A method for constructing a multi-section combined mining horizontal pillar critical thickness optimization calculation model

Abstract

The application discloses a kind of construction methods of multi-section combined mining horizontal pillar critical thickness optimization calculation model, belong to mining process technical field.The method is analyzed by the mechanical state where horizontal pillar is located, based on Mindlin medium thick plate theory, under the boundary condition of four edges fixed support, under the action of multi-stress field of upper uniform load, self gravity, two-way horizontal stress, the bottom surface is in the state of open space, the mechanical model of horizontal pillar;Finite fourier integral transformation method is used to solve and analyze the mechanical model of horizontal pillar, the internal force distribution law of horizontal pillar is obtained, based on maximum tensile stress criterion, the critical thickness optimization model of horizontal pillar is constructed, the mechanical action of horizontal pillar is clarified, the critical thickness optimization model of horizontal pillar constructed has important theoretical research significance and higher popularization and application value for accurately determining the critical thickness of horizontal pillar in mine, ensure the safety of multi-section combined mining.

Description

Technical Field

[0001] This invention relates to a method for constructing an optimization calculation model for the critical thickness of horizontal pillars in multi-level joint mining, belonging to the field of metal mine mining technology. Background Technology

[0002] The geological conditions of the mining area and the occurrence state of the ore body have always been important factors affecting the selection of mining technology. When mining inclined or steeply inclined fractured ore bodies, due to the limitations of the ore body itself, mines generally choose the access backfill method or the layered backfill method for mining. This layered, continuous, small-scale, and frequent mining and backfilling process can stably control the exposed area of ​​the stope and reduce the risk of roof collapse and sidewall spalling, thus safely and efficiently mining ore bodies under such complex geological conditions. However, due to the limitation of the mining operation area, the production capacity of this access mining process often does not reach the expected level. In order to ensure sufficient resource production and improve economic benefits, mines often adopt the dual-level or multi-level combined mining mode.

[0003] like Figure 2 As shown, this multi-section joint mining mode involves setting up one or more mining sites in two or more intermediate sections, and simultaneously carrying out mining and backfilling operations. This mining operation method can greatly compensate for the insufficient production capacity of the in-pass backfilling mining process, ensure the production scale of the enterprise, and maximize the enterprise's revenue. However, during the multi-section joint mining process, the ore body between the upper and lower intermediate sections gradually thins due to mining and backfilling, forming horizontal pillars similar to plates. The instability of the horizontal pillars that may occur during continued mining can lead to through-collapse of the backfill body in multiple intermediate sections, causing serious consequences. In order to ensure the stability of the mining sites and prevent such accidents, mines often control the horizontal pillars of a reliable thickness to ensure the stability of multiple intermediate mining sites and provide safety guarantees for the mining of deeper ore bodies.

[0004] In analyzing horizontal pillars, the ideal state is that the pillar thickness is just enough to ensure its own stability, support the upper and middle sections of the filling material to prevent large-scale collapse of the filling material, and limit the deformation of the surrounding rock to ensure the stability of the stope. This thickness of the horizontal pillar is called the critical thickness. The stress distribution of the horizontal pillar in the stope is not very clear. Therefore, the control of the horizontal pillar by the mine often deviates too much from the critical thickness. If the control of the horizontal pillar thickness is too conservative, some recoverable mineral resources will be wasted in the stope. If mining continues and the horizontal pillar thickness is less than the critical thickness, it will cause penetrating damage to the horizontal pillar. Therefore, safe and reasonable control of the horizontal pillar thickness is of great significance for the efficient recovery of mineral resources and the safe operation of multi-section joint mining mode. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing an optimization calculation model for the critical thickness of horizontal pillars in multi-level joint mining, specifically including the following steps:

[0006] (1) Stress Analysis of Horizontal Pillars: Based on the mechanical environment in which the horizontal pillars are located, the stress situation of the horizontal pillars is analyzed, such as... Figure 3 , Figure 4 As shown, this invention considers the situation where the filling material at the bottom of the horizontal pillar cannot be connected to the roof due to its own consolidation and shrinkage, and the bottom surface of the horizontal pillar is completely in an unsupported state; it considers that the uniformly distributed stress overlying the horizontal pillar is the vertical stress of the filling material, and also considers the influence of the horizontal stress in the geostress around the horizontal pillar.

[0007] (2) Establish a mechanical model of horizontal pillar: Based on Mindlin's medium-thick plate theory, establish a mechanical model of horizontal pillar. Use the finite integral transformation method to solve the mechanical model of horizontal pillar and obtain the relationship between the internal force distribution of horizontal pillar and the size of horizontal pillar itself.

[0008] This invention considers that the horizontal pillar is firmly embedded in the surrounding rock; therefore, the boundary condition of the horizontal pillar is a four-sided fixed support, and its Mindlin medium-thick plate theory fixed support boundary condition is as follows:

[0009] x = 0, x = a;

[0010] y = 0, x = b;

[0011] In the formula: x—width direction of the horizontal pillar;

[0012] y—the length direction of the horizontal pillar;

[0013] a—width of the horizontal pillar;

[0014] b—Length of the horizontal pillar;

[0015] ω—the deflection of the horizontal pillar;

[0016] —The angle of rotation of the horizontal pillar within the xoz plane, perpendicular to the mid-surface straight line before deformation;

[0017] —The angle of the horizontal pillar in the yoz plane that is perpendicular to the mid-surface straight line before deformation;

[0018] The horizontal pillar is subjected to a uniformly distributed overburden load q0, the weight of the ore body itself g, and the horizontal stress N. x N y The horizontal stress is considered as an external force acting on the horizontal pillar, and it is assumed that the horizontal stress is uniformly distributed along the four boundaries.

[0019] The calculation of in-situ stress is performed using the self-weight of the overlying strata. The vertical stress at the burial depth of the horizontal pillar can then be calculated using the following formula:

[0020] σ H =γH (1)

[0021] In the formula: σ H γ is the vertical stress, MPa; γ is the rock unit weight, MN / m³. 3 H represents the height of the overlying strata above the horizontal pillar.

[0022] Here, we assume the rock is isotropic, the two horizontal stresses are equal in magnitude, and there is no horizontal strain. The horizontal stress on the horizontal pillar can then be calculated using the following formula:

[0023]

[0024] In the formula, N x N y σ represents the horizontal stress in the x and y directions, respectively. H ρ is the vertical stress, MPa; μ is Poisson's ratio.

[0025] Based on the effects of bidirectional horizontal stress, uniformly distributed overburden load, and the weight of the ore body on the horizontal pillar, the stress state of the pillar is analyzed using Mindlin's medium-thick plate theory. Figure 5 , Figure 6 As shown, the governing equations for the horizontal pillars can be written as follows:

[0026]

[0027] In the formula: S = κGh; κ is the shear correction factor, taken as 5 / 6; G is the shear modulus of the ore body, MPa; h is the thickness of the horizontal pillar, m; D is the bending stiffness. μ is Poisson's ratio; q0 is the uniformly distributed overburden load, MPa; considering the horizontal self-weight, since the z-direction coordinate is in [-h / 2, h / 2], the self-weight of the horizontal pillar can be set as follows: ρ is the density of the pillar, kg / m³ 3 g is the acceleration due to gravity, in m / s². 2 z represents the coordinate values ​​of the internal force distribution inside the horizontal pillar along the thickness h, and its range is [-h / 2, h / 2].

[0028] The governing equations for the bending problem of a horizontal pillar based on Mindlin's thick plate theory are a system of high-order partial differential equations, requiring different two-dimensional integral transformations to be performed sequentially on the three partial differential equations. The finite integral forward transformations for the three generalized displacements are as follows:

[0029]

[0030]

[0031]

[0032] Its inverse transformation is:

[0033]

[0034]

[0035]

[0036] In the formula The span and length of horizontal pillars a and b, where n is the coordinate after finite integral transformation.

[0037] The inverse transformation is performed on each term in the governing equations as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] By performing a finite integral transformation on each term in the control equation and substituting equations (10) to (13) into the first equation of the control equation, we can obtain:

[0051]

[0052] Substituting equations (14) to (17) into the second equation of the horizontal pillar control equation, we get:

[0053]

[0054] Substituting equations (18) to (21) into the third equation of the horizontal pillar control equation, we get:

[0055]

[0056] make After Fourier finite integral transform, it becomes q mn h is the thickness of the horizontal pillar, and z is the coordinate value of the internal force distribution inside the horizontal pillar along the thickness h.

[0057] q0 is the overburden load on the horizontal pillar.

[0058] q is the sum of the overburden load and the self-weight of the horizontal pillar.

[0059] The expression is as follows:

[0060]

[0061] Its inverse transformation is:

[0062]

[0063] q(x, y) is the expression for the load on the horizontal pillar in the original coordinate system.

[0064] q(m, n) is the expression for the load on the horizontal pillar after a two-dimensional finite integral transformation.

[0065] Partial boundary conditions. Substituting these terms into the equation and combining like terms, we get:

[0066]

[0067]

[0068]

[0069] The unknown constants in the above formula are the undetermined coefficients in the formula after the finite integral transformation, which can be expressed as:

[0070]

[0071]

[0072]

[0073]

[0074] According to the boundary conditions, it can be known that Then the undetermined coefficients of the four finite integral transformations, equations (30) to (33), can be rewritten as:

[0075]

[0076] From equation (34), we know that Dk1(n), Dk2(n), Dk3(n), and Dk4(n) are x=0, x=a, y=0, and y=b, respectively, where D is the bending stiffness. Multiplying the four undetermined coefficients by the bending stiffness D gives the finite integral transformation expression of the bending moment on these four boundaries.

[0077] The finite integral transformation expression for the bending moments on these four boundaries can be obtained by simply performing the inverse transformation:

[0078]

[0079] D is the bending stiffness, a is the width of the horizontal pillar, and b is the length of the horizontal pillar.

[0080] M x (0, y), M x (a, y)M y (x, 0)M y (x, b) represent the bending moments on the four boundaries, respectively. Substituting (30) to (33) into equations (27) to (29), we can transform them into:

[0081]

[0082]

[0083]

[0084] Written in matrix form:

[0085]

[0086] It can be expressed by the following formula:

[0087]

[0088] The expressions for the R matrix in the above formula are as follows:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] R 32 =R 23 (48)

[0097]

[0098] Then express ω using an expression containing undetermined coefficients. ss , They are respectively:

[0099]

[0100]

[0101]

[0102] ω after finite Fourier integral transform ss , This can be expressed by the above formula containing undetermined coefficients. Once the undetermined coefficients are determined, the solution can be obtained using the above formula. Let m = n = 0, then the angular displacements of the two finite integral transformations are respectively:

[0103]

[0104]

[0105] In the formula, Let represent the average rotation angle on the boundary after the finite integral transformation.

[0106] The three generalized displacements also need to satisfy the remaining unsatisfied boundary conditions. Substitute into the trigonometric series middle:

[0107]

[0108]

[0109] The above two equations can be transformed into:

[0110]

[0111]

[0112] Based on the orthogonality of trigonometric series, we can obtain:

[0113]

[0114]

[0115]

[0116]

[0117] In the formula

[0118] The four undetermined coefficients containing finite integrals can then be transformed into a system of linear equations, as shown below:

[0119]

[0120]

[0121]

[0122]

[0123] Equations (63) to (66) are for solving a system of linear equations with four undetermined coefficients. By solving for the undetermined coefficients and substituting them into equations (50) to (52), the three generalized displacements after the finite integral transformation are obtained. Then, by substituting them into equations (7) to (9), the inverse transformation is completed, and ω can be obtained. With these three generalized solutions, the deflection ω and bending moment at any point on the horizontal pillar can be obtained. Stress distribution

[0124] (3) Constructing an optimized calculation model for the critical thickness of horizontal pillars: Based on the stress components of the horizontal pillars obtained by the solution, the tensile stress at the bottom of the horizontal pillars is compared and analyzed with the tensile strength of the rock mass to determine the stability of the horizontal pillars and calculate the critical thickness of the horizontal pillars.

[0125] Horizontal pillars serve several mechanical functions, including supporting the upper and middle sections of the backfill and some of the collapsed material, preventing the collapse of multiple sections of the backfill and causing penetrating damage, limiting the deformation of the surrounding rock, and ensuring the stability of the mining area. Based on the mechanical functions of horizontal pillars, this section uses the maximum tensile stress criterion to analyze the stability of horizontal pillars. The main failure mode of horizontal pillars is tensile failure of the floor. Therefore, when the tensile stress of the floor does not exceed the tensile strength of the rock mass, the horizontal pillar can remain stable, thus allowing the calculation of the critical thickness of the horizontal pillar.

[0126] The relationship between stresses and internal moments in Mindlin's thick plate theory is as follows:

[0127]

[0128] In the formula: σx σ is the normal stress in the x-direction; y σ is the normal stress in the y-direction; z τ is the normal stress in the z-direction; xy τ is the tangential stress in the xy plane; xz τ is the tangential stress on the xz plane; yz The tangential stress is on the yz plane; M x M is the bending moment in the x-direction; y M is the bending moment in the y-direction; xy is the torque on the xy plane; z is the coordinate value in the thickness direction of the horizontal pillar, ranging from [-h / 2, h / 2]; h is the thickness of the horizontal pillar; Q x Q represents the transverse shear stress experienced by the horizontal pillar in the x-direction; y y represents the transverse shear stress on the horizontal pillar in the y-direction; q represents the overburden load.

[0129] This section analyzes the stability of the horizontal pillar bottom plate by taking the stress state. Therefore, when z = h / 2, we substitute it into equation (67) to obtain each stress and write it in the form of stress tensor.

[0130]

[0131] From equation (68), it can be seen that the stress component of the bottom plate of the horizontal pillar based on Mindlin's thick plate theory is σ. x σ y τ xy All other stress components are zero, with the largest stress component denoted as σ. max In a horizontal pillar, the first principal stress at the bottom plate is tensile stress. Therefore, when σ... max Not exceeding the ultimate tensile strength σ of the rock mass t At that time, the horizontal pillar can remain stable and not be destroyed, that is, it satisfies the following formula:

[0132] σ t ≥fσ max (69)

[0133] In the formula: f is the safety factor.

[0134] Here's a recap of the overall solution process: First, we solve the system of linear algebraic equations (63) to (66) consisting of four undetermined coefficients containing finite integrals. Substituting these equations into equations (50) to (52), we obtain the three generalized shifts after the finite integral transformation. Then, substituting these into equations (7) to (9) completes the inverse transformation, allowing us to solve for ω, . The expressions for the three generalized displacements are important to note. and The two rotation functions are mixed integral transformations. If the bending moment on the boundary is to be solved, it can be solved by equation (35). During the solution process, it was found that the maximum bending moment of the horizontal pillar appears at the boundary. Therefore, the maximum stress component appears at the boundary. The bottom surface of the horizontal pillar is in a free state. As long as the tensile stress on the bottom surface is less than the tensile strength of the rock mass, it can be proven that the horizontal pillar is in a stable state. Since the overall solution process is relatively complicated, in order to facilitate the calculation of the critical thickness of the horizontal pillar, it is only necessary to calculate the maximum bending moment at the bottom boundary to obtain the maximum tensile stress at the bottom surface. The expression for the maximum bending moment is:

[0135]

[0136] Therefore, the solution process of the optimized calculation model for the critical thickness of the horizontal pillar is as follows: First, solve the system of linear algebraic equations (63) to (66) consisting of four undetermined coefficients with finite integrals. Substitute these equations into equation (70) to obtain the bending moment on the boundary. Substitute the obtained boundary bending moment into equation (67) and take z = h / 2 to obtain the maximum tensile stress at the bottom of the horizontal pillar. By comparing and analyzing this stress with the tensile strength of the rock mass, the critical thickness of the horizontal pillar can be determined. The relationship between the change in the size of the horizontal pillar and its critical thickness is as follows: Figure 7 As shown.

[0137] The beneficial effects of this invention are:

[0138] (1) The method described in this invention takes into full account the mechanical environment of the horizontal pillar and can provide a theoretical basis for reasonably determining the critical thickness of the horizontal pillar.

[0139] (2) The medium-thick plate theory used in this invention takes into account the influence of transverse shear deformation, and its calculation results are more reliable than those of the thin plate theory. The established horizontal pillar optimization calculation model is relatively simple and easy for mine workers to calculate quickly.

[0140] (3) The critical thickness of the horizontal pillar calculated by the method described in this invention is more in line with reality, and can maximize the recovery of mineral resources while ensuring the safety of multi-section joint mining. Attached Figure Description

[0141] Figure 1 This is a process flow diagram of the present invention;

[0142] Figure 2 Schematic diagram of the formation process of horizontal pillars in multi-level joint mining;

[0143] Figure 3 Schematic diagram of the stress environment of a horizontal pillar;

[0144] Figure 4 The consolidation and shrinkage of the filling material at the bottom of the horizontal pillar caused it to fail to connect to the roof.

[0145] Figure 5 3D stress diagram of a horizontal pillar;

[0146] Figure 6 A schematic diagram of two-dimensional planar mechanical equilibrium of a horizontal pillar;

[0147] Figure 7 Relationship between the size variation of a horizontal pillar and its critical thickness;

[0148] Figure 8 Diagram of the upward horizontal layered approach filling method for mining;

[0149] Figure 9 Image showing the results of vertical stress monitoring of the filling material. Detailed Implementation

[0150] The present invention will be further described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited to the content described.

[0151] Example 1

[0152] The method for constructing and applying the critical thickness optimization calculation model for horizontal pillars in multi-level joint mining as described in this invention is as follows:

[0153] (1) Background Introduction

[0154] In a lead-zinc mine in Yunnan Province, the dip angle of orebody No. 1 is generally between 45° and 55°. The maximum true thickness of the orebody is 26.69m, and the average thickness is 7.89m. The surrounding rock of orebody No. 1 is mostly strong to relatively strong, with a few being moderately strong. The rock quality (RQD value) is mostly poor, and the rock mass is mostly fractured. In some local rock sections, such as tectonic fracture zones, densely jointed and fractured zones, and foliated zones, the rock mass quality is poor, and the rock mass integrity is poor. The tensile strength of the rock mass is 1.17MPa. Based on the mining technology conditions, the mining method for orebody No. 1 is the mechanized upward-entry filling method. The intermediate section is 60m high, the bottom pillar is 8m high, the sub-section is 12m high, and the layer height is 3m. The access road is arranged along the strike. A ramp is excavated in the footwall of the ore body as an access passage for equipment between intermediate sections. Sectional connecting roads and roadways are excavated every 12m (vertical height) from the ramp. Layered connecting roads are then excavated from the section roadways to the ore body, and layered roadways are excavated within the ore body to prepare for the excavation approach. Loading chambers are excavated along the vein roadways from the footwall of the ore body, and ore passes are excavated upwards to the upper-middle section. A stope return air shaft is excavated near the footwall within the ore body to the upper-middle section. A bottom-up, layered approach mining method is adopted within the ore block. Mining approaches are arranged from the layered roadways from the footwall to the hanging wall of the ore body, with a cross-sectional dimension of 3×3m. 2 Mining methods such as Figure 8 As shown.

[0155] Due to the limited production capacity of the inlet-fill method, the mine adopted a multi-level joint mining mode, which resulted in the formation of multiple horizontal pillars. In the 1274 level, a 25m thick horizontal pillar was formed at the 1319-1344 level. The bottom of the horizontal pillar has separated from the horizontal pillar due to the settlement and consolidation of the filling material itself. As the horizontal pillar loses its bottom support, the stress continues to concentrate during the mining process. If the stress distribution of the horizontal pillar cannot be specifically described, there is a risk of instability and failure of the horizontal pillar as mining progresses.

[0156] (2) Establishing a mechanical model of horizontal pillars

[0157] The horizontal pillar formed by the multi-section joint mining has an average dip angle of 45°, a length of 105m, and a width of 42m. The 1319-1344 horizontal pillar is an inclined ore body. As mining progresses, the upper and lower ore bodies are mined simultaneously, increasing the damage to the horizontal pillar. According to stress monitoring results, the vertical stress of the 1344-11# access road filling body is 0.7MPa. (Stress monitoring data is as follows...) Figure 9 As shown, the 1319-1344 horizontal pillar is located in the middle section of 1274, with a burial depth of approximately 1000m. Calculations show that the horizontal stress is approximately 10.65MPa. Based on this patent, a mechanical model of the horizontal pillar under the dimensional conditions of the 1319-1344 horizontal pillar is established.

[0158] (3) Calculation of critical thickness of horizontal pillar

[0159] First, the system of linear algebraic equations consisting of four undetermined coefficients with finite integrals, namely equations (63) to (66), is solved. The bending moment on the boundary is obtained by substituting it into equation (70). The obtained boundary bending moment is then substituted into equation (67). Simultaneously, z = h / 2 is taken, and the maximum tensile stress at the bottom of the horizontal pillar can be obtained. The tensile strength of the rock mass is 1.17 MPa. By comparing and analyzing the calculation results with the tensile strength of the rock mass, the critical thickness of the horizontal pillar can be determined. The critical thickness of the 1319-1344 horizontal pillars under different safety factors is determined through the above calculation process, as shown in the table below.

[0160] Critical thickness of horizontal pillars 1319-1344

[0161]

[0162] (4) Production Practice

[0163] According to the original mining technology, the critical thickness of the 1319-1344 horizontal pillar is 21.27m. After mining one layer height (3m) of the 1319-1344 horizontal pillar, the horizontal pillar remains stable, but some areas show rapid development of rock mass fissures. If further mining is carried out, the horizontal pillar may become unstable and fail. Therefore, it can be determined that the horizontal pillar critical thickness optimization calculation model established by this invention can clarify the stress state of the horizontal mine and maximize the recovery of mineral resources while ensuring safety.

Claims

1. A method for constructing an optimization calculation model for the critical thickness of horizontal pillars in multi-level joint mining, characterized in that, Specifically, the following steps are included: (1) Stress analysis of horizontal pillars: Based on the mechanical environment in which the horizontal pillars are located, the stress situation of the horizontal pillars is analyzed; (2) Constructing a mechanical model of a horizontal pillar: Based on Mindlin's medium-thick plate theory, a mechanical model of a horizontal pillar is established. The finite integral transformation method is used to solve the mechanical model of the horizontal pillar to obtain the maximum bending moment of the bottom boundary of the horizontal pillar. (3) Constructing an optimization calculation model for the critical thickness of a horizontal pillar: Based on the maximum bending moment of the bottom boundary of the horizontal pillar obtained by the solution, the maximum tensile stress at the bottom of the horizontal pillar is obtained. The maximum tensile stress at the bottom of the horizontal pillar is compared and analyzed with the tensile strength of the rock mass to determine the stability of the horizontal pillar and calculate the critical thickness of the horizontal pillar. In step (1), the situation where the filling material at the bottom of the horizontal pillar cannot be connected to the roof due to its own consolidation and shrinkage is considered, and the bottom surface of the horizontal pillar is completely in an open state; the uniformly distributed stress on the horizontal pillar is considered to be the vertical stress of the filling material, and the influence of the horizontal stress in the geostress around the horizontal pillar is also considered. In step (2), it is considered that the horizontal pillar is firmly embedded with the surrounding rock. Therefore, the boundary condition of the horizontal pillar is four-sided fixed support, and its Mindlin medium-thick plate theory fixed support boundary condition is: ； ； In the formula: x—width direction of the horizontal pillar; y—the length direction of the horizontal pillar; a—width of the horizontal pillar; b—Length of the horizontal pillar; —The deflection of a horizontal pillar; —The angle of rotation of the horizontal pillar within the xoz plane, perpendicular to the mid-surface straight line before deformation; —The angle of the horizontal pillar in the yoz plane that is perpendicular to the mid-surface straight line before deformation; The expression for the maximum bending moment at the bottom boundary of the horizontal pillar mentioned in step (2) is as follows: ； Where: M x (0, y) is the bending moment at the boundary where x=0; M x (a, y) represents the bending moment at the boundary where x = a; M y (x,0) is the bending moment at the boundary where y=0; M y (x,b) represents the bending moment at the boundary y=b; k1(n), k2(n), k3(m), and k4(m) are four undetermined coefficients; D represents the bending stiffness; a represents the width of the horizontal pillar; and b represents the length of the horizontal pillar. The stress component expression for the maximum tensile stress at the bottom surface of the horizontal pillar in step (3) is: ； In the formula: The normal stress is in the x-direction; The normal stress is in the y-direction; The stress is normal in the z-direction; The stress is the tangential stress in the xy plane; The stress is the tangential stress in the xz plane; The stress is the tangential stress in the yz plane; The bending moment is in the x-direction; The bending moment is in the y-direction; Let x be the torque on the xy plane; z is the coordinate value in the thickness direction of the horizontal pillar, and its range is... h represents the thickness of the horizontal pillar. The transverse shear stress experienced by the horizontal pillar in the x-direction; The transverse shear stress experienced by the horizontal pillar in the y-direction; This refers to the overlying load.

2. The method for constructing the critical thickness optimization calculation model for horizontal pillars in multi-section joint mining according to claim 1, characterized in that: The stability of the horizontal pillar is determined by comparing the tensile stress at the bottom of the pillar with the tensile strength of the rock mass, as follows: (1) When the tensile stress at the bottom of the horizontal pillar is greater than the tensile strength of the rock mass, the horizontal pillar will become unstable; (2) When the tensile stress at the bottom of the horizontal pillar is less than the tensile strength of the rock mass, the horizontal pillar is stable; (3) When the tensile stress at the bottom of the horizontal pillar equals the tensile strength of the rock mass, it is in a critical state, and the thickness at this time is the critical thickness.

3. The method for constructing the critical thickness optimization calculation model for horizontal pillars in multi-section joint mining according to claim 2, characterized in that: The specific formula for calculating the critical thickness of a horizontal pillar is as follows: When t =fσ max when ; In the formula, Ultimate tensile strength, For the largest stress component, This is for the safety factor.

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