage of lower coal seam mining. Some of these coal mines adopted the room-and-pillar or bord-and-pillar coal mining method when mining the upper coal seam, resulting in a large number of coal pillars left in the goaf of the upper coal seam; the residual coal pillars in the goaf of the upper coal seam make the stress of the interlayer rock stratum between the upper and lower coal seams show non-uniform and stress mutation characteristics. This makes it difficult to predict the advanced abutment pressure and the caving step distance of the working face when mining the lower coal seam working face, especially when using the longwall caving method, and it is difficult to determine the advanced support distance and support strength. Summary of the Invention

[0003] In order to improve the accuracy of calculating the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf in the upper coal seam, and to solve the problems that the existing calculation of the vertical stress of the interlayer rock stratum is overly simplified and inaccurate, resulting in difficult prediction of the advanced abutment pressure and the caving step distance of the lower coal seam working face, the present invention proposes a method for calculating the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf. On the basis of the coal pillar stress transfer theory, considering the mining influence of the lower coal seam working face, the calculation of the vertical stress of the interlayer rock stratum is optimized, which specifically includes the following steps:

[0004] The first step: Assume that the lower coal seam has not been mined, and calculate the total vertical stress σ transmitted from all coal pillars in the pillar goaf of the upper coal seam to any point in the interlayer rock stratum. z总 ;

[0005] The second step: Assume that the upper coal seam has not been mined, and calculate the vertical stress σ generated at the x position of the interlayer rock stratum above the goaf of the lower coal seam when the working face of the lower coal seam advances to L. k ;

[0006] The third step: Assume that the upper coal seam has not been mined, and calculate the advanced rear abutment pressure f1(x) and the advanced front abutment pressure f2(x) generated at the x position of the interlayer rock stratum above the coal body to be mined when the working face of the lower coal seam advances to L.

[0007] The fourth step: Determine the vertical stress F at any point in the interlayer rock stratum in the lower layer of the pillar goaf of the upper coal seam when the working face of the lower coal seam advances to L.

[0008] F = k a σ z总 (K i ) + k b [f1(x) + f2(x)] + k c σ k + kz

[0009]

[0010] Where: k a is the total stress correction parameter of the coal pillar; K i is the stress correction parameter of the i-th coal pillar; k b is the advanced abutment pressure correction parameter; k c is the stress correction parameter of the goaf in the lower coal seam; k z is the comprehensive correction parameter; n is the total number of coal pillars; B is the width of the coal pillar, a is the distance between coal pillars; σ z宽 is the vertical stress transmitted by a single wide coal pillar under the condition that the coal pillar is a wide coal pillar; σ z窄 is the vertical stress transmitted by a single narrow coal pillar under the condition that the coal pillar is a narrow coal pillar;

[0011] Step 5: Determine the optimal values of the correction parameters K i , k a , k b , k c , k z ;

[0012] Step 6: Substitute the optimal correction parameters into the vertical stress F at any point in the interlayer rock stratum of the lower layer of the column goaf in the upper coal seam.

[0013] Preferably, in the first step: Take the advancing direction of the lower coal seam working face as the x-axis direction, take the bottom plate at the side of the first coal pillar in the upper coal seam that deviates from the advancing direction of the lower coal seam working face as the coordinate origin, and establish a coordinate system with the vertical upward direction as the z-axis direction.

[0014] Preferably, in the first step: Under the condition of wide coal pillars, the vertical stress is successively divided into a positive triangular area, a reverse trapezoidal area, a positive trapezoidal area, and a reverse triangular area along the coal pillar; under the condition of narrow coal pillars, the vertical stress is successively divided into a positive triangular area, a uniform stress area, and a reverse triangular area along the coal pillar; the expressions for the vertical stress transmitted by the positive triangular area, the reverse triangular area, the reverse trapezoidal area, the positive trapezoidal area, and the uniform stress area to any point in the interlayer rock stratum are respectively:

[0015]

[0016] Furthermore, it is obtained that:

[0017] σ z宽 =σ z1 +σ z3 +σ z4 +σ z2

[0018] σ z窄 =σ z1 +σ z5 +σz2

[0019] Furthermore, we obtain:

[0020]

[0021] In the formula: K is the stress coefficient of the coal pillar; x1, x2, x3, x4, and x5 are the lengths of the forward triangular area, reverse triangular area, reverse trapezoidal area, forward trapezoidal area, and uniform stress area of each coal pillar along the x-axis direction, respectively; P is the average stress exerted by the overlying strata on the coal pillar, γ is the average volume force of the overlying strata; H is the average mining depth of the upper coal seam.

[0022] Preferably, in the second step: the lower coal seam is mined by the longwall caving method, and the starting point of mining is directly below the side of the first coal pillar in the upper coal seam that deviates from the advancing direction of the lower coal seam working face.

[0023] Preferably, in the second step:

[0024]

[0025] In the formula: σ k is the vertical stress at x of the interlayer strata above the goaf of the lower coal seam; k e is the quadratic term coefficient; b is the constant term coefficient;

[0026] Through numerical simulation, calculate the vertical stress of the interlayer strata above the goaf of the lower coal seam when the working face of the lower coal seam advances to L, extract different positions x and their corresponding σ k Calculate the quadratic term coefficient k e and the constant term coefficient b.

[0027] Preferably, in the third step:

[0028]

[0029] In the formula: f c1 , f c2 are the control parameters for the magnitudes of the abutment pressure in the post-advance section and the peak abutment pressure in the pre-advance section, respectively, and the two are equal in magnitude; x c1 , x c2 are the control parameters for the degree of steepness of the abutment pressure curves in the post-advance section and the pre-advance section; k is the peak point position correction parameter; p is the distance from the peak point to the advancing position L of the working face;

[0030] Assume that the upper coal seam has not been mined yet. Through numerical simulation, calculate the abutment pressure curve of the interlayer strata in front of the working face of the lower coal seam when it advances to L, extract different positions x and their corresponding f1(x), f2(x) and calculate f c1 , f c2 , p.

[0031] Preferably, the fifth step includes: (1) establishing a numerical model, which includes the room-and-pillar goaf of the upper coal seam, and when the working face of the lower coal seam advances to L, performing numerical simulation calculations and extracting the vertical stress scatter values F of the interlayer rock strata in the numerical simulation mj ;

[0032] (2) Substitute the initial correction parameter set A j into the expression of the vertical stress F in the fourth step to obtain the theoretical calculation value F of the vertical stress of the interlayer rock strata j ; The initial correction parameter set A j includes correction parameters K i , k a , k b , k c , k d ;

[0033] (3) Use the least squares method to construct the objective function R(A j ), and substitute the vertical stress scatter value F of the interlayer rock strata in the numerical simulation mj and the theoretical calculation value F of the vertical stress of the interlayer rock strata j into the objective function

[0034] R(A j ) = ∑(F j - F mj ) 2

[0035] (4) Determine whether the objective function R(A j ) under the initial correction parameter set is a minimum value. If not, proceed to step (5); if so, the initial correction parameter is the optimal correction parameter, and proceed to step (6);

[0036] (5) Calculate the gradient of the objective function under the initial correction parameter set A j , select the direction of gradient descent to optimize the initial correction parameter set A j , and replace the initial correction parameter set A j+1 with the optimized correction parameter set A j , and repeat steps (2) to (4) until the minimum value of the objective function is found;

[0037]

[0038] Where: A j+1 is the optimized correction parameter set, A j is the set of correction parameters before optimization, which is also the initial correction parameter set; β is the learning rate; is the gradient of A j .

[0039] Preferably, it further includes a seventh step: changing the advancing distance L of the working face of the lower coal seam, and repeating the second to sixth steps to obtain the vertical stress F at any point of the interlayer rock formation corresponding to L.

[0040] The present invention has the following beneficial effects compared with the prior art:

[0041] (1) Compared with the traditional calculation method of vertical stress of the roof, the calculation method of the present invention takes into account the comprehensive influence of the residual coal pillars in the pillar goaf of the upper coal seam and the mining disturbance of the working face of the lower coal seam, greatly improving the accuracy of the calculation of the vertical stress of the interlayer rock formation.

[0042] (2) The present invention can provide a theoretical basis for the accurate calculation of the advanced abutment pressure and the caving step distance under the pillar goaf of the upper coal seam, and can prevent accidents such as sudden roof caving, hydraulic support pressing, and roof caving in the advanced support section, improving the safety of mining under the pillar goaf of the upper coal seam. Description of the Drawings

[0043] Figure 1 It is a schematic diagram of the overall vertical stress distribution of the interlayer rock formation under the pillar goaf of the upper coal seam;

[0044] Figure 2 It is a schematic diagram of the load borne by the coal pillar in the pillar goaf of the upper coal seam;

[0045] Figure 3 It is a schematic diagram of stress transfer of the wide coal pillar model;

[0046] Figure 4 It is a schematic diagram of stress transfer of the wide coal pillar model;

[0047] In the figure: lower coal seam - 1; goaf of the lower coal seam - 11; coal body to be mined back - 12; interlayer rock formation - 2; pillar goaf of the upper coal seam - 3; coal pillar - 31; coal room - 32; overlying strata 4. Detailed Embodiments

[0048] The present invention will be further described below with reference to the drawings.

[0049] As Figures 1-4 shown, the present invention proposes a calculation method for the vertical stress of the interlayer rock formation under the pillar goaf, including the following steps:

[0050] The first step: Assume that the lower coal seam 1 has not been mined, and calculate the vertical stress σ transmitted from all the coal pillars 31 in the pillar goaf 3 of the upper coal seam to the interlayer rock formation 2 z总 ; specifically as follows:

[0051] As Figure 2 shown, the average stress P acting on the coal pillar 31 by the overlying strata 4 is:

[0052]

[0053] Wherein: P is the average stress exerted by the overlying strata 4 on the coal pillar 31, in Pa; B is the width of the coal pillar 31, in m; a is the width of the coal room 32, i.e., the distance between the coal pillars 31, in m; γ is the average volumetric force of the overlying strata 4, in N / m 3 ; H is the average mining depth of the upper coal seam, in m; ρ is the extraction rate,

[0054] Such as Figure 1 、 Figures 3-4 As shown, take the advancing direction of the lower coal seam working face as the x-axis direction (in this patent, it is assumed that the strata is horizontal, i.e., the x-axis is the horizontal direction), and take the bottom plate at the side of the first coal pillar 31 in the upper coal seam that deviates from the advancing direction of the lower coal seam working face as the coordinate origin (the roof of the lower coal seam 1 is the bottom plate of the lowest interlayer rock stratum 2), and establish a coordinate system with the vertical upward direction as the z-axis direction; under the condition of a wide coal pillar, assume that the coordinates of any point M1(x, z) in the interlayer rock stratum 2 below it are such that its vertical stress is successively divided into a positive triangular area, a reverse trapezoidal area, a positive trapezoidal area, and a reverse triangular area along the coal pillar 31; under the condition of a narrow coal pillar, assume that the coordinates of any point M2(x, z) in the interlayer rock stratum 2 below it are such that its vertical stress can be successively divided into a positive triangular area, a uniform stress area, and a reverse triangular area along the coal pillar 31; the expressions for the vertical stress transmitted from the positive triangular area, the reverse triangular area, the reverse trapezoidal area, the positive trapezoidal area, and the uniform stress area to any point in the interlayer rock stratum 2 can be obtained as follows:

[0055]

[0056] Wherein: σ z1 、σ z2 、σ z3 、σ z4 、σ z5 are the vertical stresses transmitted from the positive triangular area, the reverse triangular area, the reverse trapezoidal area, the positive trapezoidal area, and the uniform stress area to the interlayer rock stratum 2, respectively, in Pa; K is the stress coefficient of the coal pillar 31; x1, x2, x3, x4, and x5 are the lengths of the positive triangular area, the reverse triangular area, the reverse trapezoidal area, the positive trapezoidal area, and the uniform stress area of each coal pillar 31 along the x-axis direction (i.e., the horizontal direction), respectively;

[0057] Furthermore, the vertical stress σ z宽 transmitted from a single wide coal pillar to any point M1(x, z) in the interlayer rock stratum 2, and the vertical stress σ z窄 transmitted from a single narrow coal pillar to any point M2(x, z) in the interlayer rock stratum 2 can be obtained, as shown in Equations (7) and (8) respectively:

[0058] σ z宽 =σ z1 +σ z3 +σ z4 +σz2 #(7)

[0059] σ z窄 = σ z1 + σ z5 + σ z2 #(8)

[0060] In the formula: σ z宽 is the vertical stress transmitted by a single wide coal pillar under the condition that coal pillar 31 is a wide coal pillar; σ z窄 is the vertical stress transmitted by a single narrow coal pillar under the condition that coal pillar 31 is a narrow coal pillar;

[0061] Assume that there are n coal pillars 31 in the pillar - type goaf 3 of the upper coal seam. Then the expression for the vertical stress transmitted by n coal pillars 31 to any point in the inter - layer rock stratum 2 is:

[0062]

[0063] In the formula: σ z总 is the vertical stress transmitted by n coal pillars 31 to any point in the inter - layer rock stratum 2, Pa; n is the total number of coal pillars 31;

[0064] Step 2: Without considering the pillar - type goaf 3 of the upper coal seam, that is, assuming that the upper coal seam has not been mined; calculate the vertical stress σ k at the x - position in the inter - layer rock stratum 2 above the goaf 11 of the lower coal seam when the working face of the lower coal seam advances to L: The lower coal seam 1 is mined by the long - wall caving method, and the starting point of mining is directly below the side of the first coal pillar 31 in the upper coal seam that deviates from the advancing direction of the lower - coal - seam working face;

[0065]

[0066] In the formula: σ k is the vertical stress at the x - position in the inter - layer rock stratum 2 above the goaf 11 of the lower coal seam, Pa; L is the advancing distance of the lower - coal - seam working face, m; k e is the quadratic - term coefficient; b is the constant - term coefficient.

[0067] Without considering the pillar - type goaf 3 of the upper coal seam, that is, assuming that the upper coal seam has not been mined, through numerical simulation, calculate the vertical stress of the inter - layer rock stratum 2 above the goaf 11 of the lower coal seam when the working face of the lower coal seam advances to L, and extract different positions x and their corresponding σ k The quadratic - term coefficient k e and the constant - term coefficient b can be calculated;

[0068] Step 3: Without considering the pillar - type goaf 3 of the upper coal seam, that is, assuming that the upper coal seam has not been mined; determine the advanced abutment pressure f(x) generated at the x - position in the inter - layer rock stratum 2 above the coal body 12 to be mined when the working face of the lower coal seam advances to L, including the advanced - rear - section abutment pressure f1(x) and the advanced - front - section abutment pressure f2(x):

[0069]

[0070] where: f1(x) and f2(x) are the abutment pressures of the super-later and super-early front sections respectively, in Pa; f c1 , f c2 are the control parameters for the peak values of the abutment pressures of the super-later and super-early front sections, and they are equal in magnitude; x c1 , x c2 are the control parameters for the curve steepness of the abutment pressures of the super-later and super-early front sections, usually taken as 4 and 6 respectively; k is the correction parameter for the peak point position; p is the distance from the peak point to the advancing position L of the working face, in m;

[0071] Without considering the pillar-type goaf 3 in the upper coal seam, that is, assuming the upper coal seam has not been mined yet, the distribution curve of the abutment pressure in the interlayer rock stratum 2 is calculated by numerical simulation when the working face in the lower coal seam advances to L, and different positions x and their corresponding f1(x), f2(x) are extracted to calculate f c1 , f c2 , p;

[0072] Step 4: Calculate the vertical stress F at any point in the interlayer rock stratum 2 under the pillar-type goaf 3 in the upper coal seam when the working face in the lower coal seam advances to L

[0073] In the previous calculation of the vertical stress generated by the coal pillar 31 in the pillar-type goaf 3 in the upper coal seam on the interlayer rock stratum 2, the influence of the mining of the lower coal seam 1 was not considered; when the working face in the lower coal seam advances to L, the influence of the pillar-type goaf 3 in the upper coal seam was not considered when calculating the vertical stress generated in the interlayer rock stratum 2 above the goaf 11 and the coal body to be mined 12 in the lower coal seam; however, the vertical stress of the interlayer rock stratum 2 will be affected by the mining of the upper and lower coal seams 1; after only room-and-pillar mining of the upper coal seam, the stress of the remaining coal pillar 31 is concentrated and transmitted to its floor (i.e., the interlayer rock stratum 2), and the distribution of the vertical stress transmitted by the coal pillar to the interlayer rock stratum 2 is as Figure 1 shown as A in Figures 3-4 and as Figure 1 shown; when only longwall caving mining is carried out on the lower coal seam 1, when the working face in the lower coal seam advances to L, the vertical stress of the roof (i.e., the interlayer rock stratum 2) of the goaf 11 in the lower coal seam decreases, as Figure 1 shown as B in Figure 1 and the vertical stress of the roof (i.e., the interlayer rock stratum 2) above the coal body to be mined 12 increases, as Figure 1 shown as C in; when room-and-pillar mining is carried out on the upper coal seam first and then longwall caving mining is carried out on the lower coal seam 1, considering the influence of the remaining coal pillar 21 in the pillar-type goaf 3 in the upper coal seam, the distribution form of the vertical stress of the interlayer rock stratum 2 above the goaf 11 in the lower coal seam isFigure 1 A in Figure 1 is superimposed with C in;

[0074] As the working face of the lower coal seam advances, the coal pillar 31 in the room-and-pillar goaf 3 of the upper coal seam will have varying degrees of stress concentration. Therefore, when calculating the stress transfer of the coal pillar 31, a coal pillar stress correction parameter is added to the vertical stress transfer formula of each coal pillar 31. Finally, σ z总 (K i ) is obtained:

[0075]

[0076] By summing up Formula (10), Formula (11), and Formula (12) and introducing the correction parameter to reconcile the differences, the expression of the vertical stress distribution of the interlayer rock stratum 2 under the room-and-pillar goaf 3 of the upper coal seam can be obtained:

[0077] F = k a σ z总 (K i ) + k b [f1(x) + f2(x)] + k c σ k + k z #(13)

[0078] In the formula: F is the vertical stress of the interlayer rock stratum 2 under the room-and-pillar goaf 3 of the upper coal seam, Pa; k a is the total stress correction parameter of the coal pillar 31; K i is the stress correction parameter of the i-th coal pillar 31; k b is the advanced abutment pressure correction parameter; k c is the stress correction parameter of the goaf 11 of the lower coal seam; k z is the comprehensive correction parameter;

[0079] It should be noted that when the working face of the lower coal seam advances to L, σ k only exists when x < L. In Formula (10), when x ≥ L, setting σ k = 0 is only to simplify Formula (13); similarly, when the working face of the lower coal seam advances to L, the advanced abutment pressures f1(x) and f2(x) only exist when x ≥ L. In Formula (11), when x < L, setting f1(x) = f2(x) = 0 is only to simplify Formula (13);

[0080] Step 5: Determine the optimal values of the correction parameters K i , k a , k b , k c , k z ; including

[0081] (1) Establish a numerical model, where the numerical model includes the pillar goaf 3 of the upper coal seam, and when the working face of the lower coal seam advances to L, perform numerical simulation calculations and extract the vertical stress scatter values F of the interlayer rock stratum 2 in the numerical simulation. mj ;

[0082] (2) Substitute the initial correction parameter set A j (In this embodiment, the initial values of the correction parameters are set as k a = 2, k b = 0.1, k c = 10, k z = 1, K i = 1) into formula (13) to obtain the theoretical calculation value F of the vertical stress of the interlayer rock stratum 2. j ;

[0083] (3) Use the least squares method to construct the objective function R(A j ), and substitute the vertical stress scatter value F of the interlayer rock stratum 2 in the numerical simulation mj and the theoretical calculation value F of the vertical stress of the interlayer rock stratum 2 into the objective function j R(A

[0084] R(A j ) = ∑(F j - F mj ) 2 #(14)

[0085] (4) Determine whether the objective function R(A j ) under the initial correction set is a minimum value. If not, go to step (5); if so, the initial correction parameters are the optimal correction parameters, and go to step (6);

[0086] (5) Calculate the gradient of the objective function under the initial correction parameter set A j through formula (15), select the direction of gradient descent to optimize the initial correction parameter set A j , and replace the initial correction parameter set A j+1 with the optimized correction parameter set A j , and repeat steps (2) to (4) until the minimum value of the objective function is found;

[0087]

[0088] Where: A j+1 is the optimized correction parameter set, A j is the set of correction parameters before optimization, which is also the initial correction parameter set; β is the learning rate; is the gradient of A j ;

[0089] Step 6: Substitute the optimal correction parameters into the vertical stress F at any point in the interlayer rock stratum of the lower layer of the upper coal seam column goaf;

[0090] Step 7: Change the advancing distance L of the working face of the lower coal seam, and repeat Steps 2 to 6 to obtain the vertical stress F at any point in the interlayer rock stratum corresponding to L.

Claims

1. A calculation method for the vertical stress of the interlayer rock stratum in the lower layer of a pillar goaf, characterized in that, Including the following steps: Step 1: Assume that the lower coal seam has not been mined, and calculate the total vertical stress σ transmitted from all coal pillars in the bord-and-pillar goaf of the upper coal seam to any point in the interlayer rock stratum. z总 ; Step 2: Assume that the upper coal seam has not been mined yet, and calculate the vertical stress σ generated at the position x of the interlayer rock above the goaf of the lower coal seam when the working face of the lower coal seam advances to L k ; The third step: Assuming that the upper coal seam has not been mined, calculate the advanced and rear abutment pressures f1(x) and f2(x) generated at the position x of the interlayer rock above the coal body to be mined when the working face of the lower coal seam advances to the position L. The fourth step: Determine the vertical stress F at any point in the interlayer rock below the pillar goaf of the upper coal seam when the working face of the lower coal seam advances to the position L. F = k a σ z总 (K i ) + k b [f1(x) + f2(x)] + k c σ k + k z Where: k a is the total stress correction parameter of the coal pillar; K i is the stress correction parameter of the i-th coal pillar; k b is the advanced abutment pressure correction parameter; k c is the stress correction parameter of the goaf in the lower coal seam; k z is the comprehensive correction parameter; n is the total number of coal pillars; B is the width of the coal pillar, a is the distance between coal pillars; σ z宽 is the vertical stress transmitted by a single wide coal pillar under the condition that the coal pillar is a wide coal pillar; σ z窄 is the vertical stress transmitted by a single narrow coal pillar under the condition that the coal pillar is a narrow coal pillar; Step 5: Determine the optimal values of the correction parameters K i , k a , k b , k c , k z ; The sixth step: Substitute the optimal correction parameter into the vertical stress F at any point in the interlayer rock below the pillar goaf of the upper coal seam.

2. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf according to claim 1, characterized in that, In the first step: Take the advancing direction of the working face of the lower coal seam as the x-axis direction, take the bottom of the first coal pillar in the upper coal seam on the side away from the advancing direction of the working face of the lower coal seam as the coordinate origin, and establish a coordinate system with the vertical upward direction as the z-axis direction.

3. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf according to claim 2, characterized in that, In the first step: Under the condition of wide coal pillars, the vertical stress is successively divided into a positive triangular area, a reverse trapezoidal area, a positive trapezoidal area, and a reverse triangular area along the coal pillar; under the condition of narrow coal pillars, the vertical stress is successively divided into a positive triangular area, a uniform stress area, and a reverse triangular area along the coal pillar; the expressions for the vertical stress transmitted from the positive triangular area, the reverse triangular area, the reverse trapezoidal area, the positive trapezoidal area, and the uniform stress area to any point in the interlayer rock are respectively: Furthermore, it is obtained that: σ z宽 = σ z1 + σ z3 + σ z4 + σ z2 σ z窄 = σ z1 + σ z5 + σ z2 Furthermore, it is obtained that: Where: K is the stress coefficient of the coal pillar; x1, x2, x3, x4, and x5 are the lengths along the x-axis of the forward triangular area, reverse triangular area, reverse trapezoidal area, forward trapezoidal area, and uniform stress area of each coal pillar, respectively; P is the average stress exerted by the overlying strata on the coal pillar, γ is the average volumetric force of the overlying strata; H is the average mining depth of the upper coal seam.

4. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf according to claim 3, characterized in that In the second step: The longwall caving method is used for coal mining in the lower coal seam, and the starting point of coal mining is directly below the first coal pillar in the upper coal seam on the side away from the advancing direction of the working face of the lower coal seam.

5. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf according to claim 4, characterized in that, In the second step: Where: σ k is the vertical stress at the x position of the interlayer rock above the gob of the lower coal seam; k e is the quadratic coefficient; b is the constant coefficient; Through numerical simulation, calculate the vertical stress of the interlayer rock above the goaf of the lower coal seam when the working face of the lower coal seam advances to L, and extract different positions x and their corresponding σ k Calculate the quadratic coefficient k e and the constant coefficient b.

6. The calculation method of the vertical stress of the interlayer rock formation in the lower layer of the column goaf according to claim 5, characterized in that In the third step: Where: f c1 , f c2 are respectively the control parameters for the abutment pressure of the super-late stage and the peak value of the abutment pressure of the super-early stage, and the two are equal in magnitude; x c1 , x c2 are the control parameters for the degree of steepness of the abutment pressure curve of the super-late stage and the abutment pressure curve of the early stage; k is the peak point position parameter; p is the distance from the peak point to the advancing position L of the working face; Assume that the upper coal seam has not been mined yet. Through numerical simulation, calculate the advanced abutment pressure curve of the interlayer rock strata when the working face of the lower coal seam advances to L, and extract different positions x and their corresponding f1(x) and f2(x) to calculate f c1 , f c2 , p.

7. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the column goaf according to claim 6, characterized in that, The fifth step includes: (1) Establish a numerical model, where the numerical model includes the pillar goaf of the upper coal seam, and when the working face of the lower coal seam advances to L, perform numerical simulation calculations and extract the vertical stress scatter values F of the interlayer rock strata in the numerical simulation mj ; (2) Substitute the initial set of correction parameters A j into the expression of the vertical stress F in the fourth step to obtain the theoretically calculated value F of the vertical stress of the interlayer rock formation j ; The initial set of correction parameters A j includes the correction parameters K i , k a , k b , k c , k d ; (3) Use the least squares method to construct the objective function R(A j ), and substitute the scatter values F mj of the vertical stress of the interlayer rock strata obtained from numerical simulation and the theoretical calculation values F j of the vertical stress of the interlayer rock strata into the objective function R(A j ) = ∑(F j -F mj ) 2 (4) Determine whether the objective function R(A j ) is a minimum value under the initial set of correction parameters. If not, proceed to step (5); if so, the initial correction parameters are the optimal correction parameters, and proceed to step (6); (5) Calculate the initial set of correction parameters A j Calculate the gradient of the following objective function, select the direction of gradient descent for the initial set of correction parameters A j Perform optimization, and replace the initial set of correction parameters A with the optimized set of correction parameters A j+1 Replace the initial set of correction parameters A j , repeat steps (2) to (4) until the minimum value of the objective function is found; Where: A j+1 is the set of optimized correction parameters, and A j is the set of correction parameters before optimization and also the initial set of correction parameters; β is the learning rate; is the gradient of A j .

8. The calculation method of the vertical stress of the interlayer rock stratum in the lower layer of the pillar goaf according to any one of claims 1-7, characterized in that, It also includes the seventh step: Change the advancing distance L of the working face of the lower coal seam, and repeat the second to the sixth steps to obtain the vertical stress F at any point in the interlayer rock corresponding to the L.

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