A method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load in the mining of the lower side slope.

Abstract

This invention provides a method for evaluating the dynamic stability of supporting coal pillars in end-side mining under non-uniformly distributed loads, belonging to the technical field of dynamic stability evaluation of supporting coal pillars in end-side mining. To address the technical problem that conventional coal pillar stability evaluation methods, which do not consider the coupling effects of blasting vibration and overlying strata, may pose risks to personnel and end-side mining machines in the design of supporting coal pillar parameters, the following technical solution is adopted: Collecting samples of retained coal and overlying strata from the end-side mining area, and testing the physical and mechanical parameters of these samples; establishing a dynamic instability criterion for supporting coal pillars based on catastrophe theory based on the dynamic response and deformation law of the supporting coal pillar under the coupled effects of non-uniformly distributed static load and blasting dynamic load; and establishing a dynamic instability criterion for the roof based on strength theory based on the relationship model between the maximum bending moment and tensile stress of the coal pillar roof under dynamic-static load coupling. This invention is used for the stability control of supporting coal pillars in open-pit coal mine end-side mining.

Description

Technical Field

[0001] This invention provides a method for evaluating the dynamic stability of a supporting coal pillar in end-side mining under non-uniformly distributed loads, belonging to the technical field of dynamic stability evaluation of supporting coal pillars in end-side mining. Background Technology

[0002] Open-pit coal mining has advantages such as high resource recovery rate, short construction period, low cost, good working conditions, high safety, and high production efficiency. However, due to limitations such as mining technology, stripping ratio, and slope stability, a large amount of coal resources will inevitably be covered at the bottom of the boundary slope during open-pit mining, resulting in resource waste and potential hazards such as spontaneous combustion of coal and reduced slope stability. Currently, end-face mining machines can be used to recover the trapped coal. During end-face mining, end-face mining machines are used to excavate the open-pit coal seam into multiple independent mining chambers. Supporting coal pillars are left between the mining chambers to ensure the safe recovery of coal resources. Therefore, studying the stability of the supporting coal pillars is of great significance for the safe and efficient operation of open-pit end-face mining.

[0003] Existing research, based on various theories such as the modified Hoek-Brown criterion, elasticity, and Winkler foundation beams, and employing theoretical modeling, numerical simulation, experiments, and case studies, has systematically explored the failure mechanism, stress distribution, plastic zone development, parameter design, and overall stability evaluation methods of end-face mining support pillars, providing important support for safe mining. However, most studies focus on the overall stability of the pillar under single factors, lacking in-depth analysis of the impact of multi-factor coupled disturbances in actual complex working conditions. For example, the impact of blasting vibration and the coupling effect of overlying strata on the support pillar is not considered. At the same time, the collaborative support of the support pillar and roof for external loads on the mining tunnel is ignored, which restricts further improvement of resource recovery rate and more accurate risk assessment.

[0004] Under actual engineering conditions, the overall stability of the supporting coal pillar in end-side mining is subject to the combined disturbance of multiple influencing factors. Moreover, its stability depends on the complex coordination mechanism between local instability of the coal pillar and the load distribution of the roof. Existing technologies are difficult to apply to these complex characteristics, leading to conservative parameter design or inaccurate risk assessment. Therefore, a new method that can comprehensively consider the coupled effects of multiple factors is proposed, which is of key significance for accurately designing coal pillar parameters, fully recovering resources, and ensuring the safe and efficient operation of end-side mining. Summary of the Invention

[0005] To address the technical problems existing in the background art, the present invention provides a method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load during end-side mining, comprising the following evaluation steps:

[0006] Step 1: Collect samples of the retained coal and overlying rock strata at the end of the coal seam, test the physical and mechanical parameters of the retained coal and overlying rock strata, and combine them with relevant production data of the mining area to select the final physical and mechanical parameters of each rock stratum, including the unit weight of the coal seam being mined, the unit weight of each layer of the overlying rock strata, the internal friction angle of the supporting coal pillar, the cohesion of the supporting coal pillar, the Poisson's ratio of the supporting coal pillar, the tensile strength of the supporting coal pillar, and the blasting vibration test data.

[0007] Step 2: Based on the dynamic response and deformation characteristics of the supporting coal pillar under the coupled action of non-uniformly distributed static load and blasting dynamic load, the total potential energy function of the coal pillar-overburden system is established, and a dynamic instability criterion for the supporting coal pillar based on catastrophe theory is established. The specific method is as follows:

[0008] Step 2.1: Calculate the average unit weight of the overlying rock layers on the top of the mining tunnel by performing a weighted average of the unit weights.

[0009] Define the overlying rock layers on the top of the mining tunnel as n layers, with the unit weights of each overlying rock layer being: γ1, γ2, γ3, ..., γ n The corresponding average thicknesses are: h1, h2, h3, ..., h n The average unit weight of the overlying rock layers is... The calculation formula is:

[0010] ;

[0011] Step 2.2: Based on the average unit weight of each overlying rock layer on the roof of the mining tunnel, calculate the actual load borne by the supporting coal pillar as the mining depth increases:

[0012] The formula for calculating the non-uniformly distributed load actually borne by the supporting coal pillar is as follows:

[0013] ;

[0014] Where x is the position of the supporting coal pillar in the direction of its strike; γ is the unit weight of the coal seam; h1 is the thickness of the coal pillar roof; α is the end face slope angle; W m W represents the width of the lower mining tunnel in the end-face mining operation. n To support the width of the coal pillar;

[0015] Step 2.3: Based on the Mohr-Coulomb strength theory and the load data obtained in Step 2.2, calculate the maximum vertical stress borne by the supporting coal pillar:

[0016] The formula for calculating the maximum vertical stress is:

[0017] ;

[0018] Where φ is the internal friction angle of the supporting coal pillar; λ is the lateral pressure coefficient; and C is the cohesion of the supporting coal pillar.

[0019] Step 2.4: Based on the optimized Sadovsky formula, fit the blasting vibration data to obtain the particle blasting vibration velocity, establish a dynamic response model of coal and rock mass under blasting dynamic load, and calculate the instantaneous maximum dynamic response of the supporting coal pillar micro-element under different blast center distances, elevation differences, and single-shot blasting charge amounts:

[0020] Based on the quasi-static method, the dynamics generated by coal and rock mass under blasting vibration are simplified to equivalent static stress for analysis. The formula for calculating the maximum dynamic response is:

[0021] ;

[0022] Where k1, r3, and r4 are attenuation coefficients; k is the site influence coefficient; d is the horizontal distance from the blast center; Q is the explosive charge, which is the total charge for simultaneous blasting and the maximum charge for micro-delay or second-delay blasting; r1 and r2 are the attenuation coefficients under different influencing factors; and z is the vertical distance between the measuring point and the blast source.

[0023] The equivalent static stress formula is:

[0024] ;

[0025] Where, β e This is the dynamic stress reduction factor;

[0026] Step 2.5: Based on the stress equilibrium theory of loose media, and combined with the derivation of the stress equilibrium differential equation, calculate the width of the plastic yield zone on one side of the coal pillar:

[0027] width of the plastic yield zone on one side of the supporting coal pillar (x) p The calculation formula is:

[0028] ;

[0029] Where h2 is the height of the mining tunnel;

[0030] Step 2.6: Based on the constitutive characteristics of the elastic core region and yield region of the supporting coal pillar, establish the total potential energy function of the coal pillar-overburden system under dynamic-static load coupling, and obtain the dynamic instability criterion of the supporting coal pillar based on catastrophe theory:

[0031] The expression for the abrupt instability criterion Δ of the supporting coal pillar is:

[0032] ;

[0033] Where e is the natural constant; σ zl To support the ultimate compressive strength of the coal pillar; σ e q(x) represents the dynamic stress generated by blasting vibration; q(x) represents the load of the overburden layer on the supporting coal pillar under non-uniformly distributed load, considering the effective area theory.

[0034] Since the supporting coal pillar is subjected to the combined effects of the overlying strata load and the dynamic load of blasting, it is determined that:

[0035] When Δ>0, the coal pillar is in a stable state;

[0036] When Δ=0, the coal pillar is in a critical instability state;

[0037] When Δ < 0, the coal pillar is in an unstable state.

[0038] Step 3: Based on the single-span simply supported beam theory in structural mechanics, establish a model relating the maximum bending moment and tensile stress of the coal pillar roof under dynamic-static load coupling, and establish a roof dynamic instability criterion based on strength theory. The specific method is as follows:

[0039] Step 3.1: Take the size of the coal pillar at the critical instability of the supporting coal pillar as the initial coal pillar size, and continuously reduce the initial coal pillar size until the supporting coal pillar is in a critical failure state, and establish the bending moment equation of the roof range of the unstable section of the supporting coal pillar.

[0040] Step 3.2: Based on the bending moment equation of the roof of the unstable section of the supporting coal pillar, calculate the maximum bending moment of a single-span simply supported beam. Further calculate the maximum tensile stress under dynamic-static load coupling. Then, based on the ultimate strength theory, calculate the dynamic safety factor F of the coal pillar roof under the combined action of static load and blasting dynamic load from the overlying strata. s ' As a criterion for dynamic instability of the coal pillar roof:

[0041] Among them, the maximum bending moment M max The calculation formula is:

[0042] ;

[0043] The expression for the intermediate variable R is:

[0044] ;

[0045] Maximum tensile stress σ tmax The expression is:

[0046] ;

[0047] The criterion for dynamic instability of the coal roof is F s ' The expression is:

[0048] ;

[0049] Among them, F s ' As a criterion for roof coal pillar failure, when F s '> 1 is in an effective state, when F s ' = 1 is in a critical state, when F s ' < 1 is in a failure state; σ tl is the tensile strength of the coal pillar roof; σ tmax is the maximum tensile stress of a single-span simply supported beam under the coupling action of dynamic and static loads.

[0050] Step 4: Based on the established dynamic instability criterion of the support coal pillar and the dynamic instability criterion of the roof, establish a relationship model between the length of the unstable section of the coal pillar and the ultimate caving distance of the roof under different coal pillar width conditions, and evaluate the dynamic stability of the support coal pillar based on the relationship model. The specific method is as follows:

[0051] Based on the dynamic instability criterion of the support coal pillar and the dynamic instability criterion of the roof, calculate the length l1 of the unstable section of the supported coal pillar and the ultimate caving length l2 of the mining roadway roof under different coal pillar sizes;

[0052] If l1 < l2, the entire mining roadway is in an effective state, then reduce the width size of the support coal pillar until l1 > l2. At this time, the support coal pillar is in a critical failure state or a failure state. Compare the widths W of all support coal pillars that satisfy l1 < l2 n , and the support coal pillar width with the smallest value is the minimum width to ensure the dynamic stability of the support coal pillar and is used as the final support coal pillar size.

[0053] The beneficial effects of the present invention compared with the prior art are as follows: The present invention proposes a method for evaluating the dynamic stability of a support coal pillar in end-wall mining under non-uniform loads. This method further considers the dynamic load of blasting vibration on the end-wall support coal pillar on the basis of the design method of the size parameters of the end-wall support coal pillar under static load. Based on Newton's theory of motion mechanics, the total potential energy function of the coal pillar-overlying rock system is constructed, and a dynamic instability criterion of the support coal pillar based on the cusp catastrophe theory is proposed. Using the single-span simply supported beam theory of structural mechanics, the dynamic instability criterion of the roof of the unstable section of the support coal pillar under the action of dynamic and static loads is deduced, and the length of the unstable section of the coal pillar and the ultimate caving distance of the roof under different coal pillar widths are compared, and then the dynamic stability of the support coal pillar is evaluated. This method breaks through the limitation of traditional single-static load analysis, realizes the quantitative coupling of non-uniform static load, blasting dynamic load and coal pillar-roof synergistic action, can evaluate the dynamic stability state of the support coal pillar under non-uniform loads, and provides a theoretical basis for the application and promotion of end-wall mining in open-pit mines. Brief Description of the Drawings

[0054] The following further describes the present invention with reference to the drawings:

[0055] Figure 1 is the step flow chart of the method for evaluating the dynamic stability of a support coal pillar in end-wall mining under non-uniform loads of the present invention;

[0056] Figure 2 This is a schematic diagram illustrating the steps of the method for evaluating the dynamic stability of a coal pillar in mining under non-uniformly distributed loads according to the present invention.

[0057] Figure 3 This is a schematic diagram of the distribution structure of the endwall rock strata in an embodiment of the present invention;

[0058] Figure 4 This is a schematic diagram of the load distribution structure of the supporting coal pillar under end-side mining in an embodiment of the present invention;

[0059] Figure 5 This is a schematic diagram of the mechanical analysis model of the cross-section of the supporting coal pillar under the load of the overlying strata in an embodiment of the present invention;

[0060] Figure 6 This is a schematic diagram of the dynamic response model of coal and rock mass under blasting dynamic load in an embodiment of the present invention;

[0061] Figure 7 This is a schematic diagram of the multi-factor dynamic stress response analysis model of the support column in an embodiment of the present invention;

[0062] Figure 8 This is a schematic diagram of the stress state of a micro-element in the transverse section of the coal pillar roof in an embodiment of the present invention. Detailed Implementation

[0063] like Figures 1 to 8 As shown, this invention proposes a method for evaluating the dynamic stability of end-side mining support coal pillars under non-uniformly distributed loads, used for stability control of support coal pillars in open-pit coal mines. Primarily, based on obtaining the physical and mechanical parameters of the coal seam and the rock strata above it, it innovatively constructs a coal pillar instability criterion based on cusp catastrophe theory by collecting blasting vibration data and combining the coupling mechanism of non-uniformly distributed loads and blasting dynamic loads, using the bifurcation set as the criterion for determining the stability state of the coal pillar. Based on the single-span simply supported beam theory and ultimate strength theory, it uses the safety factor as the criterion for determining the stability state of the coal pillar roof. By comparing the length of the instability zone and the ultimate collapse distance of the roof under different coal pillar widths, it proposes a criterion for determining the overall failure of the support coal pillar, accurately evaluating the dynamic stability of end-side mining support coal pillars under non-uniformly distributed loads, and proposing a design method for reasonable parameters of the support coal pillar.

[0064] like Figure 1 and Figure 2 As shown, an embodiment of the present invention provides a method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load during end-side mining, specifically including the following evaluation steps:

[0065] Step 1: Collect coal samples from the end face and overlying rock strata, test the physical and mechanical parameters of the coal and rock samples, and select the final physical and mechanical parameters of each rock stratum based on relevant production data of the mining area.

[0066] In this embodiment, the overlying strata refer to all strata above the roof of the mining tunnel. An EML340 end-face mining machine is used for mining, with a maximum mining height of 5m, a maximum mining width of 3.3m, and a maximum mining depth of 150m. The end-face mining coal seam is the No. 4 coal seam in a certain mining area. The strata in the mining area, from top to bottom, are: loess, alternating layers of mudstone and sandstone, No. 4 coal seam, and sandstone. Figure 3 As shown in Table 1, the thickness of coal seam #4 is 7.96m, and the horizontal angle between the step where the coal seam is located and the top of the slope is 28°. The physical and mechanical parameters of the coal and overlying rock samples were tested at the end wall and the physical and mechanical parameters obtained are shown in Table 1 below.

[0067] Table 1 Physical and mechanical parameters of coal and rock mass

[0068]

[0069] Step 2: Based on the dynamic response and deformation characteristics of the supporting coal pillar under the coupled action of non-uniformly distributed static load and blasting dynamic load, the total potential energy function of the coal pillar-overburden system was established, and a dynamic instability criterion for the supporting coal pillar based on catastrophe theory was proposed:

[0070] Step 2.1: Calculate the average unit weight of the overlying strata at the top of the mining tunnel by weighted averaging:

[0071] Assume there are n overlying rock layers on the roof of the mining tunnel, and the unit weights of each overlying rock layer are: γ1, γ2, γ3, ..., γ n The corresponding average thicknesses are h1, h2, h3, ..., hn, then the average unit weight of the overlying strata is... for:

[0072] (1);

[0073] In this embodiment, there are two overlying rock layers on the top of the mining tunnel, and the strata are relatively regular in shape. The average unit weight of the overlying rock layers is calculated by weighted averaging based on the rock layer thickness:

[0074] (2);

[0075] Step 2.2: Calculate the non-uniformly distributed load actually borne by the supporting coal pillar using the average unit weight of the overlying strata on the roof of the mining tunnel:

[0076] (3);

[0077] In this embodiment, the load distribution of the supporting coal pillar is as follows: Figure 4 As shown, the calculated non-uniformly distributed load actually borne by the supporting coal pillar is:

[0078] (4);

[0079] Step 2.3: Calculate the maximum vertical stress borne by the supporting coal pillar based on the Mohr-Coulomb strength theory and the actual load borne by the supporting coal pillar as the mining depth increases;

[0080] In this embodiment, based on A.H. Wilson's two-zone constraint theory, when the supporting coal pillar is under load, it can be divided into a plastic yield zone and an elastic core zone along the direction perpendicular to the mining depth. The plastic yield zone encloses the elastic core zone, and the width of the elastic core zone gradually decreases. The location of maximum stress is at the boundary between the yield zone and the elastic core zone. Under the load of the overlying strata, the supporting coal pillar exhibits a stress distribution pattern resembling a "saddle" with larger stresses at both ends and smaller stresses in the middle. Based on the Mohr-Coulomb strength theory, the maximum vertical stress σ borne by the coal pillar is calculated. zmax (x) is:

[0081] (5);

[0082] In this embodiment, such as Figure 5 The figure shows the mechanical analysis model of the cross-section of the supporting coal pillar; based on the Mohr-Coulomb strength theory, the maximum vertical stress σ borne by the coal pillar can be derived. zmax (x), since the load of the overlying strata increases with the mining depth under end-face mining conditions, the maximum vertical stress is located at the maximum mining depth, i.e., x=150. Calculate the maximum vertical stress borne by the supporting coal pillar at this point:

[0083] (6);

[0084] Step 2.4: Optimize the Sadovsky empirical formula to obtain the particle blasting vibration velocity. Combine the prediction formula of the main vibration frequency of blasting seismic waves to establish a dynamic response model of coal and rock mass under blasting dynamic load. According to Newton's second law, obtain the instantaneous maximum dynamic response of the micro-element of the supporting coal pillar under different blast center distances, elevation differences, and single-shot blasting charge amounts. Based on the quasi-static method, simplify the dynamics generated by the coal and rock mass under blasting vibration into equivalent static stress for analysis.

[0085] In this embodiment, the dynamic response model of coal and rock mass under blasting dynamic load is established, such as... Figure 6 As shown; the coal and rock mass is divided into multiple micro-element units. The seismic waves generated by the blasting vibration act on these micro-element units as typical damped vibrations. The maximum acceleration generated by the micro-element unit supporting the coal pillar is:

[0086] (7);

[0087] Where f is the prediction formula for the dominant frequency of blasting seismic waves; v is the influence of different elevation differences on the propagation characteristics of blasting vibration, and the optimized Sadovsky empirical formula.

[0088] (8);

[0089] According to Newton's second law, the instantaneous maximum dynamic response of the coal pillar micro-element under different blast center distances, elevation differences, and single-blast charge amounts is:

[0090] (9);

[0091] The dynamics generated by coal and rock mass under blasting vibration are simplified into equivalent static stress for analysis, and the calculation formula is as follows:

[0092] (10);

[0093] Where, β e The value of the dynamic stress reduction factor is related to the magnitude of the maximum particle vibration velocity v. The range of the dynamic stress reduction factor is shown in Table 2 below.

[0094] Table 2 Reduction coefficient of dynamic stress during blasting

[0095]

[0096] In this embodiment, monitoring data of different blasting parameters were collected under the multi-row, sequential, micro-differential blasting method. The blasting seismic wave data of four blasting operations were statistically analyzed, totaling 24 sets of valid data. The collected data are shown in Table 3 below.

[0097] Table 3 Statistical Results of Blasting Vibration Monitoring Data

[0098]

[0099] The monitoring data was mathematically fitted using the data analysis software Origin, resulting in the following prediction model for the instantaneous maximum vibration velocity and blasting main frequency under actual engineering conditions:

[0100] (11);

[0101] Substituting the vibration data into equation (11), a multi-factor dynamic response model of the supporting coal pillar under the action of blasting seismic waves is established, such as... Figure 7 As shown, the analysis shows that the instantaneous dynamic force generated by the blasting seismic wave on the coal pillar at the deepest part of the mining tunnel increases linearly with the amount of explosive charge per blast, while decreasing negatively exponentially with respect to the horizontal distance and elevation difference between the coal pillar and the seismic source.

[0102] Finally, the equivalent static stress σ of this embodiment is obtained. e =0.045kPa.

[0103] Step 2.5: Based on the stress balance theory of loose media, the width of the plastic yield zone on one side of the coal pillar is derived by combining the stress balance differential equation. The formula is improved according to the characteristics of the coal pillar without support structure and the overlying strata being subjected to non-uniform load in the open-pit end-side mining scenario, so as to obtain a formula for the width of the plastic zone on one side of the coal pillar suitable for open-pit end-side mining.

[0104] width of the plastic yield zone on one side of the supporting coal pillar (x) p for:

[0105] (12);

[0106] In this embodiment, the plastic yield zone on one side of the supporting coal pillar is calculated as follows:

[0107] (13);

[0108] Step 2.6: Under dynamic-static load coupling, establish the total potential energy function of the coal pillar-overburden system based on the constitutive relationship characteristics of the elastic core region and yield region of the supporting coal pillar, and obtain the dynamic instability criterion of the supporting coal pillar based on catastrophe theory.

[0109] Based on the cusp catastrophe theory, a bifurcation set is established according to the equilibrium surface equation and cusp relations. The criterion Δ for the catastrophe instability of the supported coal pillar under non-uniformly distributed load conditions is determined as follows:

[0110] (14);

[0111] The critical coal pillar size at the maximum mining depth location is: the width of the supporting coal pillar when the instability criterion Δ=0.

[0112] In this embodiment, since the supporting coal pillar bears the greatest load at the maximum mining depth position, the width of the supporting coal pillar corresponding to the instability criterion Δ=0 is the critical instability width of the supporting coal pillar; when the instability criterion Δ>0, the coal pillar of the corresponding width is in a stable state, and when the instability criterion Δ<0, the coal pillar of the corresponding width is in an unstable state.

[0113] Since the dimensions of the supporting coal pillars differ, their corresponding ultimate compressive strengths also differ. When the coal pillar is in a critical instability state, its maximum vertical stress is the same as the ultimate compressive strength at that size. Therefore, a convergent calculation method can be used to calculate the maximum vertical stress borne by the supporting coal pillar. Let σ be the initial value. zl =σ zmax Solve the equations (4), (6) and (13) simultaneously.

[0114] It should be noted that σ is calculated during the calculation process. zl =σ zmaxThis is not valid. Using the instability criterion ∆ as the convergence basis, the supporting coal pillar is only in a critical instability state when ∆=0. zl =σ zmax The calculation is successful, and the coal pillar size at this point is the initial design size of the coal pillar. Some calculation results are shown in Table 4 below.

[0115] Table 4. Calculation Results of Instability Criteria at 150m for Different Coal Pillar Widths

[0116]

[0117] The data in Table 4 shows that when the coal pillar width is 4.7, the stability of the coal pillar area within the mining depth range can be guaranteed. Therefore, it is set as the initial design value for the coal pillar width.

[0118] When the width of the coal pillar decreases, the position of Δ=0 will move forward to a shallower area, at which point a local instability zone will appear, and the length l of the local instability zone is the distance between the position of Δ=0 and the deepest position designed in the mining chamber.

[0119] Step 3: Based on the single-span simply supported beam theory of structural mechanics, establish the expression for the maximum tensile stress of the coal pillar roof under dynamic-static load coupling, and establish the roof dynamic instability criterion based on strength theory;

[0120] Step 3.1: Take the size of the coal pillar at which the supporting coal pillar is critically unstable as the initial coal pillar size, and continuously reduce the initial coal pillar size to reach the critical failure state of the supporting coal pillar, and establish the bending moment equation of the roof range of the unstable section of the supporting coal pillar;

[0121] When the supporting coal pillar experiences local instability, the roof of the mining tunnel and the coal pillars at both ends, which have supporting capacity, constitute a single-span simply supported beam structure. Assume the starting point of this single-span simply supported beam is m2 and the ending point is n2; let l2 = n2 - m2, where l2 is the span of the simply supported beam structure of the mining tunnel roof; through mechanical analysis, establish the bending moment equation for the roof range of the unstable section of the supporting coal pillar. The load shape of this roof section under the overlying strata is trapezoidal. Based on the load distribution shape of the overlying strata, the magnitude of the equivalent concentrated force F borne by the single-span simply supported beam is obtained:

[0122] (17);

[0123] Where q2(m2) is the point load on the top of the mining tunnel at m2, kN; q2(n2) is the point load on the top of the mining tunnel at n2, kN.

[0124] The equivalent concentrated force is located at the centroid of the load distribution area. The distance l between the endpoint n2 of the single-span simply supported beam and the centroid is:

[0125] (18);

[0126] Calculate the torque equations for the starting point m2 and the ending point n2 respectively. According to the principle of torque balance, the net torque at any point is zero, which is:

[0127] (19);

[0128] Where, ∑M m2 The resultant torque at point m2 is kN·m; ∑M n2 F is the resultant moment at point n2, in kN·m; m2 F is the support reaction force at point m2 of a single-span simply supported beam, in kN. n2 Let n2 be the support reaction force at point n2 of a single-span simply supported beam, in kN.

[0129] Substituting the equivalent concentrated force equation (17) and the centroid distance equation (18) into the moment balance equation set (19), the support reactions F at both ends of a single-span simply supported beam can be obtained. m2 F n2 :

[0130] (20);

[0131] Taking the left half of any section of the single-span simply supported beam as a free body, the equivalent concentrated force F(x) of this free body under the action of the overlying rock strata is obtained:

[0132] (twenty one);

[0133] The distance from the equivalent concentrated force F(x) to the cross section is:

[0134] (twenty two);

[0135] By combining equations (21) and (22), the arbitrary bending moment on a simply supported beam with a single span can be obtained as follows:

[0136] (twenty three);

[0137] Since the two ends of the single-span simply supported beam are actually elastic supports, the whole beam will have a vertical displacement under the load of the overlying rock strata. After the beam displacement is transformed by a second derivative, the bending moment formula is obtained. Therefore, after the second derivative, the displacement generated at the elastic supports at both ends of the single-span simply supported beam by the overlying rock strata load does not affect the bending moment of the beam.

[0138] In this embodiment, the EML340 end-face coal mining machine is used, with a maximum mining depth of 150m, therefore b=150. Let l2=n2-m2, where l2 is the span of the simply supported beam structure of the mine roof, and its maximum span is l 2max This refers to the length of the failure zone of the mine roof. The bending moment equation for the roof range of the unstable section supporting the coal pillar is calculated through mechanical analysis.

[0139] The support reaction F at the starting point of a single-span simply supported beam can be calculated using the moment balance equation. m2 :

[0140] (twenty four);

[0141] Taking the left half of any section of the single-span simply supported beam as a free body, calculate the equivalent concentrated force F(x) of this free body under the action of the overlying rock strata:

[0142] (25);

[0143] The distance from the location of the equivalent concentrated force F(x) to any of the above cross sections is:

[0144] (26);

[0145] The arbitrary bending moment on a simply supported beam with a single span is calculated by combining formulas (24), (25), and (26):

[0146] (27);

[0147] Step 3.2: Calculate the maximum bending moment of the single-span simply supported beam based on the bending moment equation of the roof range of the unstable section of the supporting coal pillar, and then calculate the maximum tensile stress of the single-span simply supported beam under dynamic-static load coupling.

[0148] After a single-span simply supported beam is subjected to compressive bending, the area above the neutral axis is the compression zone, and the area below is the tension zone. Figure 8 As shown, the compressive strength of coal and rock mass is much greater than its tensile strength. Therefore, the tension zone below the neutral axis is a weak area, and the failure mode of the coal pillar roof is tensile failure.

[0149] The maximum bending moment M borne by a single-span simply supported beam segment max for:

[0150] (28);

[0151] The intermediate variable R is:

[0152] (29);

[0153] The maximum tensile stress of a single-span simply supported beam under dynamic-static load coupling is σ. tmax :

[0154] (30);

[0155] Based on the ultimate strength theory, considering the local instability of the supporting coal pillar, a dynamic safety factor F is constructed for the roof of the coal pillar under the combined static load and blasting dynamic load of the overlying strata.s ' :

[0156] (31);

[0157] In summary, under the simultaneous action of the static load of the overlying strata and the blasting dynamic load on the roof of the local instability range of the support coal pillar, when the dynamic safety reserve coefficient F s ' > 1, the roof of the coal pillar is in a stable state; when the dynamic safety reserve coefficient F of the unstable section of the coal pillar s ' = 1, the roof of the coal pillar is in a critical instability state; when the dynamic safety reserve coefficient F of the unstable section of the coal pillar s ' < 1, the roof of the coal pillar is in an unstable state.

[0158] In this embodiment, by performing derivative analysis according to Equation (27), the maximum bending moment M of the simply supported beam with a single span is obtained max as:

[0159] (32);

[0160] where the intermediate variable R is:

[0161] (33);

[0162] The maximum tensile stress σ on the simply supported beam with a single span tmax is:

[0163] (34);

[0164] Then, after local instability occurs in the support coal pillar, for the roof of the mining chamber to maintain an effective support effect, it must satisfy:

[0165] (35);

[0166] Step 4: Use the dynamic instability criterion of the support coal pillar and the dynamic instability criterion of the roof to establish a mathematical relationship expression between the length of the unstable section and the ultimate caving distance of the roof under different coal pillar widths, and propose a dynamic failure criterion and parameter design method for the support coal pillar.

[0167] If l1 < l2, the overall mining chamber is in an effective state, then reduce the width dimension of the support coal pillar until l1 > l2. At this time, the support coal pillar is in a critical failure state or a failure state. Compare the widths W of all support coal pillars that satisfy l1 < l2 n , and use the support coal pillar width with the smallest value as the final support coal pillar size.

[0168] Calculations show that the width of the supporting coal pillar to ensure overall stability is 4.7m. Now, the coal pillar width is reduced to 4.5m for analysis. When the mining depth is 150m, the known conditions are substituted into formula (6) to obtain the maximum vertical stress σ borne by the supporting coal pillar. zmax :

[0169] (36);

[0170] Substitute the maximum vertical stress result from formula (36) into formula (13) to calculate the width x of the plastic zone on one side of the supporting coal pillar. p for:

[0171] (37);

[0172] Substituting the calculation results into the instability criterion formula (14) for the supporting coal pillar, the instability criterion Δ is calculated as follows:

[0173] (38);

[0174] Calculations showed that Δ < 0, indicating that when the width of the supporting coal pillar is 4.5m, the supporting coal pillar will become unstable at a depth of 150m in the mining chamber. Further calculations were performed on the instability criterion Δ at a depth of 149m for the same coal pillar width. The location corresponding to Δ ≥ 0 was found, and this location is the starting point of the unstable section of the supporting coal pillar.

[0175] When the coal pillar width is 4.5m and the mining chamber depth is 150m, substituting the known conditions into formula (33) to calculate the intermediate variable R is:

[0176] (39);

[0177] Substituting the calculation result of the intermediate variable R into formula (34), the maximum tensile stress of the top plate of the mining tunnel can be obtained as follows:

[0178] (40);

[0179] Obviously F s ' >1 indicates that when the supporting coal pillar is 4.5m, the mine shaft is located at a depth of 150m, and the roof of the mine shaft has not failed. Next, the failure criterion F at a mine shaft depth of 149m is calculated with the same coal pillar width. s ' Find F s ' The position corresponding to <1 is the starting position of the section where the supporting coal pillar fails.

[0180] Analyze the length \(l_1\) of the unstable section of the supported coal pillar and the length \(l_2\) of the failed section of the roof of the mined-out area under different widths of the coal pillar. If \(l_1 < l_2\), the entire mined-out area is in an effective state and the overall space of the mined-out area is stable. At this time, continue to reduce the size of the coal pillar and analyze the length \(l_1\) of the unstable section of the supported coal pillar and the length \(l_2\) of the failed section of the roof of the mined-out area using the same method until \(l_1>l_2\) and the entire mined-out area is in a failed state. Through analysis, the minimum width to ensure the dynamic stability of the supported coal pillar in this case can be finally determined to be 4.5 m. The calculation results of this implementation case are shown in Table 5 below.

[0181] Table 5 Summary of Calculation Results

[0182]

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load during end-side mining, characterized in that: The evaluation steps include the following: Step 1: Collect samples of the coal and overlying rock strata at the end of the mine, test the physical and mechanical parameters of the coal and overlying rock strata, and select the final physical and mechanical parameters of each rock stratum in combination with relevant production data of the mining area. Step 2: Based on the dynamic response and deformation characteristics of the supporting coal pillar under the coupled action of non-uniformly distributed static load and blasting dynamic load, the total potential energy function of the coal pillar-overburden system is established, and a dynamic instability criterion for the supporting coal pillar based on catastrophe theory is established. The specific method is as follows: Based on the optimized Sadovsky formula, the blasting vibration data were fitted to obtain the particle blasting vibration velocity. A dynamic response model of coal and rock mass under blasting dynamic load was established, and the instantaneous maximum dynamic response of the supporting coal pillar micro-element under different blast center distances, elevation differences, and single-shot blasting charge amounts was calculated. Based on the quasi-static method, the dynamics generated by coal and rock mass under blasting vibration are simplified to equivalent static stress for analysis. The formula for calculating the maximum dynamic response is: ； Where k1, r3, and r4 are attenuation coefficients; k is the site influence coefficient; d is the horizontal distance from the blast center; Q is the explosive charge, which is the total charge for simultaneous blasting and the maximum charge for micro-delay or second-delay blasting; r1 and r2 are the attenuation coefficients under different influencing factors; and z is the vertical distance between the measuring point and the blast source. The equivalent static stress formula is: ； Where, β e This is the dynamic stress reduction factor; Based on the stress equilibrium theory of loose media, and combined with the derivation of the stress equilibrium differential equation, the width of the plastic yield zone on one side of the coal pillar is calculated: width of the plastic yield zone on one side of the supporting coal pillar (x) p The calculation formula is: ； Where h2 is the height of the mining tunnel; Based on the constitutive characteristics of the elastic core region and yield region of the supporting coal pillar, the total potential energy function of the coal pillar-overburden system under dynamic-static load coupling is established, and the dynamic instability criterion of the supporting coal pillar based on catastrophe theory is obtained: The expression for the abrupt instability criterion Δ of the supporting coal pillar is: ； Where e is the natural constant; σ zl To support the ultimate compressive strength of the coal pillar; σ e q(x) represents the dynamic stress generated by blasting vibration; q(x) represents the load of the overburden layer on the supporting coal pillar under non-uniformly distributed load, considering the effective area theory. Since the supporting coal pillar is subjected to the combined effects of the overlying strata load and the dynamic load of blasting, it is determined that: When Δ>0, the coal pillar is in a stable state; When Δ=0, the coal pillar is in a critical state of instability; When Δ < 0, the coal pillar is in an unstable state; Step 3: Based on the single-span simply supported beam theory in structural mechanics, establish a model relating the maximum bending moment and tensile stress of the coal pillar roof under dynamic-static load coupling, and establish a dynamic failure criterion for the roof based on strength theory. The specific method is as follows: Step 3.1: Take the size of the coal pillar at the critical instability of the supporting coal pillar as the initial coal pillar size, and continuously reduce the initial coal pillar size until the supporting coal pillar is in a critical failure state, and establish the bending moment equation of the roof range of the unstable section of the supporting coal pillar. Step 3.2: Based on the bending moment equation of the roof of the unstable section of the supporting coal pillar, calculate the maximum bending moment of a single-span simply supported beam. Further calculate the maximum tensile stress under dynamic-static load coupling. Then, based on the ultimate strength theory, calculate the dynamic safety factor F of the coal pillar roof under the combined action of static load and blasting dynamic load from the overlying strata. s ' As a criterion for dynamic failure of the coal pillar roof: Among them, the maximum bending moment M max The calculation formula is: ； Where m2 is the starting point of the single-span simply supported beam, n2 is the ending point of the single-span simply supported beam, and the expression for the intermediate variable R is: ； Maximum tensile stress σ tmax The expression is: ； The dynamic failure criterion F of the coal roof s ' The expression is: ； Among them, F s ' As a criterion for roof coal pillar failure, when F s ' When F > 1, it is in an effective state. s ' When F = 1, it is in a critical state. s ' When σ is less than 1, it is in a failed state; tl σ is the tensile strength of the coal pillar roof; tmax This represents the maximum tensile stress in a single-span simply supported beam under dynamic-static load coupling. Step 4: Based on the established dynamic instability criteria and roof dynamic failure criteria of the supporting coal pillar, establish a relationship model between the length of the coal pillar instability section and the ultimate collapse distance of the roof under different coal pillar widths, and evaluate the dynamic stability of the supporting coal pillar based on the relationship model.

2. The method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load under mining conditions according to claim 1, characterized in that: The final physical and mechanical parameters of each rock layer in step 1 include: Data on coal seam bulk density, bulk density of each overlying stratum, internal friction angle of the supporting coal pillar, cohesion of the supporting coal pillar, Poisson's ratio of the supporting coal pillar, tensile strength of the supporting coal pillar, and blasting vibration detection data.

3. The method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load under mining conditions according to claim 2, characterized in that: The specific method for step 2 is as follows: Step 2.1: Perform weighted averaging on the unit weights of the overlying rock strata to calculate the average unit weight of the overlying rock strata on the roof of the mining tunnel: Define the overlying rock layers on the top of the mining tunnel as n layers, with the unit weights of each overlying rock layer being: γ1, γ2, γ3, ..., γ n The corresponding average thicknesses are: h1, h2, h3, ..., h n The average unit weight of the overlying rock layers is... The calculation formula is: ； Step 2.2: Based on the average unit weight of each overlying rock stratum on the roof of the mining tunnel, calculate the actual load borne by the supporting coal pillar as the mining tunnel depth increases: The formula for calculating the non-uniformly distributed load actually borne by the supporting coal pillar is as follows: ； Where x is the position of the supporting coal pillar in the direction of its strike; γ is the unit weight of the coal seam; h1 is the thickness of the coal pillar roof; α is the end face slope angle; W m W represents the width of the lower mining tunnel in the end-face mining operation. n To support the width of the coal pillar; Step 2.3: Based on the Mohr-Coulomb strength theory and the load data obtained in Step 2.2, calculate the maximum vertical stress borne by the supporting coal pillar: The formula for calculating the maximum vertical stress is: ； Where φ is the internal friction angle of the supporting coal pillar; λ is the lateral pressure coefficient; and C is the cohesion of the supporting coal pillar.

4. The method for evaluating the dynamic stability of a coal pillar supported by a non-uniformly distributed load under mining conditions according to claim 3, characterized in that: The specific method for step 4 is as follows: Based on the dynamic instability criterion of the supporting coal pillar and the dynamic failure criterion of the roof, the length l1 of the unstable section of the supported coal pillar and the ultimate collapse length l2 of the roof of the mining tunnel under different coal pillar sizes are calculated. If l1 < l2, the entire mining chamber is in an effective state, then reduce the width dimension of the support coal pillar until l1 > l2. At this time, the support coal pillar is in a critical failure state or a failure state. Compare the widths W of all support coal pillars that satisfy l1 < l2 n , and the support coal pillar width with the smallest value is the minimum width to ensure the dynamic stability of the support coal pillar and is used as the final support coal pillar size.

Images