A method for calculating the range of pressure relief blasting and fracturing of a deep mine fan-shaped porous roof

Abstract

The application discloses a kind of deep mine fan-shaped porous roof pressure-relief blasting fracturing range calculation methods, by considering the typical characteristics of deep impact mine roof pressure-relief blasting, first, statistics roof pressure-relief blasting fan-shaped hole arrangement, surrounding rock mechanics attribute, stress environment and explosive performance parameter;Fan-shaped hole columnar charge in blast hole is equivalent to a certain number of unit spherical charge, and the rock around blast hole is finely meshed;By the dynamic stress field excited when each blast hole each unit spherical charge explodes is vector superposition, the dynamic stress field value of each grid point of rock at different time when fan-shaped porous explosion is solved, and dynamic stress field distribution nephogram is drawn;Determine the maximum radial compressive stress and maximum tangential tensile stress of each grid point of rock in the whole process of explosion, and draw distribution nephogram;Finally, the rock dynamic damage and crack propagation discriminant formula considering the comprehensive action of crustal stress and explosive stress is established, and the fan-shaped porous roof pressure-relief blasting fracturing range is calculated.

Description

Technical Field

[0001] This invention relates to the field of coal and rock dynamic disaster prevention and control technology, specifically to a method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines. Background Technology

[0002] In recent years, thick and hard roofs above coal seams have been a major factor in inducing rockburst and strong mine earthquake disasters. Through extensive engineering practice, roof pressure relief blasting has been proven to have a good effect on reducing rockburst and impact on thick and hard roofs, and has become a core element of my country's coal mine rockburst and strong mine earthquake disaster prevention and control system.

[0003] Currently, the design of roof pressure relief blasting schemes and parameters mainly relies on engineering experience. Parameter design primarily includes the number of boreholes, borehole angles, borehole lengths, and borehole spacing. Accurate calculation or determination of the rock fracturing range caused by roof pressure relief blasting is the most important basis for designing these parameters. In deep coal mines, roof pressure relief blasting often employs a fan-shaped, multi-hole, asymmetrical arrangement. Factors such as the number of boreholes, borehole locations, charge length, ground stress, and detonation location and direction significantly influence the blasting effect. However, current calculations of the fracturing range are mainly based on simple empirical formulas, considering only borehole diameter and charge decoupling coefficients. This often leads to underestimation or overestimation of the calculated results, thus affecting the effectiveness of rockburst prevention or excessively increasing prevention costs. Therefore, establishing a theoretical calculation method for the fracturing range of fan-shaped, multi-hole roof pressure relief blasting that considers factors such as the number of boreholes, borehole locations, charge length, ground stress, and explosive performance parameters is crucial for guiding roof pressure relief blasting parameter design and on-site production decisions, and is also a necessary requirement for further promoting the widespread application of this technology. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines. This method considers factors such as the number of boreholes, borehole locations, charge length, ground stress, and explosive performance parameters to determine the fracture range caused by pressure relief blasting of the fan-shaped porous roof. This method is of great significance for guiding the design of roof pressure relief blasting parameters and making on-site production decisions.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a method for calculating the fracturing range caused by pressure relief blasting of a fan-shaped porous roof in deep mines, the specific steps of which are as follows:

[0006] Step 1: Obtain the required parameters: First, calculate the parameters for the roof pressure relief blasting fan-shaped borehole layout, including borehole location, number of boreholes (m), borehole angle (θ), borehole diameter (R0), and charge length (L); then, calculate the mechanical properties and stress environment of the surrounding rock in the blasting area, including the uniaxial compressive strength of the rock (R). c Uniaxial tensile strength R tPoisson's ratio ν and ground stress level P0; statistical explosive performance parameters, including explosive diameter R1, density ρ0, and detonation velocity C. b ;

[0007] Step 2, Mesh Generation: Each of the m boreholes with a cylindrical charge is represented as an equivalent number of n boreholes with a radius of R. b The unit spherical explosive charge is used, and the rock around each borehole is divided into a fine grid.

[0008] Step 3: Obtain the dynamic stress field distribution cloud map: First, calculate the explosion time t of each unit spherical charge in each borehole based on the charge location, detonation direction, and detonation velocity parameters. i Next, the time T required for the dynamic stress wave excited by the explosion of each unit spherical explosive charge to propagate to each grid point of the rock in step two is calculated. i Then, based on the dynamic stress wave function excited by the explosion of the unit spherical explosive charge and its propagation attenuation function in high-stress rock, the dynamic stress field σ excited at each grid point in the rock during the explosion of each unit spherical explosive charge in each borehole is determined. c1 (D j The variation of ,t) with time t, and thus the dynamic stress field σ borne by each grid point of the rock at time t, caused by the explosion of each spherical explosive charge in each borehole. c1 (D j By performing vector superposition on (t), the superimposed dynamic stress field value σ at all grid points at time t is obtained. c (D j Finally, dynamic stress field distribution cloud maps corresponding to different times are drawn.

[0009] Step 4: Determine the maximum radial compressive stress and the maximum tangential tensile stress: First, obtain the superimposed dynamic stress field value σ over the time range t during the entire explosion process of each borehole. c (D j The maximum radial compressive stress σ is determined by selecting the maximum value from the given values ​​(t, t). cmax Then, the maximum tangential tensile stress value σ is calculated according to the known formula. tmax And plot the distribution contour maps of the maximum radial compressive stress and the maximum tangential tensile stress;

[0010] Step 5: Determine the cracking range caused by the pressure relief blasting of the fan-shaped porous roof: Establish a rock dynamic failure and crack propagation discrimination formula that considers the combined effects of ground stress and explosion stress. Combine the maximum radial compressive stress value and the maximum tangential tensile stress value from Step 4 to finally calculate the cracking range caused by the pressure relief blasting of the fan-shaped porous roof.

[0011] Furthermore, in step two, the grid size is related to the calculation accuracy. The smaller the grid size, the higher the calculation accuracy. To ensure the calculation accuracy, the grid size should not exceed 0.2m × 0.2m.

[0012] Furthermore, in step three, the explosion time t is calculated. i And the time T required for dynamic stress waves to propagate to each grid point in the rock. i Specifically:

[0013] Assume the explosion stress wave velocity is C. b The position of the first detonating spherical charge is S0(x0, y0), and the position of the i-th spherical charge is S... i (x i y i Then, the explosion time t of the i-th spherical explosive charge in the borehole is... i for:

[0014]

[0015] Assume the coordinates of point P on the rock grid are P j (x j y j If the dynamic stress wave generated by the explosion of the i-th unit spherical explosive charge propagates to each grid point of the rock, then the time T required for this wave to reach all grid points is... i for:

[0016]

[0017] Furthermore, in step three, the attenuation function and the dynamic stress field σ c1 (D j The variation of ,t) with time t, and the superimposed dynamic stress field value σ at all grid points at time t. c (D j The specific calculation process for ,t) is as follows:

[0018] The dynamic stress wave function σ excited by the explosion of a single spherical explosive charge c1 (D,t) is calculated as follows:

[0019]

[0020] In the formula, P D Let be the stress wave amplitude at a distance D from the unit spherical explosive charge, and g(t) be the stress wave equation excited by the unit spherical explosive charge:

[0021] g(t)=ζ[e -At -e -Bt ]

[0022] In the formula, A, B, and ζ are constant coefficients of the stress wave equation;

[0023] The attenuation function of the explosion stress wave propagating in high-stress rock is specifically calculated as follows:

[0024]

[0025] In the formula, p d This represents the initial compressive stress of the explosion stress wave at the borehole wall; The proportional distance is equal to the distance D from the rock grid point to the center of the borehole and the equivalent radius R of the borehole. b The ratio of α(P0) to α(P0) is the explosion stress attenuation index related to ground stress.

[0026] The dynamic stress field σ generated at each grid point in the rock by the explosion of the spherical explosive charge in each borehole unit. c1 (D j The specific formula for the change of (t) with time t is:

[0027]

[0028] The dynamic stress field σ experienced by each rock grid point at time t, induced by the spherical explosive charges of each borehole and unit. c1 (D j Vector superposition is performed on the values ​​of the superimposed dynamic stress field σ at all grid points at time t. c (D j Finally, dynamic stress field distribution cloud maps corresponding to different times are plotted.

[0029] The superimposed dynamic stress field value σ c (D j The calculation process for t is as follows: Since the fan-shaped hole consists of m blast holes, when the m blast holes are detonated simultaneously, at point P in the rock grid... j (x j y j The superimposed stress field generated is:

[0030]

[0031] Furthermore, the specific discriminant formula in step five is as follows:

[0032] Based on the in-situ stress P0 of the rock in the blasting area obtained in step one, the uniaxial compressive strength R of the rock... c uniaxial tensile strength R of rock t Establish a formula for determining whether rocks are damaged under the action of explosive stress waves:

[0033] Crushing zone: σ cmax >4R c +10P0

[0034] Fractured region: σ tmax >R t

[0035] The range of rock fracture caused by decompression blasting under the combined action of ground stress and blasting stress wave can be calculated using the above discrimination criteria.

[0036] Compared with existing methods for calculating the fracture range caused by roof pressure relief blasting in coal mines, this invention can take into account the typical characteristics of roof pressure relief blasting in deep impact mines, namely, the asymmetrical fan-shaped multi-hole arrangement and the complex blasting environment. First, the arrangement of the fan-shaped boreholes for roof pressure relief blasting, the mechanical properties of the surrounding rock, the stress environment, and the performance parameters of the explosives were statistically analyzed. The columnar charges in the fan-shaped boreholes were equated to a certain number of unit spherical charges, and the rock surrounding the boreholes was finely meshed. By vector superposition of the dynamic stress fields generated by the explosion of each unit spherical charge in each borehole, the dynamic stress field values ​​of each grid point in the rock at different times during the fan-shaped multi-hole explosion were calculated, and corresponding dynamic stress field distribution cloud maps were drawn. The maximum radial compressive stress and maximum tangential tensile stress values ​​of each grid point in the rock were determined throughout the entire fan-shaped multi-hole explosion process, and distribution cloud maps of the maximum radial compressive stress and maximum tangential tensile stress were drawn. Finally, a rock dynamic failure and fracture propagation discrimination formula considering the combined effects of ground stress and explosive stress was established, and the fracture range (including the pulverization zone and the fracture zone) caused by the roof pressure relief blasting of the fan-shaped multi-hole boreholes was calculated. This invention, by considering factors such as the number and location of boreholes, charge length, ground stress, and explosive performance parameters, achieves accurate calculation of the dynamic stress field generated by fan-shaped multi-hole pressure relief blasting under deep high-stress conditions. It also establishes a rock dynamic damage and fracture propagation discrimination formula that comprehensively considers the combined effects of ground stress and explosive stress, ultimately obtaining a more accurate blasting-induced fracture range. This invention provides more guidance for the design of schemes and parameters for fan-shaped multi-hole roof pressure relief blasting in deep impact mines, helping to ensure safe mine production and save on impact prevention costs. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the location and arrangement of the fan-shaped multi-hole pressure relief blasting boreholes in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the equivalent unit spherical charge package and rock grid division of the columnar charge in the borehole in an embodiment of the present invention;

[0039] Figure 3 This is a quantitative relationship diagram between the explosion stress attenuation index and the ground stress in an embodiment of the present invention;

[0040] Figure 4 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock during the explosion process in an embodiment of the present invention at t=0.2ms;

[0041] Figure 5 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock during the explosion process in an embodiment of the present invention at t=0.5ms.

[0042] Figure 6This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock at t=0.8ms during the explosion process in an embodiment of the present invention.

[0043] Figure 7 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock at t=1.1ms during the explosion process in an embodiment of the present invention.

[0044] Figure 8 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock at t=1.4ms during the explosion process in an embodiment of the present invention.

[0045] Figure 9 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock at t=1.7ms during the explosion process in an embodiment of the present invention.

[0046] Figure 10 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock during the explosion process in an embodiment of the present invention at t=2.0ms.

[0047] Figure 11 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock during the explosion process in an embodiment of the present invention at t=2.3ms.

[0048] Figure 12 This is a cloud map showing the distribution of superimposed dynamic stress field values ​​at all grid points of the rock at t=2.6ms during the explosion process in this embodiment of the invention;

[0049] Figure 13 This refers to the maximum radial compressive stress and the distribution range of the explosion fragmentation zone at each grid point in the rock during the entire time range of the fan-shaped hole explosion process in this embodiment of the invention.

[0050] Figure 14 This refers to the maximum tangential tensile stress and the distribution range of the explosion fracture zone at each grid point in the rock during the entire time range of the fan-shaped hole explosion process in this embodiment of the invention. Detailed Implementation

[0051] The present invention will be further described below.

[0052] Example: In this example, a set of fan-shaped holes consists of three boreholes with different inclination angles and lengths, arranged as follows: Figure 1 As shown, the specific steps are as follows:

[0053] Step 1: Obtain the required parameters: First, calculate the layout parameters of the roof pressure relief blasting sector holes, including the hole positions; the number of holes m = 3; the hole angles θ1 = 30°, θ2 = 40°, θ3 = 50°; the hole diameter R0 = 54mm; and the lengths L of holes #1, #2, and #3 respectively. t1 =10m, Lt2 =12m, L t3 =15m; Charge length L c1 =5m, L c2 =6m, L c3 =7m; Detonation position S 01 (3.21, 3.83), S 02 (4.60, 3.86), S 03 (6.93, 4.00); the detonation direction was forward; the mechanical properties and stress environment of the surrounding rock in the blasting area were statistically analyzed, including the rock compressive strength R. c =120MPa, tensile strength R t =8MPa, Poisson's ratio ν = 0.25 and ground stress P0 = 10MPa; Statistical analysis of explosive performance parameters, including explosive radius R1 = 40mm and density ρ0 = 1100kg / m³. 3 Explosion speed parameter C b = 3600m / s.

[0054] Step 2, Mesh Generation: Each of the three boreholes is represented by a cylindrical charge of quantity n and radius R. b The equivalent radius of the unit spherical propellant charge is related to the radius of the cylindrical propellant charge as follows: R b = 1.2247R1, therefore the equivalent radius R of the unit spherical charge for the three boreholes is 1.2247R1. b The solution is 49mm, but for ease of calculation, this embodiment uses 50mm. Therefore, borehole #1 is divided into 50 spherical charges, borehole #2 into 60 spherical charges, and borehole #3 into 70 spherical charges, as shown below. Figure 2 As shown. Next, a finer grid was created around the borehole; in this embodiment, the grid size was chosen to be 0.2m × 0.2m.

[0055] Step 3: Obtain the dynamic stress field distribution cloud map: First, calculate the explosion time t of each unit spherical charge in the three boreholes based on the charge location, detonation direction, and detonation velocity parameters. i Specifically:

[0056] Assume the coordinates of the i-th spherical explosive charge in borehole #1 are S. 1i (x 1i y 1i The coordinates of the i-th spherical explosive charge in borehole #2 are S. 2i (x 2i y 2i The coordinates of the i-th spherical explosive charge in borehole #3 are S. 3i (x 3i y 3i According to the three blast hole detonation positions mentioned above, S is... 01(3.21, 3.83), S 02 (4.60, 3.86), S 03 (6.93, 4.00); then the explosion time t of the i-th spherical unit charge in boreholes #1, #2, and #3 is... 1i , t 2i , t 3i They are respectively:

[0057]

[0058]

[0059]

[0060] Next, the time T required for the dynamic stress wave generated by the explosion of each unit spherical explosive charge to propagate to each grid point of the rock in step two is calculated. i Specifically:

[0061] Assume the coordinates of point P on the rock grid are P j (x j y j If the time T is the time it takes for the explosive stress wave generated by the i-th explosive charge in boreholes 1#, 2#, and 3# to propagate to the rock grid point, then... 1i T 2i T 3i They are respectively:

[0062]

[0063]

[0064]

[0065] Then, based on the dynamic stress wave function excited by the explosion of a unit spherical explosive charge and its propagation attenuation function in high-stress rock, specifically:

[0066] The dynamic stress wave function σ excited by the explosion of a single spherical explosive charge c1 (D,t) is calculated as follows:

[0067]

[0068] In the formula, P D Let be the stress wave amplitude at a distance D from the unit spherical explosive charge, and g(t) be the stress wave equation excited by the unit spherical explosive charge:

[0069] g(t)=ζ[e -At -e -Bt ]

[0070] In the formula, A, B, and ζ are constant coefficients of the stress wave equation, with values ​​of A = 0.008, B = 0.012, and ζ = 6.75, respectively.

[0071] The formula for calculating the attenuation of dynamic stress waves excited by the explosion of a single spherical explosive charge in high-stress rock can be used as follows:

[0072]

[0073] In the formula, p d The initial stress of the explosion stress wave at the borehole wall can be calculated based on parameters such as explosive density, explosive detonation velocity, and charge decoupling coefficient, according to existing theories. In this embodiment, p d =2940MPa; The distance D from the rock grid point to the center of the borehole is proportional to the equivalent radius R of the borehole. b The ratio; α(P0) is the explosion stress attenuation index related to ground stress, and the relationship between α and P0 is shown in the figure. Figure 3 As shown, in this embodiment, P0 = 10 MPa, then α = 2.33.

[0074] Determine the dynamic stress field σ generated at each grid point in the rock during the explosion of the spherical explosive charge in each of the three boreholes. c1 (D j The change of ,t) with time t is as follows:

[0075]

[0076] The dynamic stress fields generated by the explosion from all spherical explosive charges in the three boreholes and experienced by each grid point on the rock at time t are vector-superimposed to obtain the superimposed dynamic stress field value σ at all grid points at time t. c (D j ,t);

[0077]

[0078] In this embodiment, the superimposed dynamic stress field values ​​at all grid points of the rock were calculated using nine time points: t=0.2ms, t=0.5ms, t=0.8ms, t=1.1ms, t=1.4ms, t=1.7ms, t=2.0ms, t=2.3ms, and t=2.6ms. Finally, dynamic stress field distribution cloud maps corresponding to different time points were plotted. The calculation results and distribution cloud maps are shown below. Figures 4 to 12 .

[0079] Step 4: Determine the maximum radial compressive stress and the maximum tangential tensile stress: First, obtain the superimposed dynamic stress field value σ over the time range t during the entire explosion process of each borehole. c (D jThe maximum radial compressive stress σ is determined by selecting the maximum value from the given values ​​(t, t). cmax Then, the maximum tangential tensile stress value σ is calculated according to the known formula. tmax And generate corresponding cloud maps respectively, such as Figure 13 and 14 As shown;

[0080] Step 5: Determine the fracture range caused by the pressure relief blasting of the fan-shaped porous roof: Establish a rock dynamic failure and fracture propagation discrimination formula that considers the combined effects of in-situ stress and blast stress, specifically as follows:

[0081] Based on the obtained in-situ stress P0 = 10 MPa in the rock of the blasting area, the uniaxial compressive strength of the rock is R. c =120MPa, the uniaxial tensile strength of the rock is R t =8MPa; The formula for determining whether rock will fail under the action of blasting stress wave is:

[0082] Crushing zone: σ cmax >4R c +10P0 = 580MPa

[0083] Fractured region: σ tmax >R t =8MPa

[0084] The range of the rock fragmentation zone under the action of in-situ stress and blasting stress wave in this embodiment can be calculated using the above discrimination formula. Figure 13 The area within the black curve is the fracture zone. Figure 14 Within the area of ​​the black curve, the final determination of the fracturing range caused by the pressure relief explosion of the fan-shaped porous top plate is obtained.

[0085] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines, characterized in that, The specific steps are as follows: Step 1: Obtain the required parameters: First, calculate the parameters for the roof pressure relief blasting fan-shaped borehole layout, including borehole location, number of boreholes (m), borehole angle (θ), borehole diameter (R0), and charge length (L); then, calculate the mechanical properties and stress environment of the surrounding rock in the blasting area, including the uniaxial compressive strength of the rock (R). c Uniaxial tensile strength R t Poisson's ratio ν and ground stress level P0; Statistical analysis of explosive performance parameters, including explosive diameter R1, density ρ0, and detonation velocity C. b ; Step 2, Mesh Generation: Each of the m boreholes with a cylindrical charge is represented as an equivalent number of n boreholes with a radius of R. b The unit spherical explosive charge is used, and the rock around each borehole is divided into a fine grid. Step 3: Obtain the dynamic stress field distribution cloud map: First, calculate the explosion time t of each unit spherical charge in each borehole based on the charge location, detonation direction, and detonation velocity parameters. i Next, the time T required for the dynamic stress wave excited by the explosion of each unit spherical explosive charge to propagate to each grid point of the rock in step two is calculated. i Then, based on the dynamic stress wave function excited by the explosion of the unit spherical explosive charge and its propagation attenuation function in high-stress rock, the dynamic stress field excited at each grid point in the rock during the explosion of each unit spherical explosive charge in each borehole is determined. The change over time t will further reveal the dynamic stress field of the rock grid points at time t, generated by the spherical explosive charges in each borehole. By performing vector superposition, the superimposed dynamic stress field values ​​at all grid points at time t are obtained. Finally, dynamic stress field distribution cloud maps corresponding to different times are plotted. The specific calculation process is as follows: The dynamic stress wave function σ excited by the explosion of a single spherical explosive charge c1 (D, t) is calculated as follows: In the formula, P D t represents the stress wave amplitude at a distance D from the unit spherical explosive charge. i Let T be the detonation time of the i-th spherical explosive charge in the borehole. i Let be the time required for the dynamic stress wave excited by the explosion of the i-th unit spherical explosive charge to propagate to all grid points in the rock, and g(t) be the equation of the stress wave excited by the unit spherical explosive charge: In the formula, A, B, and ζ are constant coefficients of the stress wave equation; The attenuation function of the explosion stress wave propagating in high-stress rock is specifically calculated as follows: In the formula, p d This represents the initial compressive stress of the explosion stress wave at the borehole wall; The proportional distance is equal to the distance D from the rock grid point to the center of the borehole and the equivalent radius R of the borehole. b The ratio of α(P0) to α(P0) is the explosion stress attenuation index related to ground stress. The dynamic stress field generated at each grid point of the rock by the explosion of the spherical explosive charge in each borehole unit. The specific formula for how it changes with time t is: Where, x i y i Let x be the coordinates of the i-th spherical medicine packet. j y j Rock grid point P j The coordinates; The dynamic stress field experienced by each rock grid point at time t, induced by the spherical explosive charges of each borehole and unit. By performing vector superposition, the superimposed dynamic stress field values ​​at all grid points at time t are finally obtained. Finally, dynamic stress field distribution cloud maps corresponding to different times are drawn; Among them, the superimposed dynamic stress field value The calculation process is as follows: Since the fan-shaped borehole consists of m boreholes, when the m boreholes are detonated simultaneously, at point P in the rock grid... j (x) j , y j The superimposed stress field generated is: ； Step 4: Determine the maximum radial compressive stress and maximum tangential tensile stress values: First, obtain the superimposed dynamic stress field values ​​over the entire time range (t) of the explosion process in each borehole. The maximum value selected from these values ​​is the maximum radial compressive stress value. Then, the maximum tangential tensile stress value is calculated according to the formula. And plot the distribution cloud maps of the maximum radial compressive stress and the maximum tangential tensile stress; Step 5: Determine the cracking range caused by the pressure relief blasting of the fan-shaped porous roof: Establish a rock dynamic failure and crack propagation discrimination formula that considers the combined effects of ground stress and explosion stress. Combine the maximum radial compressive stress value and the maximum tangential tensile stress value from Step 4 to finally calculate the cracking range caused by the pressure relief blasting of the fan-shaped porous roof.

2. The method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines according to claim 1, characterized in that, In step two, the grid size is related to the calculation accuracy. The smaller the grid size, the higher the calculation accuracy. To ensure the calculation accuracy, the grid size should not exceed 0.2m × 0.2m.

3. The method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines according to claim 1, characterized in that, In step three, the explosion time t is calculated. i And the time T required for dynamic stress waves to propagate to each grid point in the rock. i Specifically: Assume the explosion stress wave velocity is C. b The position of the first detonating spherical charge is S0(x0, y0), and the position of the i-th spherical charge is S... i (x) i , y i If , then the explosion time t of the i-th spherical explosive charge in the borehole is... i for: Assume rock grid point P j coordinates (x) j , y j Then, the time T required for the dynamic stress wave excited by the explosion of the i-th unit spherical explosive charge to propagate to each grid point of the rock is... i for: 。 4. The method for calculating the fracture range caused by pressure relief blasting of a fan-shaped porous roof in deep mines according to claim 1, characterized in that, The specific discriminant formula in step five is as follows: Based on the in-situ stress P0 of the rock in the blasting area obtained in step one, the uniaxial compressive strength R of the rock... c uniaxial tensile strength R of rock t Establish a formula for determining whether rocks are damaged under the action of explosive stress waves: Grinding area: Fractured zone: The range of rock fracture caused by decompression blasting under the combined action of ground stress and blasting stress wave can be calculated using the above discrimination criteria.

Images