A method for calculating the failure depth of a stope floor considering the combined action of static and dynamic loads

Abstract

The application discloses a kind of mining floor failure depth calculation methods considering dynamic and static load combined action, it is related to mining floor failure depth calculation technical field, comprising: (1) considering the dynamic load generated by roof weighting and support pressure distribution law, constructs mining floor dynamic and static load combined action mechanics model;(2) define static load stress parameters, obtain each static load stress component of mining floor caused by support pressure static load;(3) define dynamic load stress parameters and floor rock mass mechanics parameters, calculate each dynamic load stress component of floor caused by dynamic load;(4) the stress component at any point of mining floor under dynamic and static load combined action is obtained by stress superposition;(5) according to Mohr-Coulomb criterion, the floor cumulative maximum failure depth in the process of dynamic load action is calculated.The application embodiment comprehensively considers the influence of dynamic load and support pressure static load combined action on mining floor failure depth when roof weighting, and the maximum failure depth of floor obtained by calculation is more in line with actual situation.

Description

Technical Field

[0001] This invention relates to the field of research on the risk assessment of water inrush in the mining floor, specifically a method for calculating the failure depth of the mining floor considering the combined effects of dynamic and static loads. Background Technology

[0002] The high water pressure environment faced in deep mining exacerbates the threat of water inrush to the mining floor, and even slight negligence can lead to major disasters. Water inrush at the mining floor has become one of the significant threats to deep coal resource mining in my country. Accurate calculation of the stress distribution and failure characteristics of the mining floor is a crucial foundation for evaluating safe mining operations in confined aquifers.

[0003] Numerous examples of mine water inrush accidents show that most floor water inrushes occur during the initial and periodic pressure periods of the working face. From a mechanical perspective, this is because, on the one hand, the supporting pressure is strongest during the initial and periodic pressure periods, resulting in greater floor damage depth; on the other hand, the collapse and fracture of the roof strata create a brief but intense dynamic load disturbance, causing the floor to bear a large dynamic load, further exacerbating the damage to the floor strata and increasing the floor damage depth.

[0004] Previous theoretical studies on the depth of floor failure only considered the influence of static load on the support pressure in the mining area. This is obviously inconsistent with the statistical laws of actual water inrush accidents in the mining area floor. The destructive effect of dynamic load disturbance on the mining area floor cannot be ignored. Therefore, this application comprehensively considers the combined effects of static load on the support pressure and dynamic load on roof fracture, and provides a theoretical calculation method for the depth of floor failure in the mining area under the combined action of static and dynamic loads, providing a theoretical basis for the risk assessment of water inrush in the coal seam floor. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method for calculating the maximum failure depth of the stope floor considering the combined effects of dynamic loads from the roof and static loads from the supporting pressure, thus resolving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] This invention provides a method for calculating the maximum failure depth of the floor slab in a deep mining area under combined dynamic and static loads, comprising the following steps:

[0008] (1) Based on the distribution law of dynamic stress generated by roof rock mass fracture and mining support pressure, a mechanical model of dynamic and static combined action of mining floor is constructed:

[0009] According to the theory of mine pressure, after coal seam mining, the supporting pressure of the stope floor will change due to the influence of overburden movement. The load borne by the stope floor during the roof pressure period is shown in the figure. During the initial and periodic roof pressure of the working face, there will be obvious dynamic load disturbance. Therefore, the load borne by the stope floor mainly includes: ① after the coal mining face is moved, the uncollapsed rock strata above the stope transmit the supporting pressure static load to the coal seam floor through the surrounding rock of the stope in the form of "roof pressure"; ② and the dynamic load disturbance caused by the fracture of the roof rock strata during the periodic roof pressure.

[0010] Therefore, based on the distribution characteristics of the support pressure, and to simplify the calculation, the support pressure is linearized, and a coordinate system is established with the working face position as the origin, the working face direction as the x-axis, and the z-axis direction vertically downwards. The simplified support pressure distribution model of the stope is shown in the attached figure. Figure 3 As shown; where: a is the stress reduction zone, a = 0 in the initial pressure stage; b and c are the stress increase zones; d is the dynamic load range; γ is the average unit weight of the overlying strata on the floor; H is the burial depth of the coal seam floor; K1γH is the load of the caving zone in the goaf, K1 = 0 for the initial pressure; K2γH is the advance support pressure of the working face.

[0011] (2) Define the static load stress parameters, and calculate the static load stress components of the stope floor caused by the static load of the support pressure based on the stress solution at any point when the semi-plane is subjected to a vertically distributed force:

[0012] The static stress field generated by the supporting pressure q(x) can be obtained from the stress solution at any point when the half-plane is subjected to a vertically distributed force. Taking a small length dε, the solution formula for the static stress field of the base plate is as follows:

[0013]

[0014] (3) Define the dynamic load stress parameters and the rock mass mechanical parameters of the bottom plate, and calculate the dynamic load stress components of the bottom plate caused by the dynamic load;

[0015] Optionally, in step (3), the dynamic stress can be expressed as:

[0016]

[0017] In the formula: σ0 is the dynamic load amplitude; ω is the dynamic load frequency; t1 is the dynamic load duration; according to mine microseismic monitoring, the dynamic load intensity in the mine is generally 1.5MPa to 15MPa, the frequency is generally tens to 100Hz, and the duration is generally 0.01 to 0.1s.

[0018] According to the basic principles of elastic dynamics, neglecting body forces, the equations of motion and physical equations of an elastic medium can be expressed as follows:

[0019]

[0020]

[0021] In the formula: u and w are the displacements in the x and z directions, respectively; ρ is the density of the bottom rock layer; λ=μE / [(1+μ)(1-2μ)], G=E / 2(1+μ), where E is the elastic modulus and μ is Poisson's ratio.

[0022] Combining equations (3) and (4), we can obtain:

[0023]

[0024] Applying a Laplace transform to time t in equation (5), the Laplace transform and its inverse transform are defined as follows:

[0025]

[0026] In the formula: s is the Laplace transform parameter.

[0027] Simultaneously, when the dynamic load stress is transferred to the stope floor, the initial state of the floor is static, that is:

[0028]

[0029] Therefore, equation (5) can be transformed by Laplace transformation into:

[0030]

[0031] To solve equation (8), a Fourier transform is performed on x. The Fourier transform and its inverse are defined as follows:

[0032]

[0033] In the formula: ξ is the Fourier transform parameter with respect to x.

[0034] Equation (8), after Fourier transformation and written in matrix form, is as follows:

[0035]

[0036] Let the state components Equation (10) can then be transformed into the following system of differential equations:

[0037]

[0038] According to matrix calculus, the solution to equation (9) can be expressed as:

[0039]

[0040] In the formula: Let G(ρ,E,μ,ξ,z,s) = exp[zA(ρ,E,μ,ξ,s)], then equation (12) can be expressed in matrix form:

[0041]

[0042] In the formula: G 11 =G 44 = (1+Bξ)ch(Mz)-Bξch(Nz),

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] The relationship between any depth h of the stope floor and the surface state vector is as follows:

[0051]

[0052] The boundary conditions at the top of the base plate (z = 0) and at infinity (z = ∞) can be expressed as:

[0053]

[0054] After performing Laplace transform on t and Fourier transform on x in equation (15), and substituting it into equation (14), the various dynamic stresses of the working surface bottom plate can be obtained.

[0055] (4) The stress components at any point on the bottom plate of the mining area under the combined action of static and dynamic loads are obtained by stress superposition.

[0056] The stress components of the bottom plate of the mining area are composed of the additional static stress caused by the support pressure and the additional dynamic stress caused by the dynamic load from the roof.

[0057] (5) Based on the stress component solution at any point on the base plate, and combined with the Mohr-Coulomb criterion, the cumulative maximum failure depth of the base plate during the dynamic loading process is calculated:

[0058] Furthermore, in step (5), the yield criterion for determining the maximum failure depth of the stope floor is selected as the shear failure criterion. Therefore, according to the Mohr-Coulomb yield failure criterion, the stress state of the stope floor rock strata when shear failure occurs satisfies:

[0059]

[0060] In the formula: c and c represent the internal friction angle and cohesion of the bottom rock strata, respectively, which can be obtained by laboratory testing.

[0061] The calculated vertical stress σ at any point on the base plate z Horizontal stress σ x and shear stress τ xz Substituting into equation (16) yields the maximum damage depth of the base plate.

[0062] The beneficial effects of this invention compared to existing technologies are as follows: By statistically analyzing the spatiotemporal distribution patterns of mine water inrush accidents, this invention discovers that floor water inrush accidents mostly occur during the initial and periodic pressure periods of the working face. Based on comprehensively considering the combined dynamic and static loads on the floor during roof pressure, this invention constructs a method for determining the maximum damage depth of the stope floor under roof pressure. This invention can accurately calculate the damage depth of the stope floor that better reflects real-world conditions, providing effective theoretical guidance for safe mining under pressure and the prevention and control of coal mine floor water inrush. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the mechanical model of the working face floor under the combined dynamic and static loads, which is used to calculate the failure depth of the floor considering the combined dynamic and static loads.

[0064] Figure 2 A schematic diagram of the initial stress stage of dynamic and static loads on the stope floor, which is used to calculate the failure depth of the stope floor considering the combined effects of dynamic and static loads.

[0065] Figure 3 A schematic diagram of the dynamic and static load stress cycle stage of the stope floor plate under the calculation method for the failure depth of the stope floor plate considering the combined action of dynamic and static loads.

[0066] Figure 4 A schematic diagram of the dynamic load stress time history curve for the calculation method of the failure depth of the stope floor considering the combined effects of dynamic and static loads;

[0067] Figure 5 This method for calculating the failure depth of the stope floor considering the combined effects of static and dynamic loads involves calculating the vertical stress σ of the stope floor. z Cloud map;

[0068] Figure 6This method for calculating the failure depth of the stope floor considering the combined effects of static and dynamic loads involves calculating the shear stress τ of the stope floor. xz Cloud map;

[0069] Figure 7 This diagram illustrates the cumulative failure depth of the floor during dynamic loading, which is part of the method for calculating the failure depth of the stope floor considering the combined effects of static and dynamic loads.

[0070] Figure 8 A schematic diagram of the borehole layout for measuring the depth of damage to the floor slab in the mining area;

[0071] Figure 9 A schematic diagram of the borehole layout for measuring the depth of damage to the floor of the mining area.

[0072] Figure 10 Schematic diagram of the results of borehole 1 for observing water leakage at the depth of damage to the bottom plate of the mining area;

[0073] Figure 11 Schematic diagram of the results of borehole 2 for observing water leakage at the depth of damage to the bottom plate of the mining area;

[0074] Figure 12 A schematic diagram of the measured water leakage from borehole 3, which shows the depth of damage to the bottom plate of the mining area. Detailed Implementation

[0075] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0076] This invention provides a technical solution: a method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads, comprising the following steps:

[0077] (1) As Figures 1 to 2 As shown, according to the mine pressure theory, after coal seam mining, the supporting pressure of the stope floor will change due to the influence of overburden movement. The load borne by the stope floor during roof pressure is shown. During the initial and periodic roof pressure of the working face, there will be significant dynamic load disturbances. Therefore, the load borne by the stope floor mainly includes: the static load of the uncollapsed upper rock strata transmitting supporting pressure to the coal seam floor in the form of "roof pressure" after the coal face is mined; and the dynamic load disturbance caused by roof strata fracture during periodic roof pressure. Considering the supporting pressure and dynamic load distribution law, a mechanical model of the combined dynamic and static load action of the stope floor is constructed, as shown below. Figure 3 As shown;

[0078] (2) Based on the distribution characteristics of the support pressure, in order to simplify the calculation, the support pressure is linearized, and a coordinate system is established with the working face position as the origin, the working face direction as the x-axis direction, and the z-axis direction vertically downward. The simplified support pressure distribution model of the mining area is as follows: Figure 3 As shown; where: a is the stress reduction zone, a = 0 in the initial pressure stage; b and c are the stress increase zones; d is the dynamic load range; γ is the average unit weight of the overlying strata on the floor; H is the burial depth of the coal seam floor; K1γH is the load of the caving zone in the goaf, K1 = 0 for the initial pressure; K2γH is the advance support pressure of the working face; the above parameters can be obtained by actual measurement. Combining the measured static load stress parameters, the static load stress components of the mining floor caused by the static load of the support pressure are obtained from the stress solution at any point when the half-plane is subjected to vertical distributed force; the static load stress field generated by the support pressure q(x) can be obtained from the stress solution at any point when the half-plane is subjected to vertical distributed force. Taking a small length dε, the solution formula for the static load stress field of the floor is:

[0079]

[0080] (3) Define the dynamic stress parameter. The dynamic stress can be expressed as:

[0081]

[0082] In the formula: σ0 is the dynamic load amplitude; ω is the dynamic load frequency; t1 is the dynamic load duration; according to mine microseismic monitoring, the dynamic load intensity in the mine is generally 1.5MPa to 15MPa, the frequency is generally tens to 100Hz, and the duration is generally 0.01 to 0.1s; the above parameters can be obtained by actual measurement.

[0083] Calculate the dynamic stress components of the base plate caused by the dynamic load;

[0084] According to the basic principles of elastic dynamics, neglecting body forces, the equations of motion and physical equations of an elastic medium can be expressed as follows:

[0085]

[0086]

[0087] In the formula: u and w are the displacements in the x and z directions, respectively; ρ is the density of the bottom rock layer; λ=μE / [(1+μ)(1-2μ)], G=E / 2(1+μ), where E is the elastic modulus and μ is Poisson's ratio.

[0088] Combining equations (3) and (4), we can obtain:

[0089]

[0090] Applying a Laplace transform to time t in equation (5), the Laplace transform and its inverse transform are defined as follows:

[0091]

[0092] In the formula: s is the Laplace transform parameter.

[0093] Simultaneously, when the dynamic load stress is transferred to the stope floor, the initial state of the floor is static, that is:

[0094]

[0095] Therefore, equation (5) can be transformed by Laplace transformation into:

[0096]

[0097] To solve equation (8), a Fourier transform is performed on x. The Fourier transform and its inverse are defined as follows:

[0098]

[0099] In the formula: ξ is the Fourier transform parameter with respect to x.

[0100] Equation (8), after Fourier transformation and written in matrix form, is as follows:

[0101]

[0102] Let the state components Equation (10) can then be transformed into the following system of differential equations:

[0103]

[0104] According to matrix calculus, the solution to equation (9) can be expressed as:

[0105]

[0106] In the formula: This represents the state vector at z = 0 after Laplace and Fourier transformations.

[0107] Let G(ρ,E,μ,ξ,z,s)=exp[zA(ρ,E,μ,ξ,s)], then equation (12) can be expressed in matrix form:

[0108]

[0109] In the formula: G 11 =G 44 = (1+Bξ)ch(Mz)-Bξch(Nz),

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] The relationship between any depth h of the stope floor and the surface state vector is as follows:

[0118]

[0119] The boundary conditions at the top of the base plate (z = 0) and at infinity (z = ∞) can be expressed as:

[0120]

[0121] After performing Laplace transform on t and Fourier transform on x in equation (15), and substituting it into equation (14), the dynamic stress fields of the mining floor can be obtained.

[0122] (4) The stress components of the mining floor under the combined action of dynamic and static loads are obtained by stress superposition.

[0123] (5) Since the maximum failure depth of the bottom plate is generally shear failure, based on the solution results of each stress component and combined with the Mohr-Coulomb yield failure criterion, the stress state of the bottom plate rock strata in the stope when shear failure occurs satisfies:

[0124]

[0125] in: ω is the internal friction angle of the base rock strata; c is the cohesion, which can be obtained by laboratory testing.

[0126] The calculated vertical stress σ at any point on the base plate z Horizontal stress σ x and shear stress τ xz Substituting into equation (16) yields the maximum damage depth of the base plate.

[0127] The following detailed description is provided in conjunction with specific examples:

[0128] This embodiment uses the 8031 ​​working face of a coal mine to illustrate the invention and verify the correctness of the calculation method for the failure depth of the stope floor under combined dynamic and static loads. This working face mines Coal Mine No. 8, with an average coal seam thickness of 3.5m and an elevation of -465 to -495m. The initial pressure step is 33-40m, and the periodic caving step is 20-30m. The mining area has experienced multiple floor water inrush accidents during the initial and periodic roof pressure periods. Based on actual mining data and field observations, the floor strata parameters are taken as averages: elastic modulus E = 16.6 GPa, Poisson's ratio μ = 0.25, and density ρ = 2650 kg / m³. 3 internal friction angle The cohesion c = 2.4 MPa. During the initial pressure on the working face, the length of the stress-increased zone in the advanced support was b = 10 m, c = 25 m, γH = 10 MPa, and the stress concentration factor K2 = 2.1. Simultaneously, based on microseismic monitoring during the working face mining, a seismic event with an energy of 4 × 10⁻⁶ MPa occurred approximately 10 m ahead of the working face within the immediate roof during the initial pressure. 4 For a vibration event of the J magnitude, considering the attenuation law of dynamic load transmission, the estimated parameters of the dynamic load q(t) acting on the base plate are: σ0=8MPa, ω=20Hz, t1=0.05s, the calculation time of the dynamic load is 0.1s, and the range of action is d=20m.

[0129] Based on the above parameters, the vertical stress, horizontal stress, and shear stress of the stope floor plate under static and dynamic loads were solved using MATLAB programming. Then, by vector superposition, the changes of the three stress components at each location of the stope floor plate with the dynamic loading time were obtained.

[0130] like Figure 5 As shown, the vertical stress response process of the working face floor plate under combined dynamic and static loads is as follows: Before the dynamic load is applied (t = 0 s), the working face floor plate is only subjected to the static load of the working face support pressure. Due to the support pressure, the vertical stress field of the floor plate is non-uniformly distributed. The floor plate under the goaf is in the stress relief zone, while the floor plate under the unmined area is in the stress concentration zone, with the maximum vertical stress σ... z The stress reached 20.6 MPa. Located approximately 10 m from the working face, the unmined area floor plate had a vertical stress concentration zone with an influence depth of 48 m. Between 0.01 s and 0.05 s, the dynamic stress propagated deeper into the floor plate, superimposing with the static stress generated by the support pressure. This significantly impacted the stress field distribution of the mining floor plate, further exacerbating the non-uniformity of the floor plate stress field. The overall stress level of the floor plate within the dynamic load range increased markedly, and the degree and extent of stress concentration in the unmined area floor plate continued to expand. Specifically, the vertical stress σ... zThe peak pressure reached 27.4 MPa, with a maximum influence depth of approximately 64 m, an increase of about 33.3% compared to the static load. At t = 0.06 s, the dynamic load stress was completed, but the stress generated by the dynamic load continued to affect the floor plate, causing the floor plate stress field to be in a state of dynamic change. The stress concentration and stress relief degree of the floor plate were also in a state of dynamic change. At t = 0.1 s, due to the attenuation effect, the dynamic response of the stope floor plate was basically completed, and the floor plate stress field at this time was basically the same as before the dynamic load.

[0131] like Figure 6 As shown, under static load of the supporting pressure (t=0s), a shear stress concentration zone is formed in the unmined area floor plate, with a maximum shear stress of 5.2MPa. The positive and negative shear stresses are distributed in an antisymmetric manner. It can be inferred that the floor plate at the location with higher shear stress is prone to shear failure, forming a water-conducting channel in the floor plate. The dynamic load stress is transferred to the floor plate, which has a significant impact on the shear stress distribution of the floor plate. The maximum shear stress increases to 7.1MPa, which is about 36.5% higher than that under static load. The horizontal influence range and influence depth are further expanded.

[0132] like Figure 7 As shown, the calculated maximum failure depth of the stope floor is 11.5m at t=0s due to static load of the support pressure. As the dynamic stress is transmitted in the floor, the cumulative failure depth gradually increases. Before 0.025s, the dynamic load is in the compressive stress stage, the stress concentration level of the floor increases, and the cumulative failure depth increases rapidly. After 0.025s, the dynamic stress turns into tensile stress, but due to the transmission effect of the dynamic stress, the cumulative failure depth continues to increase. At 0.05s, the dynamic load is completed, and the maximum failure depth of the floor reaches 16.7m. Finally, the maximum failure depth of the floor reaches 16.9m, which is 5.4m higher than that under static load of the support pressure, an increase of 46.9%.

[0133] The above-mentioned calculation method for the maximum failure depth of the stope floor considering the combined effects of static and dynamic loads was applied to an engineering example. The calculation showed that when the working section reached the initial pressure position, considering only the static load of the support pressure, the maximum failure depth of the floor was 11.5m; when considering the influence of the dynamic load disturbance from the roof pressure, the maximum failure depth of the floor could reach 16.9m. For example... Figures 8-12 As shown, the calculation results were compared with the actual measurements from the on-site borehole water injection test. The on-site measurements revealed that the maximum failure depth of the floor slab before the initial pressure was 11.7m, and the maximum failure depth after the initial pressure was 18.7m. The calculation results of the above example show that the calculated failure depth of the stope floor slab under the dynamic load of roof fracture during the initial pressure does not match the actual situation on site. However, the maximum failure depth of the floor slab obtained using this example has a smaller error compared with the measured results. Therefore, it can be seen that the present invention is scientifically reliable, has high calculation accuracy, and fully meets the actual needs of on-site engineering.

[0134] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads, comprising the following steps: (1) Based on the dynamic stress generated by the fracture of the roof rock mass and the distribution law of the support pressure in the mining area, a mechanical model of the combined dynamic and static loads of the mining floor is constructed; (2) Define the static load stress parameters and calculate the static load stress components of the mining floor caused by the static load of the support pressure based on the stress solution at any point when the half-plane is subjected to vertical distributed force. (3) Define the dynamic load stress parameters and the rock mass mechanical parameters of the bottom plate, and calculate the dynamic load stress components of the bottom plate caused by the dynamic load; The specific theoretical calculation method for the dynamic stress field of the base plate in step (3) is as follows: The dynamic stress generated by the fracture of the top strata can be expressed as: （2） In the formula: This refers to the dynamic load amplitude. For dynamic load frequency; This refers to the duration of dynamic load application. According to mine microseismic monitoring, the dynamic load intensity in mines is generally 1.5MPa to 15MPa, the frequency is generally tens to 100Hz, and the duration is generally 0.01 to 0.1s. According to the basic principles of elastic dynamics, neglecting body forces, the equations of motion and physical equations of an elastic medium can be expressed as follows: （3） （4） In the formula: and They are respectively direction and Displacement in direction; The density of the base strata; , ,in For elastic modulus, Poisson's ratio; Combining equations (3) and (4), we can obtain: （5） For the time of equation (5) t Perform the Laplace transform. The Laplace transform and its inverse transform are defined as follows: （6） In the formula: s These are the Laplace transform parameters; Simultaneously, when the dynamic load stress is transferred to the stope floor, the initial state of the floor is static, that is: （7） Therefore, equation (5) can be transformed by Laplace transformation into: （8） To solve equation (8), for x The Fourier transform, and its inverse, are defined as follows: （9） In the formula: For about x Fourier transform parameters; Equation (8), after Fourier transformation and written in matrix form, is as follows: （10） Let the state components Then equation (10) can be transformed into the following system of differential equations: （11） According to matrix calculus, the solution to equation (9) can be expressed as: （12） In the formula: express The state vector after Laplace and Fourier transformations; make Equation (12) can be expressed in matrix form: （13） In the formula: , ， ， ， ， ， ， ， ， ， ， ， ， ； For any depth of the mining floor h The relationship with the surface state vector is as follows: （14） Top of the base plate and infinity The boundary conditions can be expressed as: （15） Perform a cross equation (15) t Laplace transform and x After Fourier transformation, substituting into equation (14) yields the dynamic stress components at any point on the bottom plate of the working surface. (4) The stress components at any point on the bottom plate of the mining area under the combined action of static and dynamic loads are obtained by stress superposition; (5) Based on the stress component solution at any point on the base plate, the maximum cumulative failure depth of the base plate during the dynamic load process is calculated by combining the Mohr-Coulomb criterion. The method for calculating the maximum failure depth of the stope floor includes: a mechanical model of the combined dynamic and static loads on the stope floor, a theoretical calculation method, dynamic stress response characteristics of the stope floor, and analysis of the failure depth of the stope floor.

2. The method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads as described in claim 1, characterized in that, The principle for establishing the dynamic and static load combined action mechanical model of the stope floor in step (1) is as follows: According to the mine pressure theory, after the coal seam is mined, the stope floor will be subjected to the supporting pressure due to the redistribution of the surrounding rock stress; in addition, the stope floor is also subjected to significant dynamic load disturbance during the initial and periodic pressure of the working face roof; therefore, the load borne by the stope floor mainly includes: ① After the coal mining working face is mined, the uncollapsed rock strata above the stope transmit the supporting pressure static load to the coal seam floor through the surrounding rock of the stope in the form of "roof pressure"; ② The dynamic load disturbance caused by the fracture of the roof rock strata during the periodic pressure of the roof.

3. The method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads as described in claim 1, characterized in that, The specific theoretical calculation method for the static stress field of the base plate in step (2) is as follows: Based on the distribution characteristics of the support pressure, in order to simplify the calculation, the support pressure is... Linearization processing is performed, and a coordinate system is established with the working surface position as the origin, and the working surface orientation is... x Axial direction, z The simplified model of the stope support pressure distribution is shown with the axis pointing vertically downwards; where: a This is the stress reduction zone, the initial pressure stage. a =0; b , c This is a region of increased stress. d This refers to the range of dynamic load application. The average unit weight of the overlying strata on the base plate; H This refers to the burial depth of the coal seam floor. For the load on the collapse zone within the goaf, for the initial pressure, K 1 = 0; The working face is under advanced support pressure; the support pressure The resulting static stress field can be obtained from the stress solution at any point on a half-plane subjected to a vertically distributed force, taking a small length d. ε, The formula for solving the static stress field of the base plate is as follows: （1）。 4. The method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads according to claim 1, characterized in that, In step (4), the vertical stress, horizontal stress, and shear stress at any point on the bottom plate of the mining area can be composed of the additional static stress caused by the support pressure and the additional dynamic stress caused by the dynamic load from the top plate.

5. The method for calculating the failure depth of the stope floor considering the combined effects of dynamic and static loads according to claim 1, characterized in that, In step (5), the yield criterion for determining the maximum failure depth of the stope floor is the shear failure criterion. Therefore, according to the Mohr-Coulomb yield failure criterion, the stress state of the rock strata in the stope floor when shear failure occurs satisfies: （16） In the formula: and These are the internal friction angle and cohesion of the bottom rock strata, respectively, which can be obtained by laboratory testing. The vertical stress of the base plate at any point will be calculated. Horizontal stress and shear stress Substituting into equation (16) yields the maximum damage depth of the base plate.

Images