A method for determining blast hole spacing based on ground improvement and left over suspended roof treatment

Abstract

The application discloses a blast hole spacing determination method based on ground improvement and left hanging roof treatment, which comprises the following steps: establishing a hanging roof goaf top arch structure treatment model, calculating the bending moment and the maximum tensile stress of the hanging arch roof; based on the relationship between the tensile stress and the tensile strength, calculating the safety thickness of the hanging arch roof; replacing the static tensile strength with the dynamic tensile strength to determine the hanging arch roof damage criterion considering the blasting collapse critical load; and obtaining the optimal solution of the blast hole spacing. Through the construction of the hanging roof goaf top arch structure treatment model, the comprehensive blasting peak value and equivalent pressure, and the optimization of the blast hole spacing, the application can effectively control the secondary damage of the mine rock mass fracture, underground water, external dynamic load and other engineering geological factors on the hanging arch, reduce the probability of secondary accidents such as the collapse of the hanging arch roof, impact earthquake, overburden sliding, surface subsidence and the like, and can eliminate the hidden danger of the hanging roof and strip the surface together with the goaf.

Description

Technical Field

[0001] The present invention belongs to the technical field of underground mine engineering geological disaster prevention and resource exploitation, and particularly relates to a method for determining blasthole spacing based on ground reform and exposure-remaining hanging roof management. Background Art

[0002] During caving mining, influenced by factors such as rock mass lithology, blasting organization and construction, and stope structural parameters, some working faces experience failure of blasting-induced caving after mining, resulting in the failure of the suspended arch roof in the goaf to collapse promptly. After the blasting-induced operation, the suspended arch roof, under its own weight, forms an arched suspended roof structure due to the stress arch effect. As mining progresses, widespread suspended roof problems have emerged in the mines. Furthermore, due to engineering geological factors such as rock mass fissures, groundwater, and external dynamic loads, the damage to the suspended arch roof has intensified, potentially leading to major accidents such as suspended arch roof collapse, impact earthquakes, overburden slippage, and surface subsidence, seriously impacting mine safety and production.

[0003] The open-pit deep hole blasting method is a method for managing hidden dangers in suspended roof goaf areas of mines by the caving method, which completely strips off the ground surface together with the goaf to form a certain open-pit mining boundary. From the ground surface to the top of the goaf, a safe thickness of the suspended arch roof is reserved, and the suspended arch roof of the goaf is collapsed by deep hole blasting technology to complete the filling, thereby managing the remaining goaf. Chinese invention patent CN113670146A discloses a method for blasting deep-buried goaf in the open air, which calculates the radius of the blasthole crushing zone and the fracture zone, clarifies the range of the blasthole spacing, determines the height of the lower blasting layer, the spacing between the upper open-pit layer and the lower downward layer, the total height of the downward layer blasting, and the height of the upper open-pit layer, and calculates the delay time between each layer and between holes in the detonation network, thereby overcoming the high clamping effect caused by the high thickness-span ratio of the deep-buried goaf. However, when the mine blasting-induced roof caving fails and an arched suspended roof structure is produced, this method is not applicable. It is impossible to obtain the optimal blasting hole spacing and eliminate the hidden dangers of suspended roofs, which is not conducive to the advancement of the "underground to open-pit" process of resource mining. Summary of the Invention

[0004] In order to solve at least one of the problems existing in the prior art, the present invention provides a method for determining the blasthole spacing based on the treatment of suspended roofs left over from underground conversion to exposed mining, which is used to determine the optimal blasthole spacing for open-pit deep hole blasting to treat arched suspended roof goafs, so as to eliminate the hidden dangers of suspended roofs and promote the process of "underground to open-pit" resource mining.

[0005] To achieve the purpose of the present invention, the present invention provides a method for determining the blasthole spacing based on the treatment of the remaining hanging roof after ground reform, comprising the following steps:

[0006] According to the treatment method of arched suspended roof goaf by open-pit deep hole downward blasting, the safe thickness of the suspended arch roof was reserved. On the basis of simplifying the suspended arch roof into a two-hinged arch, a top arch structure treatment model of the suspended roof goaf was constructed.

[0007] Based on the two-hinge arch theory, the bending moment and maximum tensile stress of the cantilevered arch roof are calculated. According to the basic condition that "when the maximum tensile stress of the cantilevered arch roof exceeds the tensile stress threshold that the stress arch bearing area can withstand, the cantilevered arch roof will collapse", the ultimate stable thickness within the stress arch bearing area, i.e., the safe thickness of the cantilevered arch roof h, is calculated. s .

[0008] The blasting load is equivalent to a uniformly distributed load acting on the ground with a preset safety thickness. The dynamic tensile strength is used instead of the static tensile strength to calculate the critical load of blasting collapse and determine the failure criterion of the suspended arch roof.

[0009] Under the condition that the uniformly distributed load of suspended arch roof blasting is equal to the blasting peak equivalent pressure at the maximum dynamic tensile strength, the optimal solution of blasting hole spacing is determined.

[0010] Preferably, according to the method for treating suspended goaf with open-pit deep hole downward blasting, the top arch structure of the goaf is simplified to a two-hinged arch structure with a thickness equal to the safe thickness of the suspended arch roof reserved for treatment. A model for treating suspended goaf with top arch structure is constructed. The basic assumptions of the model are as follows:

[0011] (1) The blasting load on the suspended arch roof is simplified to a uniformly distributed load q1. Assuming that the arched suspended arch roof remains relatively stable under its own weight and is damaged under the disturbance of the blasting dynamic load, the critical blasting dynamic load that causes the suspended arch roof to collapse is q d .

[0012] (2) The internal force distribution of the rock arch satisfies the two-hinge arch theory. Based on the parabolic arch axis equation, the parametric equations of the rock arch span and rise are obtained.

[0013]

[0014] Where: f is the arch height; l is the length of the arch, f / l is the sag ratio, and x is the position variable along the span of the arch, representing the horizontal distance from the centerline of the arch bottom to the current point.

[0015] (3) Assuming that the arch ring undergoes tensile failure, the unfavorable section of the rock arch is at the mid-span section. Considering the mid-span section, the axial pressure and shear force at the mid-span section are small and can be ignored.

[0016] (4) The stability of the suspended arch top plate can be regarded as the balance between the tensile force generated by the maximum bending moment within the stress arch ring and the bending strength of the arch ring.

[0017] Preferably, based on the two-hinge arch theory, the bending moment of the cantilevered arch top plate is calculated, including:

[0018] The two-hinged arch is calculated based on the parabolic arch axis equation, and its typical equation is listed with a simply supported curved beam as the basic structure:

[0019] δ 11 X1+Δ 1p =0

[0020] Where: δ 11 is the horizontal displacement coefficient; X1 is the horizontal thrust of the support; Δ 1p is the displacement of the basic structure in the direction X1 when the load acts alone, which is considered as a free term. When calculating the coefficient and free term, the influence of axial pressure and shear force on the mid-span section is ignored. Therefore, the horizontal thrust X1 of the support is

[0021]

[0022] Where: y is the vertical coordinate of any section; M p I is the bending moment generated by the overhanging arch top plate under the overlying load; c and A c are the arch section inertia moment and the arch ring cross-sectional area, respectively, which can be expressed as

[0023]

[0024] A c =bh

[0025] Among them, b is the span of the suspended roof goaf, b=l; h is the thickness of the suspended arch roof.

[0026] Calculation of the bending moment M and the maximum bending moment M of the cantilever arch roof using the superposition method max Since the bending moment distribution of the cantilever arch top plate is similar to that of a simply supported beam, the maximum bending moment value is at the mid-span position (x = b / 2). Therefore, the maximum bending moment value M can be obtained by combining the above formulas. max for

[0027]

[0028] Where: q0 and q1 are the basic load and additional load borne by the cantilever arch top plate respectively.

[0029] Preferably, based on the theory of elastic mechanics, the maximum tensile stress σ of the cantilever arch top plate is calculated according to the relationship between internal force and bending moment. t,max

[0030]

[0031] Preferably, the stability of the suspended arch roof can be regarded as the balance between the tension generated by the maximum bending moment within the stress arch ring and the bending strength of the arch ring. Without considering the blasting load, the safe thickness h of the suspended arch roof is calculated based on the statically indeterminate structure of the arch. s

[0032]

[0033] Where: k is the safety factor.

[0034] Preferably, since the tensile strength under blasting load is much greater than the static tensile strength, the dynamic tensile strength [σ] of the cantilevered arch roof is used. d,max Static tensile strength of the alternative cantilevered arch roof [σ] t,max When the maximum tensile stress of the suspended arch roof is the dynamic tensile strength, the critical load q of the suspended arch roof caused by blasting collapse is d for

[0035]

[0036] Preferably, a collapse failure criterion is proposed based on the relationship between the tensile stress and tensile strength of the cantilevered arch roof. t,max Greater than or equal to dynamic tensile strength [σ] d,max , that is, q1≥q d When the maximum tensile stress σ t,max Less than dynamic tensile strength [σ] d,max , that is, q1<q d At that time, the blasting load failed to cause the suspended arch roof to collapse.

[0037] Preferably, since the uniformly distributed load of the suspended arch roof blasting under the maximum dynamic tensile strength is equal to the blasting peak equivalent pressure, the critical load q of the suspended arch roof blasting collapse is substituted into d , obtain the blasthole spacing a and the span b of the suspended roof goaf, the arch height f and the safety thickness h s Relationship between:

[0038]

[0039] Where: d c is the blasting charge diameter; d b is the diameter of the blasthole; ρ e is the density of blasting explosive; V VOD is the blasthole volume.

[0040] The present invention also provides a blasthole spacing calculation system for treating an arched suspended roof goaf by open-pit deep hole blasting.

[0041] The invention also provides a device.

[0042] The present invention also provides a computer-readable storage medium.

[0043] Compared with the existing technology, the beneficial effects of the present invention are at least:

[0044] 1. The present invention can completely collapse the suspended arch roof at one time through the optimized design of the blasting hole spacing, avoiding the occurrence of "secondary suspended roof" and effectively controlling the damage caused by blasting to the surrounding engineering bodies.

[0045] 2. The present invention can effectively control the secondary damage to the suspended arch caused by engineering geological factors such as mine rock cracks, groundwater, external dynamic loads, etc., reduce the probability of secondary accidents such as suspended arch roof collapse, impact earthquakes, overburden sliding, surface collapse, etc., and eliminate the hidden dangers of mine suspended roof.

[0046] 3. This method completely strips the ground surface, including the goaf, to create a controlled surface, fundamentally resolving the problem of surface cracking. This controlled surface serves as the first phase of open-pit mining, effectively advancing the transition from underground to open-pit resource extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of a method for determining blasthole spacing based on treatment of exposed and remaining hanging roofs provided by an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the construction of an open-pit deep hole blasting method for treating an arched suspended roof goaf according to an embodiment of the present invention;

[0049] Figure 3 This is a construction flow chart of the open-pit deep hole blasting treatment of an arched suspended roof goaf according to an embodiment of the present invention;

[0050] Figure 4 This is a model diagram of the top arch structure management of the suspended roof goaf area according to an embodiment of the present invention;

[0051] Figure 5 Schematic diagram of the two-hinged arch structure of the suspended arch roof in the goaf according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0053] See also Figure 2 and Figure 3The construction method of open-pit deep hole blasting to treat goaf includes the following: using open-pit deep hole blasting to treat the suspended arch goaf, stripping from the surface to the top of the goaf, and reserving a safe thickness of the suspended arch roof. The suspended arch roof of the goaf is collapsed through deep hole blasting technology to complete the filling, and the surface and goaf are completely stripped to form a certain treatment state, fundamentally eliminating the hidden dangers of the suspended roof goaf and solving the problem of surface cracking. The formed treatment state serves as the first phase of open-pit mining in the mine, effectively promoting the process of "underground to open-pit" resource mining.

[0054] See also Figure 1 The present invention provides a method for determining the blasthole spacing based on the treatment of the remaining hanging roof in the ground reform, comprising the following steps:

[0055] Step 1: Based on the method for controlling suspended goaf with open-pit deep hole downward blasting, a safe thickness of the suspended arch roof is reserved. Based on simplifying the suspended arch roof into a two-hinged arch, a model for controlling the top arch structure of the suspended goaf is constructed.

[0056] See also Figure 4 A model for the management of the top arch structure of a suspended goaf is established. Since the buried depth of the suspended goaf is relatively shallow, the suspended arch roof is subject to horizontal tectonic stress and vertical gravity of the overlying rock mass. Therefore, only the deadweight of the suspended arch roof is considered, and the blasting load is simplified to a uniformly distributed load, which is applied to the arched suspended arch roof that is about to collapse. Based on the method for managing suspended goaf using open-pit deep-hole downward blasting, the top arch structure of the goaf is simplified to a two-hinged arch structure, and a safe thickness of the suspended arch roof is reserved to construct a model for the management of the top arch structure of a suspended goaf.

[0057] In this step, based on the existing method for managing suspended goaf areas using open-pit deep-hole downward blasting (which is not described here), the suspended arch roof structure of the goaf is simplified to a two-hinged arch structure, with a reserved safe thickness for the suspended arch roof, to construct a model for managing the suspended goaf arch structure. The basic assumptions of the model are as follows:

[0058] (1) The blasting load on the suspended arch roof is simplified to a uniformly distributed load q1. Assuming that the arched suspended arch roof remains relatively stable under its own weight, but is damaged under the disturbance of the blasting dynamic load, the critical blasting dynamic load that causes the suspended arch roof to collapse is q d .

[0059] (2) The internal force distribution of the rock arch satisfies the two-hinge arch theory. Based on the parabolic arch axis equation, the parametric equations for the rock arch span and rise are obtained:

[0060]

[0061] Where: f is the arch height, l is the length of the arch, f / l is the sag ratio, and x is the position variable along the span of the arch, which represents the horizontal distance from the center line of the arch bottom to the current point.

[0062] (3) Assuming that the arch ring undergoes tensile failure, the unfavorable section of the rock arch is at the mid-span section. Considering that the axial pressure and shear force at the mid-span section are small, they can be ignored.

[0063] (4) The stability of the suspended arch top plate can be regarded as the balance between the tensile force generated by the maximum bending moment within the stress arch ring and the bending strength of the arch ring.

[0064] Step 2: Based on the two-hinge arch theory, calculate the bending moment and maximum tensile stress of the cantilever arch top plate. Based on the basic condition that "when the maximum tensile stress of the cantilever arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the cantilever arch top plate will collapse", calculate the ultimate stable thickness within the stress arch bearing area, that is, the safe thickness of the cantilever arch top plate h s .

[0065] See also Figure 5 , based on the parabolic curve arch axis equation to calculate the two-hinged arch, the typical equation is listed with the simply supported curved beam as the basic structure

[0066] δ 11 X1+Δ 1p =0

[0067] Where: δ 11 is the horizontal displacement coefficient; X1 is the horizontal thrust of the support; Δ 1p It is the displacement along the X1 direction caused by the load acting alone on the basic structure, which is regarded as a free term.

[0068] When calculating the horizontal displacement coefficient and the free term, the influence of the axial pressure and shear force on the mid-span section is ignored. Therefore, the horizontal thrust X1 of the support is

[0069]

[0070] Where: y is the vertical coordinate of any section; M p is the bending moment generated by the cantilevered arch top plate under the overlying load; l is the length of the cantilevered arch top plate; I c and A c are the arch section inertia moment and the arch ring cross-sectional area, respectively, which can be expressed as

[0071]

[0072] A c =bh

[0073] Among them, b is the span of the suspended roof goaf, b=l; h is the thickness of the suspended arch roof.

[0074] Calculation of the bending moment M and the maximum bending moment M of the cantilever arch roof using the superposition method max :

[0075] M=Mp -X1y

[0076] Since the bending moment distribution of the cantilever arch top plate is similar to that of a simply supported beam, the maximum bending moment value is at the mid-span position (x = b / 2). Therefore, the maximum bending moment value M can be obtained by combining the above formulas: max for:

[0077]

[0078] Where q0 and q1 are the basic load and additional load on the cantilever arch top plate, respectively, and f is the arch height.

[0079] Based on the theory of elastic mechanics and the relationship between internal force and bending moment, the maximum tensile stress σ of the cantilever arch top plate is calculated. t,max :

[0080]

[0081] The stability of the suspended arch roof can be regarded as the balance between the tensile force generated by the maximum bending moment within the stress arch ring and the bending strength of the arch ring. Without considering the blasting load, the safe thickness h of the suspended arch roof is calculated based on the statically indeterminate structure of the arch. s :

[0082]

[0083] Where: k is the safety factor.

[0084] Step 3: Equivalently treat the blasting load as a uniformly distributed load acting on the ground surface with a preset safety thickness of the suspended arch roof. Use dynamic tensile strength instead of static tensile strength to calculate the critical load of blasting collapse and determine the failure criterion of the suspended arch roof.

[0085] Since the tensile strength under blasting load is much greater than the static tensile strength, the dynamic tensile strength of the cantilevered arch roof [σ] is used. d,max Static tensile strength of the alternative cantilevered arch roof [σ] t,max When the maximum tensile stress of the suspended arch roof is the dynamic tensile strength, the critical load q of the suspended arch roof caused by blasting collapse is d for

[0086]

[0087] According to the relationship between the tensile stress and tensile strength of the cantilevered arch roof, the collapse failure criterion is proposed. t,max Greater than or equal to dynamic tensile strength [σ] d,max , that is, q1≥q d When the maximum tensile stress of the cantilevered arch roof σ t,max Less than dynamic tensile strength [σ] d,max , that is, q1<qd When , the blasting load fails to collapse the cantilever arch top plate, q1 is the additional load on the cantilever arch top plate.

[0088] Step 4: Under the condition that the uniformly distributed load of the suspended arch roof blasting is equal to the blasting peak equivalent pressure under the maximum dynamic tensile strength, determine the optimal solution for the blasting hole spacing.

[0089] Since the uniformly distributed load of the suspended arch roof blasting under the maximum dynamic tensile strength is equal to the equivalent pressure of the blasting peak, the critical load q of the suspended arch roof blasting collapse is substituted into d , obtain the blasthole spacing a and the span b of the suspended roof goaf, the arch height f and the safe thickness h of the suspended arch roof s Relationship between:

[0090]

[0091] Where: d c is the blasting charge diameter; d b is the diameter of the blasthole; ρ e is the density of blasting explosive; V VOD is the blasthole volume.

[0092] When explosives explode, a pressure wave is generated. The pressure varies over time and reaches a maximum value, which is the blasting peak pressure. The complex blasting pressure wave is represented by an equivalent constant pressure, which is the blasting peak equivalent pressure. The blasting peak equivalent pressure has the same effect as the actual blasting peak pressure in terms of certain key effects (such as the degree of damage to the surrounding medium). In some embodiments of the present invention, for safety reasons, considering the most dangerous situation, the blasting peak equivalent pressure is equal to the blasting peak pressure. In other embodiments, the blasting peak equivalent pressure can also take other values, such as a value of the blasting peak equivalent pressure that is less than the blasting peak pressure.

[0093] In some embodiments of the present invention, a system for determining blasthole spacing for treating an arched suspended-roof goaf in open-pit deep hole blasting is further provided, for implementing the aforementioned method. The system includes the following modules:

[0094] The model building module is used to reserve the safe thickness of the suspended arch roof. Based on simplifying the suspended arch roof into a two-hinged arch, a model for the roof arch structure management of the suspended goaf is constructed.

[0095] The tensile stress and safety thickness determination module is used to calculate the bending moment and maximum tensile stress of the cantilever arch top plate based on the two-hinge arch theory. It is also used to calculate the ultimate stable thickness within the stress arch bearing area, i.e., the safety thickness h of the cantilever arch top plate, based on the basic condition that "when the maximum tensile stress of the cantilever arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the cantilever arch top plate will collapse." s ;

[0096] The roof failure criterion determination module is used to treat the blasting load as a uniformly distributed load acting on the ground surface with a preset safety thickness of the cantilevered roof. The static tensile strength of the cantilevered roof is replaced by the dynamic tensile strength of the cantilevered roof to calculate the critical load of blasting collapse. The cantilevered roof failure criterion is determined based on the maximum tensile stress and dynamic tensile strength of the cantilevered roof.

[0097] The blasting hole spacing determination module is used to determine the optimal solution for the blasting hole spacing under the condition that the uniformly distributed load of the suspended arch roof blasting is equal to the blasting peak equivalent pressure under the maximum dynamic tensile strength.

[0098] In some embodiments of the present invention, a device is also provided, comprising a processor and a memory, wherein the memory is used to store instructions or computer programs, and the processor is used to execute the instructions or computer programs in the memory so that the device performs the steps of the method described in the aforementioned embodiment.

[0099] In some embodiments of the present invention, a computer-readable storage medium is further provided, wherein instructions are stored in the computer-readable storage medium. When the instructions are executed on a device, the device executes the steps of the method described in the aforementioned embodiment.

[0100] The present invention constructs a model for the management of the top arch structure in the suspended roof goaf area, comprehensively considers the blasting peak equivalent pressure, and optimizes the blasting hole spacing to effectively control the secondary damage to the suspended arch caused by engineering geological factors such as mine rock fissures, groundwater, and external dynamic loads, thereby reducing the probability of secondary accidents such as collapse of the suspended arch roof, impact earthquakes, overburden sliding, and surface collapse, eliminating the hidden dangers of the suspended roof, and facilitating the complete stripping of the surface together with the goaf to form a certain management state. As a first-phase project for open-pit mining of mines, the present invention effectively promotes the process of "underground to open-pit" resource mining.

[0101] The above embodiments are preferred implementation methods of the present invention, but the implementation methods of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations and simplifications made without violating the basic principles and ideas of the present invention are equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for determining blasthole spacing based on the treatment of residual hanging roofs left over from ground reform, characterized in that: The following steps are involved: Reserve the safe thickness of the suspended arch roof, simplify the suspended arch roof into a two-hinged arch, and build a roof arch structure management model for the suspended goaf area; Based on the two-hinge arch theory, the bending moment and maximum tensile stress of the cantilevered arch roof are calculated. Based on the basic condition that "when the maximum tensile stress of the cantilevered arch roof exceeds the tensile stress threshold that the stress arch bearing area can withstand, the cantilevered arch roof collapses", the ultimate stable thickness within the stress arch bearing area, i.e., the safe thickness h of the cantilevered arch roof, is calculated. s ; The blasting load is equivalent to a uniformly distributed load acting on the ground surface with a preset safety thickness of the cantilevered arch roof. The static tensile strength of the cantilevered arch roof is replaced by the dynamic tensile strength of the cantilevered arch roof to calculate the critical load of blasting collapse. The failure criterion of the cantilevered arch roof is determined based on the maximum tensile stress and dynamic tensile strength of the cantilevered arch roof. Under the condition that the uniformly distributed load of suspended arch roof blasting is equal to the blasting peak equivalent pressure at the maximum dynamic tensile strength, the optimal solution of blasting hole spacing is determined; When constructing the arch structure management model for the suspended goaf, only the deadweight of the suspended arch roof is considered, and the blasting load is simplified to a uniformly distributed load, which is applied to the suspended arch roof that is about to collapse. Based on the two-hinge arch theory, the bending moment of the cantilevered arch roof is calculated, including: The two-hinged arch is calculated based on the parabolic arch axis equation, and the equation is listed as follows using a simply supported curved beam as the basic structure: d 11 X1+D 1p =0 Where: δ 11 is the horizontal displacement coefficient; X1 is the horizontal thrust of the support; Δ 1p is the displacement of the basic structure along the X1 direction when the load acts alone, which is regarded as a free term; When calculating the coefficients and free terms, the effects of axial pressure and shear force on the mid-span section are ignored. Therefore, the horizontal thrust X1 of the support is: Where: y is the vertical coordinate of any section; M p is the bending moment generated by the cantilevered arch top plate under the overlying load; l is the length of the cantilevered arch top plate; I c and A c are the moment of inertia of the arch section and the cross-sectional area of ​​the arch ring, respectively; x is the position variable along the span direction of the rock arch; The bending moment M of the cantilever arch top plate is: M=M p -X1y Maximum bending moment value M max for: Where: q0 and q1 are the basic load and blasting load on the cantilever arch top plate respectively; f is the arch height; Maximum tensile stress σ of cantilever arch top plate t,max The expression is: Where: b is the span of the suspended roof goaf, h is the thickness of the suspended arch roof; The stability of the suspended arch roof can be regarded as the balance between the tensile force generated by the maximum bending moment within the stress arch ring and the bending strength of the arch ring. Without considering the blasting load, the safe thickness h of the suspended arch roof is calculated based on the statically indeterminate structure of the arch. s : Where: k is the safety factor, σ t,max is the maximum tensile stress of the cantilever arch top plate, q0 is the basic load on the cantilever arch top plate, and f is the arch height; Since the tensile strength under blasting load is much greater than the static tensile strength, the dynamic tensile strength of the cantilevered arch roof [σ] is used. d,max Static tensile strength of the alternative cantilevered arch roof [σ] t,max When the maximum tensile stress of the suspended arch roof is the dynamic tensile strength, the critical load q of the suspended arch roof caused by blasting collapse is d for: According to the relationship between the tensile stress and tensile strength of the suspended arch roof, the collapse failure criterion is determined: when the maximum tensile stress σ t,max Greater than or equal to dynamic tensile strength [σ] d,max , that is, q1≥q d When the maximum tensile stress σ t,max Less than dynamic tensile strength [σ] d,max , that is, q1<q d When the blasting load fails to collapse the suspended arch roof; The expression of the blasthole distance a is: Where: d c is the blasting charge diameter; d b is the diameter of the blasthole; ρ e is the density of blasting explosive; V VOD is the blasthole volume; b is the span of the suspended roof goaf; f is the arch height; h s It is the safe thickness of the suspended arch top plate.

2. A blasthole spacing determination system for deep hole blasting in open pits to treat arched suspended goafs is characterized by: For implementing the method according to claim 1, the system comprises the following modules: The model building module is used to reserve the safe thickness of the suspended arch roof. Based on simplifying the suspended arch roof into a two-hinged arch, a model for the roof arch structure management of the suspended goaf is constructed. The tensile stress and safety thickness determination module is used to calculate the bending moment and maximum tensile stress of the cantilever arch top plate based on the two-hinge arch theory. It is also used to calculate the ultimate stable thickness within the stress arch bearing area, i.e., the safety thickness h of the cantilever arch top plate, based on the basic condition that "when the maximum tensile stress of the cantilever arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the cantilever arch top plate will collapse." s ; The roof failure criterion determination module is used to treat the blasting load as a uniformly distributed load acting on the ground surface with a preset safety thickness of the cantilevered roof. The static tensile strength of the cantilevered roof is replaced by the dynamic tensile strength of the cantilevered roof to calculate the critical load of blasting collapse. The cantilevered roof failure criterion is determined based on the maximum tensile stress and dynamic tensile strength of the cantilevered roof. The blasting hole spacing determination module is used to determine the optimal solution for the blasting hole spacing under the condition that the uniformly distributed load of the suspended arch roof blasting is equal to the blasting peak equivalent pressure under the maximum dynamic tensile strength.

3. A device, characterized in that The device includes a processor and a memory, wherein the memory is used to store instructions or computer programs, and the processor is used to execute the instructions or computer programs in the memory, so that the device performs the steps of the method according to claim 1.

4. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, which, when executed on a device, cause the device to perform the steps of the method according to claim 1 .

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