Calculation method for coal mine overlying strata separation layer grouting space

Abstract

The invention provides a calculation method for a coal mine overlying strata separation layer grouting space. The method comprises the following steps that firstly, a sinking curve equation of overlying strata below a key layer L1 section is established; 2, determining the position H1 of a key layer; 3, establishing a morphological equation of the overlying rock arch structure; 4, determining the L2 size when the sinkage of the key layer is 0; 5, determining the volume V3 of the grouting amount required by a left half separation layer area below a key layer of the thickness of an overlying strata unit in the trend; and 6, according to the required grouting volume V3 of the left half separation layer area below the key layer of the thickness of the overlying strata unit in the trend, the required grouting volume V of the separation layer area below the key layer of the thickness of the overlying strata unit in the trend is obtained. According to the method, the quantitative calculation problem of the overlying strata separation layer filling space is solved, overlying strata separation layer filling is converted into quantitative filling from experiential and semi-experiential blind filling, and the problem that the overlying strata separation layer grouting filling effects are different due to different human experiences is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of coal mine fracture space treatment, involves the calculation of grouting space, and specifically relates to a calculation method for the grouting space of separated strata in overlying strata of coal mines. Background Technique

[0002] Strata separation is a phenomenon of separation along the bedding plane during the subsidence movement of overlying strata in coal mining, which is commonly present in various combinations of overlying strata in mining fields. This phenomenon belongs to the category of strata movement caused by coal mining, and its essence is the product of self-regulation of the stress field in overlying strata caused by coal seam mining, and it is affected by three factors: rock stratum properties, overlying strata structure, and mining factors. The existing judgment of strata separation believes that the movement of key strata controls the generation, development, and spatio-temporal distribution of strata separation; strata separation in overlying strata mainly occurs under each key stratum, and the maximum development height of strata separation in overlying strata stops at the main key stratum of overlying strata.

[0003] In the prior art, physical similarity simulation is usually used to analyze the development law of voids in separated strata during coal seam mining to master the development of injectable space in separated strata of overlying strata. However, physical similarity simulation cannot obtain the three-dimensional development characteristics of voids in separated strata of overlying strata, nor can it quantitatively analyze the size and geometric characteristics of injectable space.

[0004] In order to further study the evolution characteristics of voids in separated strata of overlying strata, a three-dimensional discrete element numerical calculation method is used to simulate the coal mining process and analyze the change law of voids in separated strata of overlying strata. However, numerical simulation is only a qualitative expression and cannot achieve quantitative analysis.

[0005] Generally speaking, in the prior art, the position and timing of the development of separated strata in overlying strata have been mainly studied through various theories and methods, and there is no calculation of the size of the space of separated strata in overlying strata, resulting in blindness in using grouting filling of separated strata in overlying strata to control mining subsidence and the inability to quantify the filling volume. However, the prediction of the filling volume is the key to project construction cost control, quality control, and process control. Therefore, there is an urgent need for a calculation method for the grouting space of separated strata in overlying strata of coal mines to accurately calculate the grouting space of separated strata in overlying strata of coal mines and provide a basis for the design of the filling volume of coal gangue and the grouting system. Summary of the Invention

[0006] Aiming at the deficiencies existing in the prior art, the purpose of the present invention is to provide a calculation method for the grouting space of separated strata in overlying strata of coal mines to solve the technical problem that the calculation accuracy of the grouting space of separated strata in overlying strata of coal mines and the required grouting volume in the prior art needs to be further improved.

[0007] To solve the above technical problems, the present invention adopts the following technical solutions to achieve:

[0008] A calculation method for the grouting space of separated strata in overlying strata of coal mines, the method comprising the following steps:

[0009] Step 1: Establish the subsidence curve equation of the overlying strata below the key layer L1 section and determine the caving boundary of the overlying strata.

[0010] Step 2: Determine the key layer position H1.

[0011] Step 3: Establish the morphological equation of the overlying strata arch structure and determine the arch morphology of the overlying strata failure in the dip direction.

[0012] Step 4: According to the key layer position H1 determined in Step 2 and the morphological equation of the overlying strata arch structure in Step 3, determine the L2 dimension when the subsidence of the key layer is 0.

[0013] Step 5: According to the subsidence curve equation of the overlying strata below the key layer L1 section established in Step 1, the key layer position H1 determined in Step 2, and the L2 dimension obtained when the subsidence of the key layer is 0 in Step 4, take the thickness of the upward overlying strata unit, and perform integral calculation on the volume of the grouting amount required for the separated layer area below the key layer to obtain the volume V3 of the grouting amount required for the left half of the separated layer area below the key layer with the thickness of the upward overlying strata unit.

[0014] The volume V3 of the grouting amount required for the left half of the separated layer area below the key layer with the thickness of the upward overlying strata unit is as follows:

[0015]

[0016] In the formula:

[0017] V3 is the volume of the grouting amount required for the left half of the separated layer area below the key layer with the thickness of the upward overlying strata unit, and the unit is m 3 ;

[0018] z is the thickness of the upward overlying strata unit, and the unit is m;

[0019] L2 is the length of the semi-arch area of the overlying strata, and the unit is m;

[0020] L is the dip length of the working face, and the unit is m;

[0021] H1 is the key layer position, and the unit is m;

[0022] w(x) is the dependent variable of the subsidence curve equation of the overlying strata below the key layer L1 section, and the unit is m;

[0023] x is the independent variable of the dip length of the working face, and the value range of x is L2 ≤ x ≤ L / 2, and the unit is m;

[0024] H0 is the separation height of the overlying strata below the key layer, that is, the maximum subsidence of the key layer, and the unit is m;

[0025] B is an intermediate quantity.

[0026] Step 6: Based on the volume V3 of the grouting amount required for the left half of the separated layer area below the key layer of the overlying rock unit thickness in the strike direction obtained in Step 5, obtain the volume V of the grouting amount required for the separated layer area below the key layer of the overlying rock unit thickness in the strike direction.

[0027] Compared with the prior art, the present invention has the following technical effects:

[0028] (Ⅰ) The present invention solves the problem of quantitative calculation of the injectable space of overlying rock separated layers, transforming the filling of overlying rock separated layers from empirical and semi-empirical blind filling into quantitative filling, and changing the problem of different grouting filling effects of overlying rock separated layers caused by different human experiences.

[0029] (Ⅱ) The calculation method of the injectable space of overlying rock separated layers in the present invention can predict the filling amount before the implementation of the project, providing key parameter indicators for project budget, cost control, quality control and process control during project construction, and providing a basis for the design of the filling amount and filling system of coal gangue. Description of the Drawings

[0030] Figure 1 It is a schematic diagram of the calculation model of the separated layer shape of the roof in the coal mine goaf.

[0031] Figure 2 It is a schematic diagram of the calculation principle of the separated layer shape of the roof in the coal mine goaf.

[0032] The meanings of the various reference numerals in the figure are as follows: 1 - key layer, 2 - support structure, 3 - coal seam, 4 - working face, 5 - overlying rock separated layer, 6 - goaf.

[0033] The following further elaborates on the specific content of the present invention in conjunction with embodiments. Specific Embodiments

[0034] It should be noted that all the calculation methods, theories and concepts in the present invention, unless otherwise specified, all adopt the calculation methods, theories and concepts known in the prior art. For example, the probability integral method of mining damage adopts the known probability integral method of mining damage.

[0035] It should be noted that in mining engineering, the working face refers to the working place for mining minerals or rocks, which moves with the progress of excavation. In the present invention, the working face refers to the plane where the coal seam is mined.

[0036] In the present invention, the internal friction angle refers to the physical and mechanical properties of each rock layer above the stope, and the unit is °.

[0037] In the present invention, the cohesion refers to the mutual attraction between adjacent parts within each rock layer.

[0038] The following are specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments, and any equivalent transformation based on the technical solution of this application falls within the protection scope of the present invention.

[0039] Embodiment:

[0040] This embodiment provides a calculation method for the grouting space of separated strata in overlying strata of coal mines, and this method includes the following steps:

[0041] Step 1, establish the subsidence curve equation of the overlying strata below the key stratum L1 section, and determine the caving boundary of the overlying strata.

[0042] In this embodiment, in the separated strata area that appears above the roof rock stratum, a grouting space is generated. At this time, the shape of the coal seam roof can be determined with reference to the surface subsidence curve, such as Figure 1 shown.

[0043] In this embodiment, for the convenience of calculation, a unit width is taken along the working face strike to establish a two-dimensional plane mechanical model. In Figure 1 and Figure 2 , taking the left arch foot of the arch BCD as the origin O, the horizontal right direction (i.e., the working face dip length direction) as the x-axis direction, and the vertical upward direction as the y-axis direction, a two-dimensional rectangular coordinate system is established.

[0044] From Figure 1 the geometric relationship in, the subsidence curve equation of the overlying strata below the key stratum L1 section is:

[0045] w(x) = H1 - H0s(x) (1)

[0046] In the formula:

[0047] w(x) is the dependent variable of the subsidence curve equation of the overlying strata below the key stratum L1 section, with the unit of m;

[0048] x is the independent variable of the working face dip length, and the value range of x is L2 ≤ x ≤ L / 2, with the unit of m;

[0049] H1 is the key stratum position, that is, the distance between the key stratum and the coal seam, with the unit of m;

[0050] H0 is the separated strata height of the overlying strata below the key stratum, that is, the maximum subsidence amount of the key stratum, with the unit of m;

[0051] s(x) is the subsidence height coefficient of the overlying strata with the abscissa of x below the key stratum L1 section.

[0052] Due to the swelling property of the caved roof rock, its maximum subsidence amount is generally less than the mining thickness, that is:

[0053] H0 = ηH (2)

[0054] In the formula:

[0055] $H_0$ is the separation height of the overlying strata below the key stratum, with the unit of m;

[0056] $\eta$ is the subsidence coefficient of the key stratum during the mining process of the working face;

[0057] $H$ is the mining height of the working face, with the unit of m.

[0058] When $x$ is at the position of $L_2$, the subsidence of the key stratum is 0. When $x$ is at the middle position $L / 2$ of the goaf, the subsidence of the key stratum reaches the maximum $H_0$. Then the following conditions need to be satisfied:

[0059]

[0060] In the formula:

[0061] $s(L_2)$ is the overlying strata subsidence height coefficient when the abscissa below the key stratum is $L_2$;

[0062] $s(L / 2)$ is the overlying strata subsidence height coefficient when the abscissa below the key stratum is $L / 2$.

[0063] The expression of the mining subsidence and movement of the key stratum is established by the probability integral method of mining damage science as:

[0064]

[0065] In the formula:

[0066] $s(x)$ is the overlying strata subsidence height coefficient when the abscissa below the $L_1$ section of the key stratum is $x$;

[0067] $x$ is the independent variable of the dip length of the working face, and the value range of $x$ is $L_2\leq x\leq L / 2$, with the unit of m;

[0068] $a$ is the slope of the line connecting the middle of the model goaf $L / 2$ to the subsidence boundary of the key stratum;

[0069] $b$ is the intercept of the line connecting the middle of the model goaf $L / 2$ to the subsidence boundary of the key stratum;

[0070] $t$ is the length of any point at the key stratum from the origin of the coordinate system, with the unit of m.

[0071] Substituting Equation (3) into Equation (4) gives:

[0072]

[0073] In the formula:

[0074] $a$ is the slope of the line connecting the middle of the model goaf $L / 2$ to the subsidence boundary of the key stratum;

[0075] $L$ is the dip length of the working face, with the unit of m;

[0076] L2 is the length of the overlying semi-arch area, in meters.

[0077] b is the intercept of the line from the model goaf L / 2 to the subsidence boundary of the key layer.

[0078] In step 1, by combining equations (1) to (5), the equation for the subsidence curve of the overburden below the key layer L1 segment can be obtained as:

[0079]

[0080] Where:

[0081] w(x) is the dependent variable of the overburden subsidence curve equation below the key layer L1 segment, unit: m;

[0082] x is the independent variable of the inclined length of the working face, and the value range of x is L2≤x≤L / 2, and the unit is m;

[0083] H1 is the key layer position, in m;

[0084] H0 is the separation height of the overburden below the key layer, in m;

[0085] s(x) is the subsidence height coefficient of the overburden when the horizontal coordinate is x below the key layer L1 segment;

[0086] erf() is the Gaussian error function;

[0087] L2 is the length of the overburden semi-arch area, in meters;

[0088] L is the inclined length of the working face, in m;

[0089] t is the length from any point on the key layer to the origin of the coordinate system, in meters.

[0090] In formula (6), H1 is still an unknown quantity. According to the key layer theory, the key layer position is determined, and the key layer position includes the main key layer position and the sub-key layer position. The main key layer refers to the rock layer that controls the overall overlying rock layer, and the sub-key layer refers to the rock layer that controls the rock layer below it. From the perspective of spatial position, the main key layer is above the sub-key layer.

[0091] Step 2: Determine the key layer H1.

[0092] In step 2, the specific solution process of the key layer H1 is:

[0093] Step 201, determine the positions of all hard rock layers inside the overburden.

[0094] In this embodiment, the position of the first hard rock layer is preliminarily determined based on the borehole columnar diagram and the corresponding rock physical and mechanical indicators.

[0095] In this embodiment, it is assumed that the first layer of rock stratum is the first layer of hard rock stratum, and the rock stratum above the first layer of hard rock stratum is the second layer of rock stratum. Starting from the bottom and going up, the rock strata are numbered layer by layer. The rock strata from the first layer of hard rock stratum to the m-th layer of rock stratum deform coordinately with the first layer of hard rock stratum, while the (m + 1)-th layer of rock stratum does not deform coordinately with the first layer of hard rock stratum. Then, the (m + 1)-th layer of rock stratum is the second layer of hard rock stratum. Since the rock strata from the first layer to the m-th layer deform coordinately, the curvature of each rock stratum is the same, and each rock stratum forms a combined beam. According to the principle of the combined beam, the load acting on the first layer of hard rock stratum can be derived as follows:

[0096]

[0097] In the formula:

[0098] q1(x)| m is the sum of the action loads of all rock strata from the first layer of hard rock stratum to the m-th layer of rock stratum on the first layer of hard rock stratum, with the unit of N / m;

[0099] x is the acting length of each rock stratum load, with the unit of m;

[0100] E1 is the elastic modulus of the first layer of hard rock stratum, with the unit of Pa;

[0101] h1 is the thickness of the first layer of hard rock stratum, with the unit of m;

[0102] i is the sequence number of the rock stratum layer number;

[0103] m is the number of rock stratum layers;

[0104] γ i is the unit weight of the i-th layer of rock stratum, i = 1, 2,..., m, with the unit of N / m 3 ;

[0105] h i is the thickness of the i-th layer of rock stratum, i = 1, 2,..., m, with the unit of m;

[0106] E i is the elastic modulus of the i-th layer of rock stratum, i = 1, 2,..., m, with the unit of Pa.

[0107] Considering the load formed by the (m + 1)-th layer on the first layer of hard rock stratum is:

[0108]

[0109] In the formula:

[0110] q1(x)| m+1 is the sum of the action loads of all rock strata from the first layer of hard rock stratum to the (m + 1)-th layer of rock stratum on the first layer of hard rock stratum, with the unit of N / m;

[0111] x is the acting length of the loads of each rock stratum, with the unit of m;

[0112] i is the serial number sequence of the rock stratum numbers;

[0113] m + 1 is the number of rock strata;

[0114] E1 is the elastic modulus of the first hard rock stratum, with the unit of Pa;

[0115] h1 is the thickness of the first hard rock stratum, with the unit of m;

[0116] γ i is the unit weight of the i-th rock stratum, i = 1, 2, …, m + 1, with the unit of N / m 3 ;

[0117] h i is the thickness of the i-th rock stratum, i = 1, 2, …, m + 1, with the unit of m;

[0118] E i is the elastic modulus of the i-th rock stratum, i = 1, 2, …, m + 1, with the unit of Pa.

[0119] Since the (m + 1)-th layer is a hard rock stratum, the deflection of the (m + 1)-th layer is less than that of the lower rock strata, and the rock strata above the (m + 1)-th layer no longer require the lower rock strata to bear the loads they bear. Then, there must be:

[0120] q1(x) m+1 <q1(x) m (9)

[0121] In the formula:

[0122] q1(x)| m+1 is the sum of the acting loads of all rock strata from the first hard rock stratum to the (m + 1)-th rock stratum on the first hard rock stratum, with the unit of N / m;

[0123] x is the acting length of the loads of each rock stratum, with the unit of m;

[0124] m + 1 is the number of rock strata;

[0125] m is the number of rock strata;

[0126] q1(x)| m is the sum of the acting loads of all rock strata from the first hard rock stratum to the m-th rock stratum on the first hard rock stratum, with the unit of N / m.

[0127] Substitute formulas (7) and (8) into formula (9) and simplify to obtain:

[0128]

[0129] In the formula:

[0130] γ m+1 is the unit weight of the (m + 1)-th layer of rock stratum, with the unit of N / m 3 ;

[0131] E i is the elastic modulus of the i-th layer of rock stratum, where i = 1, 2, …, m, with the unit of Pa;

[0132] h i is the thickness of the i-th layer of rock stratum, where i = 1, 2, …, m, with the unit of m;

[0133] E m+1 is the elastic modulus of the (m + 1)-th layer of rock stratum, with the unit of Pa;

[0134] i is the sequence number of the layer number of the rock stratum;

[0135] m is the number of layers of the rock stratum;

[0136] m + 1 is the number of layers of the rock stratum;

[0137] h m+1 is the thickness of the (m + 1)-th layer of rock stratum, with the unit of m;

[0138] γ i is the unit weight of the i-th layer of rock stratum, where i = 1, 2, …, m, with the unit of N / m 3 .

[0139] Equation (10) is the formula for determining the position of the hard rock stratum. During specific determination, start calculating layer by layer upward from the first layer of rock stratum above the coal seam. When and satisfy Equation (10), then stop calculating upward. At this time, starting from the first layer of rock stratum upward, the m-th layer of rock stratum is the first layer of hard rock stratum.

[0140] Starting from the first layer of hard rock stratum, determine the position of the second layer of hard rock stratum in the same judgment method as the first layer of hard rock stratum until the position of the uppermost layer of hard rock stratum is determined, denoted as the n-th layer of hard rock stratum. By judging the position of the hard rock stratum, the position of the hard rock stratum in the overlying strata and the soft rock stratum group it controls are obtained.

[0141] Step 202: According to the position of the hard rock stratum obtained in Step 201, determine the key strata existing in the rock stratum through the break distance of the rock beam and the spatial horizon.

[0142] In this embodiment, each hard rock stratum is regarded as a fixed-ended beam. From the mechanical model of the fixed-ended beam and according to the theory of material mechanics analysis (taking one hard rock stratum as an example), the normal stress at any point within the hard rock stratum is:

[0143]

[0144] In the formula:

[0145] σ is the normal stress per unit width at any point within the hard rock stratum, with the unit of N / m;

[0146] M is the bending moment of the cross-section where any point within the hard rock stratum is located, with the unit of N·m;

[0147] y is the distance between any point within the hard rock stratum and the neutral axis of the cross-section, with the unit of m;

[0148] h is the thickness of the hard rock stratum, with the unit of m.

[0149] From the analysis of the hard rock stratum, it can be seen that the maximum bending moment of the hard rock stratum occurs at both ends of the hard rock stratum, that is:

[0150]

[0151] In the formula:

[0152] M max is the maximum bending moment of the hard rock stratum, with the unit of N·m;

[0153] q is the acting load of the overlying strata, with the unit of N / m;

[0154] l is the exposed length of the hard rock stratum along the strike, with the unit of m.

[0155] The maximum tensile stress corresponding to the maximum bending moment of the hard rock stratum is:

[0156]

[0157] In the formula:

[0158] σ max is the maximum tensile stress corresponding to the maximum bending moment per unit width of the hard rock stratum, with the unit of N / m; q is the acting load of the overlying strata, with the unit of N / m;

[0159] l is the exposed length of the hard rock stratum along the strike, with the unit of m;

[0160] h is the thickness of the hard rock stratum, with the unit of m.

[0161] When σ max = σ t , the hard rock stratum fractures. From Equation (13), the breaking distance of the hard rock stratum is:

[0162]

[0163] In the formula:

[0164] L k is the breaking distance of the k-th layer of hard rock stratum, with the unit of m;

[0165] hk is the thickness of the k-th hard rock layer, with the unit of m;

[0166] σ t is the tensile strength per unit width of the k-th hard rock layer, with the unit of N / m;

[0167] q k is the load borne by the k-th hard rock layer, with the unit of N / m.

[0168] In this embodiment, the rock layer between the k-th hard rock layer and the (k + 1)-th hard rock layer is the soft rock layer group controlled by the k-th hard rock layer. From Equation (7), it can be seen that q k is determined as follows:

[0169]

[0170] In the formula:

[0171] q k is the load borne by the k-th hard rock layer, with the unit of N / m;

[0172] E k,0 is the elastic modulus of the k-th hard rock layer, with the unit of Pa;

[0173] h k,0 is the thickness of the k-th hard rock layer, with the unit of m;

[0174] m k is the number of soft rock layers in the soft rock layer group controlled by the k-th hard rock layer;

[0175] h k,j is the thickness of the j-th soft rock layer in the soft rock layer group controlled by the k-th hard rock layer, with the unit of m;

[0176] k is the k-th hard rock layer;

[0177] j is the layer number of the soft rock layer in the soft rock layer group controlled by the k-th hard rock layer;

[0178] γ k,j is the unit weight of the j-th soft rock layer in the soft rock layer group controlled by the k-th hard rock layer, with the unit of N / m 3 ;

[0179] E k,j is the elastic modulus of the j-th soft rock layer in the soft rock layer group controlled by the k-th hard rock layer, with the unit of Pa.

[0180] If the k-th hard rock layer is a key layer, the breaking distance of the k-th hard rock layer should be greater than the breaking distances of all the hard rock layers above it, that is, it should satisfy:

[0181] L k >L k+1(16)

[0182] In the formula:

[0183] L k is the breaking distance of the k-th hard rock stratum, with the unit of m;

[0184] L k+1 is the breaking distance of the (k + 1)-th hard rock stratum, with the unit of m.

[0185] Step 203: According to Step 202 and in combination with the mine borehole columnar section and the rock mechanics data provided by the mine party, determine the key stratum position H1.

[0186] Step 3: Establish the morphological equation of the overlying rock arch structure and determine the arch shape of the inclined overlying rock failure.

[0187] In this embodiment, according to the physical similarity simulation experiment and the numerical calculation results, it can be known that the failure shape in the inclined section of the overlying rock is symmetric along the dip, presenting a geometric shape of arch + beam, and the semi-arch shapes on the left and right sides are symmetric. The morphological equation of the semi-arch can be determined according to the morphological equation of the overlying rock arch structure. The shape of the overlying rock arch structure is the arch BCD, as Figure 2 shown by the red curve in

[0188] Since the failure shape in the inclined section of the overlying rock is symmetric along the dip, it is only necessary to determine the semi-arch shape from the abscissa of 0 to the abscissa of L2, and the semi-infinite subsidence basin curve between the abscissa of L2 and the abscissa of L / 2. The coordinates of point A are (L / 2, 0).

[0189] In Figure 2 shown arch BCD, assume that the constraint forces at the left arch foot B are F along the x-axis bx and F along the y-axis by , and the constraint forces at the right arch foot D are F along the x-axis dx and F along the y-axis dy . From the equilibrium equation, we get:

[0190] F bx -F dx = 0 (17)

[0191] In the formula:

[0192] F bx is the horizontal constraint force at the left arch foot B, with the unit of N;

[0193] F dx is the horizontal constraint force at the right arch foot D, with the unit of N.

[0194] From the equilibrium equation, we also get:

[0195] F by+F dy +q1L - qL = 0 (18)

[0196] In the formula:

[0197] F by is the vertical constraint force at the left arch foot B, with the unit of N;

[0198] F dy is the vertical constraint force at the right arch foot D, with the unit of N;

[0199] q1 is the load acting on the floor, with the unit of N / m;

[0200] L is the dip length of the working face, with the unit of m;

[0201] q is the load acting on the overlying strata, with the unit of N / m.

[0202] Meanwhile, the bending moment equation of the left half arch BC at the crown C is obtained by the section method as follows:

[0203] In the formula:

[0204] M BC (x) is the bending moment of the left half arch BC at the crown C, with the unit of N·m;

[0205] x is the load acting length at any position of the left half arch BC, with the unit of m;

[0206] F by is the vertical constraint force at the left arch foot B, with the unit of N;

[0207] L is the dip length of the working face, with the unit of m;

[0208] F bx is the horizontal constraint force at the left arch foot B, with the unit of N;

[0209] h BCD is the height of the arch BCD, with the unit of m;

[0210] q is the load acting on the overlying strata, with the unit of N / m;

[0211] q1 is the load acting on the floor, with the unit of N / m.

[0212] In addition, the bending moment equation of the right half arch CD at the crown C is obtained by the section method as follows:

[0213] In the formula:

[0214] M CD (x) is the bending moment of the right half arch CD at the crown C, with the unit of N·m;

[0215] x is the load acting length at any position of the right half arch CD, with the unit of m;

[0216] F dy is the vertical constraint force at the right arch foot D, with the unit of N;

[0217] L is the dip length of the working face, with the unit of m;

[0218] F dx is the horizontal constraint force at the right arch foot D, with the unit of N;

[0219] h BCD is the height of the arch BCD, with the unit of m;

[0220] q is the load acting of the overlying strata, with the unit of N / m;

[0221] q1 is the load acting of the floor, with the unit of N / m.

[0222] From M BC (x) = 0 and M CD (x) = 0, it can be obtained that:

[0223]

[0224] In the formula:

[0225] F bx is the horizontal constraint force at the left arch foot B, with the unit of N;

[0226] F dx is the horizontal constraint force at the right arch foot D, with the unit of N;

[0227] q is the load acting of the overlying strata, with the unit of N / m;

[0228] q1 is the load acting of the floor, with the unit of N / m;

[0229] L is the dip length of the working face, with the unit of m;

[0230] h BCD is the height of the arch BCD, with the unit of m.

[0231] From M BC = 0 and M CD = 0, it is also obtained that:

[0232]

[0233] In the formula:

[0234] F by is the vertical constraint force at the left arch foot B, with the unit of N;

[0235] F dy is the vertical constraint force at the right arch springing D, with the unit of N;

[0236] q is the load exerted by the overlying strata, with the unit of N / m;

[0237] q1 is the load exerted by the floor, with the unit of N / m;

[0238] L is the dip length of the working face, with the unit of m.

[0239] Since the rock strata have the property of being compressive but not tensile, according to the theory of the reasonable arch axis of the arch, the equation of the reasonable arch axis of the arch can be determined.

[0240] Let the axis equation of the semi-arch BC section be:

[0241]

[0242] In the formula:

[0243] y is the dependent variable of the morphological equation of the overlying rock arch structure, with the unit of m;

[0244] y1(x) is the dependent variable of the axis equation of the semi-arch BC section, with the unit of m;

[0245] x is the independent variable of the dip length of the working face, and the value range of x is with the unit of m.

[0246] Let the axis equation of the semi-arch CD section be:

[0247]

[0248] In the formula:

[0249] y is the dependent variable of the morphological equation of the overlying rock arch structure, with the unit of m;

[0250] y2(x) is the dependent variable of the axis equation of the semi-arch CD section, with the unit of m;

[0251] x is the independent variable of the dip length of the working face, and the value range of x is with the unit of m.

[0252] Take an axial section K on the semi-arch BC section. Thus, the bending moment of any axial section K of the semi-arch BC section (0 ≤ x ≤ L / 2) is

[0253]

[0254] In the formula:

[0255] M BK (x) is the bending moment of any axial section K of the semi-arch BC section (0 ≤ x ≤ L / 2), with the unit of N·m;

[0256] x is the independent variable of the dip length of the working face, and the value range of x is 0 ≤ x ≤ L / 2, with the unit of m;

[0257] F by is the vertical constraint force at the left arch springing B, with the unit of N;

[0258] F bx is the horizontal constraint force at the left arch springing B, with the unit of N;

[0259] H3 is the distance between any point on the half arch and the coal seam, with the unit of m;

[0260] q is the load acting on the overlying strata, with the unit of N / m;

[0261] q1 is the load acting on the floor, with the unit of N / m;

[0262] ξ is the load acting length within the range of 0 to x, with the unit of m.

[0263] Equation (25) can be arranged as:

[0264]

[0265] In the formula:

[0266] M BK (x) is the bending moment of any cross-section K of the half arch BC section (0 ≤ x ≤ L / 2), with the unit of N·m; x is the independent variable of the dip length of the working face, and the value range of x is 0 ≤ x ≤ L / 2, with the unit of m;

[0267] F by is the vertical constraint force at the left arch springing B, with the unit of N;

[0268] F bx is the horizontal constraint force at the left arch springing B, with the unit of N;

[0269] H3 is the distance between any point on the half arch and the coal seam, with the unit of m;

[0270] q is the load acting on the overlying strata, with the unit of N / m;

[0271] q1 is the load acting on the floor, with the unit of N / m.

[0272] Similarly, the bending moment of any cross-section K of the half arch CD section (L / 2 ≤ x ≤ L) is:

[0273]

[0274] In the formula:

[0275] M DKM(x) is the bending moment of any cross-section K of the semi-arch CD segment (L / 2 ≤ x ≤ L), with the unit of N·m; x is the independent variable of the working face dip length, and the value range of x is L / 2 ≤ x ≤ L, with the unit of m.

[0276] F dy is the vertical constraint force at the right arch foot D, with the unit of N.

[0277] L is the working face dip length, with the unit of m.

[0278] F dx is the horizontal constraint force at the right arch foot D, with the unit of N.

[0279] H3 is the distance between any point on the semi-arch and the coal seam, with the unit of m.

[0280] q is the load exerted by the overlying strata, with the unit of N / m.

[0281] q1 is the load exerted by the floor, with the unit of N / m.

[0282] ξ is the load acting length within the range of L / 2 to x, with the unit of m.

[0283] Equation (27) can be rearranged as:

[0284]

[0285] In the formula:

[0286] M DK M(x) is the bending moment of any cross-section K of the semi-arch CD segment (L / 2 ≤ x ≤ L), with the unit of N·m.

[0287] x is the independent variable of the working face dip length, and the value range of x is L / 2 ≤ x ≤ L, with the unit of m.

[0288] F dy is the vertical constraint force at the right arch foot D, with the unit of N.

[0289] L is the working face dip length, with the unit of m.

[0290] F dx is the horizontal constraint force at the right arch foot D, with the unit of N.

[0291] H3 is the distance between any point on the semi-arch and the coal seam, with the unit of m.

[0292] q is the load exerted by the overlying strata, with the unit of N / m.

[0293] q1 is the load exerted by the floor, with the unit of N / m.

[0294] From M BK(x) = 0 and M KD When (x) = 0, the reasonable arch axis equation of arch BCD can be obtained as (rocks are resistant to compression but not to tension, and there will be normal stress when the bending moment is not zero):

[0295]

[0296] In the formula:

[0297] y(x) is the dependent variable of the morphological equation of the overlying rock arch structure, with the unit of m;

[0298] x is the independent variable of the working face dip length, and the value range of x is 0 ≤ x ≤ L, with the unit of m;

[0299] h BCD is the height of arch BCD, with the unit of m;

[0300] L is the working face dip length, with the unit of m.

[0301] In formula (29), the height h of arch BCD BCD is still an unknown quantity. According to the stability of the arch, the horizontal binding force at the arch foot should be less than or equal to the sum of the maximum friction force and cohesion at the arch foot, that is

[0302]

[0303] In the formula:

[0304] F bx is the horizontal binding force at the left arch foot B, with the unit of N;

[0305] F by is the vertical binding force at the left arch foot B, with the unit of N;

[0306] is the internal friction angle, with the unit of °;

[0307] c0 is the cohesion, with the unit of N.

[0308] In the critical state, the height h of arch BCD can be obtained BCD as:

[0309]

[0310] In the formula:

[0311] h BCD is the height of arch BCD, with the unit of m;

[0312] q is the load acting on the overlying strata, with the unit of N / m;

[0313] q1 is the load acting on the floor, with the unit of N / m;

[0314] Let \(L\) be the dip length of the working face, with the unit of \(m\).

[0315] Let \(\varphi\) be the internal friction angle, with the unit of °.

[0316] Let \(c_0\) be the cohesion, with the unit of \(N\).

[0317] Substituting Equation (31) into Equation (29), the reasonable arch axis equation of arch BCD is obtained as follows:

[0318] In the formula:

[0319] Let \(y(x)\) be the dependent variable of the morphological equation of the overlying rock arch structure, with the unit of \(m\).

[0320] Let \(x\) be the independent variable of the dip length of the working face, where the value range of \(x\) is \(0\leq x\leq L\), with the unit of \(m\); let \(q\) be the load acting on the overlying strata, with the unit of \(N / m\).

[0321] Let \(q_1\) be the load acting on the floor, with the unit of \(N / m\).

[0322] Let \(L\) be the dip length of the working face, with the unit of \(m\).

[0323] Let \(\varphi\) be the internal friction angle, with the unit of °.

[0324] Let \(c_0\) be the cohesion, with the unit of \(N\).

[0325] Step 4: According to the key stratum position \(H_1\) determined in Step 2 and the morphological equation of the overlying rock arch structure in Step 3, determine the dimension \(L_2\) when the subsidence of the key stratum is 0.

[0326] In this embodiment, according to the key stratum position \(H_1\) determined in Step 2 and the morphological equation of the overlying rock arch structure in Step 3, that is, Equation (32), let \(y(x)=H_1\), and the obtained \(x\) is \(L_2\).

[0327] Step 5: According to the subsidence curve equation of the overlying rock below the key stratum L1 section established in Step 1, the key stratum position \(H_1\) determined in Step 2, and the dimension \(L_2\) when the subsidence of the key stratum is 0 obtained in Step 4, take the thickness of the overlying rock unit in the upward direction, and perform integral calculation on the required grouting volume of the separated layer area below the key stratum to obtain the required grouting volume \(V_3\) of the left - hand part of the separated layer area below the key stratum for the thickness of the overlying rock unit in the upward direction.

[0328] In this embodiment, for the required grouting volume of the separated layer area below the key stratum, it can be solved by curve integration. The curve equation in this area is:

[0329] \(H_1 - w(x)=H_0s(x)\) (33)

[0330] In the formula:

[0331] H1 is the key layer horizon, with the unit of m;

[0332] w(x) is the dependent variable of the overlying strata subsidence curve equation below the L1 section of the key layer, with the unit of m;

[0333] x is the independent variable of the working face dip length, and the value range of x is L2 ≤ x ≤ L / 2, with the unit of m;

[0334] H0 is the separation height of the overlying strata below the key layer, with the unit of m;

[0335] s(x) is the overlying strata subsidence height coefficient when the abscissa is x below the L1 section of the key layer.

[0336] Integrating and solving Equation (33), the volume V3 of the grouting amount required for the left - hand half separation area below the key layer of the overlying strata unit thickness in the strike direction is:

[0337]

[0338] In the formula:

[0339] V3 is the volume of the grouting amount required for the left - hand half separation area below the key layer of the overlying strata unit thickness in the strike direction, with the unit of m 3 ;

[0340] z is the overlying strata unit thickness in the strike direction, with the unit of m;

[0341] L2 is the length of the overlying strata semi - arch area, with the unit of m;

[0342] L is the working face dip length, with the unit of m;

[0343] H1 is the key layer horizon, with the unit of m;

[0344] w(x) is the dependent variable of the overlying strata subsidence curve equation below the L1 section of the key layer, with the unit of m;

[0345] x is the independent variable of the working face dip length, and the value range of x is L2 ≤ x ≤ L / 2, with the unit of m;

[0346] H0 is the separation height of the overlying strata below the key layer, that is, the maximum subsidence amount of the key layer, with the unit of m;

[0347] B is an intermediate quantity.

[0348] Step 6: According to the volume V3 of the grouting amount required for the left - hand half separation area below the key layer of the overlying strata unit thickness obtained in Step 5, obtain the volume V of the grouting amount required for the separation area below the key layer of the overlying strata unit thickness in the strike direction.

[0349] In Step 6, due to the reason of left - right symmetry, the volume V of the grouting amount required for the separation area below the key layer of the overlying strata unit thickness in the strike direction is:

[0350] V = 2V3 (35)

[0351] Wherein:

[0352] V is the volume of grouting required for the separated layer area below the key stratum with the thickness of the overlying rock unit in the strike direction, and the unit is m 3 ;

[0353] V3 is the volume of grouting required for the left half of the separated layer area below the key stratum with the thickness of the overlying rock unit in the strike direction, and the unit is m 3 .

[0354] Specifically in this embodiment, taking the engineering geological conditions of a certain mine as the research background, the working face layout parameters are selected as shown in Table 1.

[0355] Table 1 Working face layout parameters

[0356]

[0357] (1) Solving for the L2 dimension when the subsidence of the key stratum is 0.

[0358] According to the determined distance H1 = 44.5m between the key stratum and the coal seam and substituting it into the reasonable arch axis equation (32), we can get:

[0359]

[0360] Substituting the basic parameters of the working face in Table 1 into the above formula, we can get:

[0361] y(x) = 44.5 = 1.598853x - 0.00533x 2

[0362] Further solving the equation, the caving boundaries below the semi-arch area of the overlying rock are respectively:

[0363] x1 = 31m, x2 = 269m

[0364] Since the dip length of the working face is 300m and due to symmetry, the caving boundary of the semi-arch area of the overlying rock corresponding to the left L2 section is x1 = 31m, that is, L2 = 31m.

[0365] (2) According to formula (34), the volume of grouting required for the left half of the separated layer area below the key stratum with the thickness of the overlying rock unit in the strike direction, V3, is:

[0366]

[0367] Solving the above equation, we can get:

[0368] V3 = 25.65m 3

[0369] According to symmetry, the volume V of the grouting amount required for the separated layer area under the key stratum of the overlying rock unit thickness in the strike direction, that is, the total grouting amount required for the separated layer area of the overlying rock corresponding to the L1 section when the overlying rock unit thickness is in the strike direction, is as follows:

[0370] V = 2V3 = 51.3 m 3 .

Claims

1. A method for calculating the grouting space of overburden separation layer in coal mines, characterized in that: The method comprises the following steps: Step 1: Establish the sinking curve equation of the overburden below the key layer L1 segment and determine the overburden collapse boundary; Step 2, determine the key layer H1; Step 3: Establish the morphological equation of the overburden arch structure and determine the arch morphology that tends to damage the overburden; Step 4, according to the key layer position H1 determined in step 2 and the morphological equation of the overburden arch structure in step 3, determine the size of L2 when the key layer subsidence is 0; Step 5: According to the sinking curve equation of the overburden below the key layer L1 segment established in step 1, the key layer position H1 determined in step 2, and the L2 size when the key layer sinking amount is 0 obtained in step 4, the overburden unit thickness on the strike is taken, and the required grouting volume of the delamination area below the key layer is integrated and solved to obtain the required grouting volume V3 of the left half of the delamination area below the key layer of the overburden unit thickness on the strike; The required grouting volume V3 of the left half of the separation layer below the critical layer of the overburden unit thickness is: Where: V3 is the grouting volume required for the left half of the separation zone below the key layer of the overburden unit thickness in the strike direction, in m 3 ; z is the thickness of the overburden unit on strike, in m; L2 is the length of the overburden semi-arch area, in meters; L is the inclined length of the working face, in m; H1 is the key layer position, in m; w(x) is the dependent variable of the overburden subsidence curve equation below the key layer L1 segment, unit: m; x is the independent variable of the inclined length of the working face, and the value range of x is L2≤x≤L / 2, and the unit is m; H0 is the separation height of the overburden below the key layer, that is, the maximum subsidence of the key layer, in m; B is the intermediate amount; Step six, according to the grouting volume V3 required for the abscission zone in the left half below the key layer of the overburden unit thickness on the strike obtained in step five, obtain the grouting volume V required for the abscission zone below the key layer of the overburden unit thickness on the strike.

2. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 1, characterized in that: In step 1, the equation of the sinking curve of the overburden below the key layer L1 is: Where: w(x) is the dependent variable of the overburden subsidence curve equation below the key layer L1 segment, unit: m; x is the independent variable of the inclined length of the working face, and the value range of x is L2≤x≤L / 2, and the unit is m; H1 is the key layer position, that is, the distance between the key layer and the coal seam, in m; H0 is the separation height of the overburden below the key layer, that is, the maximum subsidence of the key layer, in m; s(x) is the subsidence height coefficient of the overburden when the horizontal coordinate is x below the key layer L1 segment; erf() is the Gaussian error function; L2 is the length of the overburden semi-arch area, in meters; L is the inclined length of the working face, in meters.

3. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 1, characterized in that: In step 2, the specific solution process of the key layer H1 is: Step 201, determining the positions of all hard rock layers within the overburden; Step 202, according to the position of the hard rock layer obtained in step 201, determine the key layer existing in the rock layer through the rock beam breaking distance and the spatial layer position; Step 203 , determining the key layer position H1 according to step 202 .

4. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 3, characterized in that: In step 201, the positions of all hard rock layers in the overburden are determined as follows: Starting from the first rock layer, the layers are numbered one by one. If the relationship between the mth rock layer and the m+1th rock layer satisfies: Then the mth rock layer is the first hard rock layer; Where: γ m+1 is the bulk density of the m+1th rock layer, in N / m 3 ; E i is the elastic modulus of the i-th rock layer, i = 1, 2, …, m, in Pa; i is the layer number sequence of the rock layer; m is the number of layers in the rock formation; h i is the thickness of the i-th rock layer, i = 1, 2, ..., m, in m; E m+1 is the elastic modulus of the m+1th rock layer, in Pa; h m+1 is the thickness of the m+1th rock layer, in meters; γ i is the bulk density of the i-th rock layer, i = 1, 2, ..., m, in N / m 3 ; Starting from the first hard rock layer, the position of the second hard rock layer is determined in the same way as the first hard rock layer, until the top hard rock layer is determined, which is recorded as the nth hard rock layer.

5. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 3, characterized in that: In step 202, the key layer is determined in the following manner: If the k-th hard rock layer is the key layer, the breaking distance of the k-th hard rock layer is greater than the breaking distance of all the hard rock layers above the k-th hard rock layer, that is, it satisfies: L k >L k+1 Where: L k is the breaking distance of the kth hard rock layer, in m; L k+1 is the breaking distance of the k+1th hard rock layer, in m.

6. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 1, characterized in that: In step 3, the morphological equation of the overburden arch structure is: Where: y(x) is the dependent variable of the morphological equation of the overburden arch structure, unit: m; x is the independent variable of the inclined length of the working face, the value range of x is 0≤x≤L, and the unit is m; q is the load acting on the overlying rock strata, in N / m; q1 is the load acting on the bottom plate, in N / m; L is the inclined length of the working face, in m; is the internal friction angle, in degrees; c0 is the cohesion, unit is N.

7. The method for calculating the grouting space of overburden separation layer in coal mine according to claim 1, characterized in that: In step 6, the required grouting volume V of the delamination area below the critical layer of the overburden unit thickness is: V=2V3 Where: V is the volume of grouting required for the delamination area below the critical layer of the overburden unit thickness on the strike, in m 3 ; V3 is the grouting volume required for the left half of the separation zone below the key layer of the overburden unit thickness in the strike direction, in m 3 .

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