Method for researching action mechanism of peripheral hole blasting on top plate based on vibration theory

Abstract

The invention discloses a method for researching an action mechanism of peripheral hole blasting on a roof based on a vibration theory, which comprises the following steps of: after smooth blasting, full-section one-time drifting and blasting, crushing rocks by high-temperature and high-pressure detonation gas and diffusing outwards, acting on the roof in the forms of shock waves and stress waves, and attenuating a dynamic load acting on the roof into the stress waves. By means of the method, it can be obtained that the top plate cannot be subjected to pressure damage due to the blasting dynamic load, meanwhile, the peak load of the blasting dynamic load borne by the top plate is exponentially decreased along with the increase of the blast hole length and the charging diameter and is exponentially increased along with the decrease of the charging length, and meanwhile the tension-compression zoning phenomenon generated when the top plate acts on the blasting dynamic load is obtained; and the tension-compression inflection point is close to the two clamped ends, so that the tension-compression zoning phenomenon is generated due to the fact that the beam resists the bending moment of the fixed ends, and dangerous areas in the vibration process are arranged near the support and the middle point of the beam.

Description

Technical Field

[0001] The present invention relates to the technical field of blasting mechanism research, and in particular to a method for studying the mechanism of action of peripheral hole blasting on roof based on vibration theory. Background Art

[0002] Rapid excavation is one of the hot issues in coal industry research. With the rapid development of coal mine excavation machinery and equipment in recent years, the efficiency of comprehensive excavation has been significantly improved. Although the efficiency of blasting excavation is far lower than that of comprehensive excavation and the safety is also lower, it still accounts for a large proportion in coal mine tunnel excavation due to its better geological adaptability. Blasting first acts on the periphery of the blasthole in the form of shock waves, and then gradually decays into stress waves and seismic waves. The roof is at risk of compressive damage under the action of stress waves. At the same time, the up and down vibration of the roof particles makes it appear as deflection on a macro scale, which poses a risk of tensile damage, that is, the roof The vibration effect of the roof before blasting is supported by the rocks below. The blasting causes the roof to lose support from below, and the roof changes from a three-dimensional stress state to a two-dimensional stress state, showing an unloading effect. Under the influence of the vibration effect and the unloading effect, the stability of the roof is bound to be seriously affected, and the risk of over-excavation, under-excavation, and even falling and injuring people will increase. The blasting rock must first be broken and thrown out during blasting excavation. Scholars have conducted systematic research on the arrangement of blastholes, blasthole size, and amount of explosives from the perspective of rock breaking, which provides an important basis for the selection of blasting parameters.

[0003] In blasting design, the charge amount and blasthole depth of the slot holes and auxiliary holes are large, but they are generally arranged in the middle and lower part of the tunnel, far away from the roof. Studies have shown that the explosion stress decays exponentially in the rock. The load of the slot holes and auxiliary holes on the roof is small, and the threat to the stability of the roof is relatively small. The peripheral holes must ensure that the cross-section and shape of the tunnel meet the design requirements. The upper peripheral holes are close to the roof and the load acting on the roof is large. If the blasting parameters of the peripheral holes are unreasonable, it is easy to cause over-excavation, under-excavation, or even large-scale collapse of the roof. After searching, the research on the blasting parameters of the peripheral holes is still blank at this stage. Summary of the invention

[0004] The purpose of the present invention is to solve the shortcomings of the prior art and propose a research method based on vibration theory on the mechanism of action of peripheral eye blasting on the roof.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The research method of the mechanism of the peripheral hole blasting on the roof based on the vibration theory adopts smooth blasting and the whole section is formed at one time. After the blasting, the high-temperature and high-pressure detonation gas breaks the rock and diffuses outward, which will act on the roof in the form of shock wave and stress wave. The dynamic load acting on the roof is attenuated into stress wave, and the peak value expression of the dynamic load on the blasthole wall is:

[0007]

[0008] In the formula, ρ 0 is the top plate density, 2300kg / m 3 ; D is the detonation velocity, 3800m / s; γ is the isentropic index of the explosive, generally taken as 3.0; d c is the diameter of the medicine roll, 35mm; d b is the diameter of the blast hole, 42mm; l c is the charge length, 1.2m; l b is the blasthole length, 2.8m;

[0009] Due to geometric attenuation and energy loss during the propagation of stress waves, the stress peak value will continue to decrease. The relationship between the stress peak value and the distance can be expressed as:

[0010]

[0011] Where: is the relative distance, r is the distance from the center of the charge, r b is the blasthole radius. According to the blasting design, this calculation takes α stress decay exponent, α = 2-v / (1-v); Poisson's ratio v = 0.2, α = 1.75;

[0012] The stress waves generated by blasting different blastholes will interact with each other. Micro-difference blasting can make the stress waves superimposed to reduce the vibration effect. The cut holes and auxiliary holes are far away from the roof, and the stress decays quickly. This paper assumes that the blasting dynamic load on the roof comes from the surrounding holes. The peak load acting on the roof is obtained by formula (A2);

[0013] According to formulas (A1) and (A2), the peak load acting on the top plate during blasting is 6.73 MPa. 2 =13.07MPa and σ 3 =6.05MPa), the measured compressive strength of sandy mudstone is 35MPa;

[0014] According to the force conditions, the force balance of the separated body in the vertical direction and the moment balance equation around the center point of the separated body are written as

[0015]

[0016] Where ρ is the beam density; S is the cross-sectional area of ​​the beam. By Taylor series expansion, ignoring the second-order and higher-order terms, we have Substituting into equation (A3) we get

[0017]

[0018] From the relationship between bending moment and deflection in material mechanics

[0019]

[0020] Substituting into the differential equation of lateral vibration

[0021]

[0022] Then get

[0023]

[0024] Assume that the solution of equation (A7) is

[0025] w(x,t)=g(x)sinωt (A8)

[0026] Substituting equation (A8) into equation (A7) yields

[0027]

[0028] The characteristic equation corresponding to the above formula is

[0029]

[0030] Solved

[0031]

[0032] The general solution is

[0033]

[0034] Special solution

[0035]

[0036] Then the solution of equation (7) is

[0037]

[0038] The initial condition is that when t = 0, w(x, t) = 0. From the above formula (14), it can be seen that the initial condition is automatically satisfied. Now consider the boundary conditions:

[0039] The model is clamped on both sides, so the boundary conditions are

[0040]

[0041] make have to

[0042]

[0043] Solve the above equations and substitute them into equation (A14) to obtain the top plate deflection equation:

[0044] Rock is a brittle material, and its tensile strength is much lower than its compression and shear strength. When tensile failure occurs locally in the rock beam, it is equivalent to reducing the thickness of the rock beam, and the stress environment will be further deteriorated. Therefore, the tensile strength is used as the criterion for roof instability. During the vibration of the roof, the tensile stress at any time and any position is different. From material mechanics, it is known that the tensile stress is the largest at the position farthest from the neutral layer when the beam is bent. Therefore, the following failure criterion is established:

[0045]

[0046] The advantages of the present invention are as follows: through the method of the present invention, it can be concluded that the roof will not be compressed and damaged due to the blasting dynamic load. At the same time, the peak load of the blasting dynamic load on the roof decreases exponentially with the increase of the blasthole length and the charge diameter, and increases exponentially with the decrease of the charge length. At the same time, the tension and compression zoning phenomenon generated by the roof when the blasting dynamic load acts is obtained, and the tension and compression inflection point is close to the two fixed support ends. It is also concluded that the tension and compression zoning phenomenon is caused by the beam resisting the bending moment of the fixed end, and the vicinity of the support and the midpoint of the beam is a dangerous area in the vibration process. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is the model diagram of the lateral forced vibration of the beam with fixed support at both ends;

[0048] Figure 2 is a schematic diagram of beam deflection;

[0049] Figure 3 This is the calculation model diagram of beam lateral vibration;

[0050] Figure 4 is the periodic variation of the stress on the top plate with time;

[0051] Figure 5 It is the actual variation curve of the maximum stress on the top plate surface;

[0052] Figure 6 It is the variation law of the maximum stress on the top plate surface in the length direction;

[0053] Figure 7 This is the law of influence of blasthole diameter on maximum tensile stress. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] The research method of the mechanism of the effect of peripheral eye blasting on the roof based on vibration theory adopts smooth blasting, and the whole section is formed at one time. After the blasting, the high-temperature and high-pressure detonation gas breaks the rock and diffuses outward, which will act on the roof in the form of shock waves and stress waves. The upper rock layer hinders the movement of the roof. If the blasting energy is too large, the roof may be compressed or tensile due to deflection. The unloading effect of the lower rock being broken and thrown out seriously deteriorates the stress condition of the roof. The blasting dynamic load acting on the roof is a function of time. During the dynamic load action time, the roof deflects upward, but when the blasting load disappears, due to the imbalance of force and elastic energy, the roof will rebound to the tunnel space and produce vibration. Due to the damping effect, the amplitude will gradually decrease and eventually disappear and reach static equilibrium.

[0056] The roof not only has to bear the dynamic load from below, but also the dynamic resistance from the overburden, which belongs to the forced vibration problem in vibration theory. From a macroscopic point of view, the roof will fluctuate up and down near the equilibrium zone, and the roof deflection curve is different at every moment. From material mechanics, it can be seen that during the up and down vibration of the roof, one side of the upper and lower surfaces must be tensile and the other side must be compressed. The compressive strength of rock materials is much higher than the tensile strength, and the roof is prone to tensile failure and instability. The dynamic load acting on the roof is attenuated into a stress wave, and the peak value expression of the dynamic load on the blasthole wall is:

[0057]

[0058] In the formula, ρ 0 is the top plate density, 2300kg / m 3 ; D is the detonation velocity, 3800m / s; γ is the isentropic index of the explosive, generally taken as 3.0; d c is the diameter of the medicine roll, 35mm; d b is the diameter of the blast hole, 42mm; l c is the charge length, 1.2m; l b is the blasthole length, 2.8m;

[0059] Due to geometric attenuation and energy loss during the propagation of stress waves, the stress peak value will continue to decrease. The relationship between the stress peak value and the distance can be expressed as:

[0060]

[0061] Where: is the relative distance, r is the distance from the center of the charge, r b is the blasthole radius. According to the blasting design, this calculation takes α stress decay exponent, α = 2-v / (1-v); Poisson's ratio v = 0.2, α = 1.75;

[0062] The stress waves generated by blasting different blastholes will interact with each other. Micro-difference blasting can make the stress waves superimposed to reduce the vibration effect. The cut holes and auxiliary holes are far away from the roof, and the stress decays quickly. This paper assumes that the blasting dynamic load on the roof comes from the surrounding holes. The peak load acting on the roof is obtained by formula (A2);

[0063] According to formulas (A1) and (A2), the peak load acting on the top plate during blasting is 6.73 MPa. 2 =13.07MPa and σ 3 =6.05MPa), the measured compressive strength of sandy mudstone is 35MPa; during blasting excavation, the strain rate is very large, and the dynamic compressive strength growth factor can reach 2. This strength is higher than the peak load acting on the roof during blasting. Therefore, at the beginning of blasting, the compressive stress generated by the blasting on the roof will not damage the roof. When the length of the blasthole remains unchanged, as the length of the charge increases, the peak stress acting on the roof shows a power exponential increase trend. It can be concluded that the peak load acting on the roof is very sensitive to the blasthole diameter, drilling length and charge length, and the blasting parameters will have an important impact on the stability of the roof.

[0064] During blasting, the roof moves under the vibration effect and unloading effect, and the two sides of the tunnel can provide reaction force and bending moment for the roof. Therefore, the model constructed in this embodiment is along the span direction of the tunnel (the model length is the tunnel width), and the boundary is set to be fixed at both ends.

[0065] The dynamic load on the lower surface of the roof caused by blasting is a function of time. Since any function can be expanded by Fourier series, the dynamic load can be expressed as the addition of trigonometric functions. However, studies have shown that there is a dominant frequency in blasting loads. Therefore, it is assumed that the dynamic load expression on the lower surface of the roof is, starting from the time of blasting.

[0066] When the surrounding holes are blasted, when the roof is deflected upward under the action of dynamic load, the upper roof will prevent the roof from continuing to move upward through squeezing. The greater the deflection, the greater the resistance. Assuming that the load on the upper surface of the roof is also in a sinusoidal relationship with time, the expression is, and the direction is downward. For the convenience of theoretical analysis, the following assumptions are made:

[0067] ① During blasting, the coal and rock below the roof will be thrown out along the length of the blasthole, and the broken rock will no longer provide support for the roof; ② During the vibration process, the dynamic load above the roof is evenly distributed, and the bottom is also subject to a uniformly distributed dynamic load, with the direction perpendicular to the roof; ③ The damping effect is not considered during the vibration process of the roof; ④ The roof is an elastic deformable body.

[0068] Figure 1is the lateral forced vibration model of the fixed-end beam. In the figure, b is the extrusion stress when the maximum deflection occurs, MPa; l is the tunnel width, m; ω is the dominant frequency of the blasting load, 40Hz. Assume that the fixed-end beam has the following shape at any moment of vibration: Figure 2 f(x,t) is the lateral disturbance load on the load caused by the blasting action, which is Figure 1 The difference in lateral load. w(x,t) is the deflection of the beam. The red area microelement is used as the separated body, and the force diagram of the separated body is obtained ( Figure 3 ), M and Q are the bending moment and shear force on the interface, respectively.

[0069] According to the force conditions, the force balance of the separated body in the vertical direction and the moment balance equation around the center point of the separated body are written as

[0070]

[0071] Where ρ is the beam density; S is the cross-sectional area of ​​the beam. By Taylor series expansion, ignoring the second-order and higher-order terms, we have Substituting into equation (A3) we get

[0072]

[0073] From the relationship between bending moment and deflection in material mechanics

[0074]

[0075] Substituting into the differential equation of lateral vibration

[0076]

[0077] Then get

[0078]

[0079] Assume that the solution of equation (A7) is

[0080] w(x,t)=g(x)sinωt (A8)

[0081] Substituting equation (A8) into equation (A7) yields

[0082]

[0083] The characteristic equation corresponding to the above formula is

[0084]

[0085] Solved

[0086]

[0087] The general solution is

[0088]

[0089] Special solution

[0090]

[0091] Then the solution of equation (7) is

[0092]

[0093] The initial condition is that when t = 0, w(x, t) = 0. From the above formula (14), it can be seen that the initial condition is automatically satisfied. Now consider the boundary conditions:

[0094] The model is clamped on both sides, so the boundary conditions are

[0095]

[0096] make have to

[0097]

[0099] Solve the above equations and substitute them into equation (A14) to obtain the top plate deflection equation:

[0100] Rock is a brittle material, and its tensile strength is much lower than its compression and shear strength. When tensile failure occurs locally in the rock beam, it is equivalent to reducing the thickness of the rock beam, and the stress environment will be further deteriorated. Therefore, the tensile strength is used as the criterion for roof instability. During the vibration of the roof, the tensile stress at any time and any position is different. From material mechanics, it is known that the tensile stress is the largest at the position farthest from the neutral layer when the beam is bent. Therefore, the following failure criterion is established:

[0101]

[0102] Assume that the design length of the test tunnel is 2056.9m. The maximum measured principal stress is the vertical stress, which is 16.23MPa. The intermediate principal stress and the minimum principal stress are 13.7MPa and 6.05MPa respectively. The normal tunnel section of the 3203 high-pressure extraction tunnel is 18.5m away from the coal seam roof. Based on the engineering geological conditions of the test tunnel, the elastic modulus of the roof is E = 1GPa. The tensile strength of the direct roof [σ t ]=2.2MPa. The compressive stress of the upper roof on the immediate roof is b=5.86MPa.

[0103] Substituting the test tunnel data into formula (A17) can obtain the roof stress distribution. Figure 4is the curve of the stress change over time at different positions of the beam. It can be seen that the top plate moves periodically under the dynamic load, and the amplitude of each position of the beam is different. It can be seen that the blasting time is generally within 10ms, and the real stress change trend of the top plate over time is as follows Figure 5 As shown in the figure. During the explosion process, there is a tension-compression partition phenomenon within the beam, and it increases approximately linearly with time. Figure 6 , starting from the fixed support end on the left side of the model, the stress on the beam surface is the maximum compressive stress at all times. As time goes by, the compressive stress also gradually increases. This is because the dynamic load below the top plate gradually increases and the upward deflection of the top plate increases. When the coordinates of the beam gradually increase, the compressive stress gradually decreases, and a tensile-compressive inflection point appears at 0.72m, and then enters the tensile stress zone. When the length of the beam reaches 2.78, it enters the compressive stress zone again.

[0104] After exceeding the tension-compression inflection point, the top plate enters the tensile stress zone. The closer to the midpoint of the beam, the greater the tensile stress. Since the model is symmetrical about the midpoint of the beam, when deflection occurs, the tensile stress at the midpoint of the beam is the largest, and the stress is symmetrically distributed.

[0105] The reason for the appearance of compressive stress near the fixed end is that compressive stress is generated in the beam to resist the bending moment of the fixed end. It can be imagined that if the two boundaries are simply supported, there will be no tension-compression partition phenomenon in the beam. Although the deflection curves on the upper surface of the beam are all greater than zero (moving upward), one side is a concave function and the other side is a convex function near the tension-compression inflection point. From formula (A17), it can be seen that the second-order derivative of the deflection curve is stress. According to mathematical knowledge, the second-order derivative of the concave function is positive and the convex function is negative. It can be seen that near the tension-compression inflection point, the stress has different signs. The tension-compression partition phenomenon makes it impossible to only consider the upper surface of the beam when considering the maximum stress. If the upper surface is in the compressive stress zone, the lower surface must be in the tensile stress zone. When judging whether the beam is unstable during vibration, the tension of the lower surface must be considered. According to symmetry, the magnitude of the compressive stress on the upper surface represents the magnitude of the tensile stress on the lower surface.

[0106] From the previous analysis, it can be seen that the maximum stress increases monotonically with the blasting time. In order to analyze the influence of blasthole length, charge length and blasthole diameter on stress, the blasting time t=0.01s is given, and the stress at this time is the maximum stress state of the roof.

[0107] It can be seen that when the charge length is constant, as the length of the blasthole increases, the peak stress acting on the top plate decreases, the deflection of the top plate decreases, and the tensile stress decreases. When the length of the blasthole is different, the stress value along the span direction of the beam is obtained by substituting it into formula (A17). From different positions of the top plate, when the length of the blasthole is different, there is a tensile and compressive partition phenomenon. The tensile stress is the largest in the middle of the beam, and there is a compressive stress zone near the fixed support end.

[0108] When the length of the blasthole is 1.4m, the absolute value of the compressive stress at the two boundaries of the model exceeds the tensile strength. When the beam is bent, the stress values ​​of the upper and lower surfaces are equal, and one side is under tension and the other side is under compression. It can be seen that local tensile failure may occur near the boundary of the lower surface of the model, which is not conducive to the stability of the roof. When the length of the blasthole continues to increase, the maximum tensile stress in the roof decreases significantly. When the length of the blasthole increases to 1.8m, the maximum tensile stress in the roof is reduced to 1.49MPa, and the roof is stable. Therefore, from the perspective of roof vibration stability, when the charge length of the test tunnel is 1.2m, the blasthole length of 1.8m can ensure the stability of the roof.

[0109] When the blasthole length is selected as 1.8m, the stress on the top plate surface at different charge lengths is obtained by substituting into formula (17). Because the blasthole length is 1.8m and the length of a single charge roll is 0.3m, the following 6 cases are set. As the charge length increases, the values ​​of the top plate in tension or compression are increasing, and the growth rate is very large. Taking the position near the midpoint of the beam as an example, when the charge length is 0.3m, the tensile stress is 0.02MPa, the stress is very small, and the top plate is stable. When the charge length reaches 1.8m, the tensile stress increases to 3.79MPa, which exceeds the tensile strength of the top plate, and the risk of instability of the top plate increases. From the perspective of different positions on the top plate, there is still a tension-compression partition phenomenon under different charge lengths. The middle position of the upper surface of the beam is tensile, and the end is compressed. The tension-compression inflection point changes the same as the blasthole length. The bold stress in the table indicates that when the charge length is equal to or exceeds 1.5m, the tensile stress generated in the middle of the upper surface of the roof is greater than the tensile strength, and at the same time, tensile failure will occur at the support position of the lower surface. When the charge length is 1.2m, the tensile stress generated on the upper surface of the roof is less than the tensile strength, and there will be no tensile failure on the lower surface. Therefore, when the blasthole length is 1.8m, the charge length of 1.2m will not cause tensile failure of the roof.

[0110] The length of the blasthole is fixed at 1.8m and the charge length is 1.2m. Substituting into formula (A17) we can analyze the stress distribution law under different blasthole diameters. Figure 7 As shown. It can be seen that as the diameter of the blasthole increases, the maximum tensile stress of the roof decreases exponentially. When the diameter of the blasthole is 36mm, the maximum tensile stress of the roof reaches 5.32MPa, which is greater than the tensile strength of the roof, and the risk of roof instability is high. When the diameter of the blasthole is 42mm, the maximum tensile stress of the roof will quickly become 2.11MPa, which is less than the tensile strength of the roof. Selecting a blasthole diameter of 42mm can ensure the stability of the roof.

Claims

1. A research method based on vibration theory on the mechanism of action of peripheral hole blasting on roof, characterized by: Smooth blasting is used to form a tunnel in the entire section at one time. After blasting, the high-temperature and high-pressure detonation gas breaks the rock and diffuses outward, acting on the roof in the form of shock waves and stress waves. The dynamic load acting on the roof decays into a stress wave, and the peak value of the dynamic load on the blasthole wall is expressed as: Where ρ0 is the top plate density, 2300kg / m 3 ; D is the detonation velocity, 3800m / s; γ is the isentropic index of the explosive, generally taken as 3.0; d c is the diameter of the medicine roll, 35mm; d b is the diameter of the blast hole, 42mm; l c is the charge length, 1.2m; l b is the blasthole length, 2.8m; Due to geometric attenuation and energy loss during the propagation of stress waves, the stress peak value will continue to decrease. The relationship between the stress peak value and the distance can be expressed as: Where: is the relative distance, r is the distance from the center of the charge, r b is the blasthole radius. According to the blasting design, this calculation takes α stress decay exponent, α = 2-v / (1-v); Poisson's ratio v = 0.2, α = 1.75; The stress waves generated by blasting different blastholes will interact with each other. Micro-difference blasting can make the stress waves superimposed to reduce the vibration effect. The cut holes and auxiliary holes are far away from the roof, and the stress decays quickly. This paper assumes that the blasting dynamic load on the roof comes from the surrounding holes. The peak load acting on the roof is obtained by formula (A2); According to formulas (A1) and (A2), the peak load acting on the top plate during blasting is 6.73 MPa. The compressive strength of the sandy mudstone was measured to be 35 MPa in a triaxial compression test conducted indoors (σ2 = 13.07 MPa and σ3 = 6.05 MPa). According to the force conditions, the force balance of the separated body in the vertical direction and the moment balance equation around the center point of the separated body are written as Where ρ is the beam density; S is the cross-sectional area of ​​the beam. By Taylor series expansion, ignoring the second-order and higher-order terms, we have Substituting into equation (A3) we get From the relationship between bending moment and deflection in material mechanics Substituting into the differential equation of lateral vibration Then get Assume that the solution of equation (A7) is w(x,t)=g(x)sinωt (A8) Substituting equation (A8) into equation (A7) we obtain The characteristic equation corresponding to the above formula is Solved The general solution is Special solution Then the solution of equation (7) is The initial condition is that when t = 0, w(x, t) = 0. From the above formula (14), it can be seen that the initial condition is automatically satisfied. Now consider the boundary conditions: The model is clamped on both sides, so the boundary conditions are make have to Solve the above equations and substitute them into equation (A14) to obtain the top plate deflection equation: Rock is a brittle material, and its tensile strength is much lower than its compression and shear strength. When tensile failure occurs locally in the rock beam, it is equivalent to reducing the thickness of the rock beam, and the stress environment will be further deteriorated. Therefore, the tensile strength is used as the criterion for roof instability. During the vibration of the roof, the tensile stress at any time and any position is different. From material mechanics, it is known that the tensile stress is the largest at the position farthest from the neutral layer when the beam is bent. Therefore, the following failure criterion is established:

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