Blast hole pitch determination method based on ground change dew left suspended roof treatment

Abstract

The invention discloses a blast hole pitch determination method based on treatment of a remain suspended roof of ground change dew, which comprises the following steps of: establishing a treatment model of a top arch structure of a suspended roof goaf, and calculating the bending moment and the maximum tensile stress of a top plate of the suspended roof goaf; calculating the safety thickness of the suspended arch top plate based on the relationship between the tensile stress and the tensile strength; the static tensile strength is replaced by the dynamic tensile strength, and a suspended arch top plate damage criterion considering the blasting caving critical load is determined; and obtaining an optimal solution of the blasting hole distance. According to the method, secondary damage of engineering geological factors such as mine rock mass cracks, underground water and external dynamic loads to the suspended arch is effectively controlled by constructing the suspended roof goaf top arch structure treatment model, integrating the blasting peak value and the equivalent pressure and optimizing the blasting hole distance; the probability of occurrence of secondary accidents such as collapse of suspended arch top plates, impact earthquakes, overlying strata slippage and surface collapse is reduced, hidden dangers of suspended roofs can be eliminated, and the surface and the goaf are completely stripped.

Description

Technical Field

[0001] The 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 the mining process of caving, affected by factors such as rock mass lithology, blasting organization construction, and mining field structural parameters, some working faces failed to blast induced roof caving after mining, and the suspended arch roof in the goaf did not collapse in time. After the blasting induced operation, the suspended arch roof was subjected to its own weight and formed an arched suspended roof structure under the action of the stress arch effect. With the continuous advancement of mining work, large-scale mining field suspended roof problems have occurred. In addition, affected by engineering geological factors such as mine rock fissures, groundwater, and external dynamic loads, the damage to the arched suspended roof has intensified, which is likely to cause major accidents such as collapse of the suspended arch roof, impact earthquakes, overburden sliding, and surface collapse, seriously affecting mine safety 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 an open-pit deep buried goaf blasting method, which calculates the radius of the blasthole crushing zone and the fissure zone, clarifies the range of the blasthole spacing, determines the single-layer 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 upper open-pit layer height, and calculates the delay time between each layer and between holes in the detonation network, so as to overcome 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, and 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 the remaining suspended roof after underground conversion to exposed earth, which is used to determine the optimal blasthole spacing for the treatment of arched suspended roof goaf by open-pit deep hole blasting, so as to eliminate the hidden dangers of suspended roof and promote the process of "underground to open-pit" resource exploitation.

[0005] In order 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 suspended roof in the ground modification, comprising the following steps:

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

[0007] Based on the two-hinged arch theory, the bending moment and maximum tensile stress of the suspended arch top plate are calculated. According to the basic condition that "when the maximum tensile stress of the suspended arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the suspended arch top plate will collapse", the ultimate stable thickness within the stress arch bearing area, i.e., the safe thickness h of the suspended arch top plate, 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 in treatment, and a treatment model for the top arch structure of the suspended goaf 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. It is assumed 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 sagittal height ratio, and x is the position variable along the span direction of the rock arch, which represents the horizontal distance from the center line of the bottom of the rock arch 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-hinged arch theory, the bending moment of the cantilever arch top plate is calculated, including:

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

[0019] δ 11 X1+Δ 1p =0

[0020] Where: 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 X1 direction when the load acts alone, which is regarded 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 ordinate of any section; M p I is the bending moment of the cantilevered arch slab under the overlying load; c and A c are the moment of inertia of the arch section and the cross-sectional area of ​​the arch ring, 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 suspended arch roof using the superposition method max Since the bending moment distribution of the cantilever arch top plate is similar to that of the 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 suspended arch top slab respectively.

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

[0030]

[0031] Preferably, 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. Without considering the blasting load, the safe thickness h of the suspended arch top plate is calculated according to the primary 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 cantilever arch top plate is used. d,max Static tensile strength of the alternative suspended 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 suspended 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 of the suspended arch roof σ t,max Less than dynamic tensile strength [σ] d,max , that is, q1<q d At that time, the blasting load failed to collapse the suspended arch roof.

[0037] Preferably, 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 value, 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 blasthole diameter; ρ e V is the density of blasting explosive; VOD is the blast hole volume.

[0040] The invention also provides a blasthole spacing calculation system for treating an arched suspended-roof goaf area 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 prior art, 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, avoid the generation of "secondary suspended roof", and effectively control 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 collapse of the suspended arch roof, impact earthquakes, sliding of the overburden, surface collapse, etc., and eliminate the hidden dangers of mine suspended roofs.

[0046] 3. The present invention completely strips the surface and the goaf to form a certain governance realm, fundamentally solving the problem of surface cracking. The governance realm formed is the first phase of open-pit mining, effectively promoting the process of "underground to open-pit" resource mining. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of a method for determining blasthole spacing based on ground modification and exposed residual suspended roof management provided by an embodiment of the present invention;

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

[0049] Figure 3 A construction flow chart of an open-pit deep hole blasting method for treating an arched suspended roof goaf according to an embodiment of the present invention;

[0050] Figure 4 A diagram showing a model for managing the top arch structure of a suspended goaf area according to an embodiment of the present invention;

[0051] Figure 5 It is a 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] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 creative work 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 contents: using open-pit deep hole blasting to treat suspended arch goaf, stripping from the surface to the top of the goaf, and reserving the safe thickness of the suspended arch roof, using deep hole blasting technology to collapse the suspended arch roof of the goaf to complete the filling, stripping the surface together with the goaf, forming a certain treatment realm, fundamentally eliminating the hidden dangers of suspended roof goaf, and solving the problem of surface cracking. The formed treatment realm is the first phase of open-pit mining in the mine, which effectively promotes 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 suspended roof in the ground modification, comprising the following steps:

[0055] Step 1: According to the method of controlling the suspended roof goaf area by open-pit deep hole downward blasting, reserve the safe thickness of the suspended arch roof slab, and construct the top arch structure control model of the suspended roof goaf area on the basis of simplifying the suspended arch roof slab into a two-hinged arch.

[0056] See also Figure 4 , a model for the treatment of the top arch structure of the suspended goaf is established. Since the suspended goaf is shallowly buried, the suspended arch roof is subject to the tectonic stress in the horizontal direction and the gravity of the overlying rock in the vertical direction. 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. According to the treatment method of the suspended goaf by deep open-pit downward blasting, the top arch structure of the goaf is simplified to a two-hinged arch structure, and the safety thickness of the suspended arch roof is reserved to construct a model for the treatment of the top arch structure of the suspended goaf.

[0057] In this step, according to the method for managing suspended goaf areas in open-pit deep hole downward blasting (which is an existing management method and will not be described in detail here), the suspended arch roof structure of the goaf is simplified to a two-hinged arch structure, and the safety thickness of the suspended arch roof is reserved to construct a model for managing the suspended goaf roof 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. It is assumed 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 of 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 sagittal height ratio, and x is the position variable along the span direction of the rock arch, which represents the horizontal distance from the center line of the bottom of the rock arch 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-hinged arch theory, calculate the bending moment and maximum tensile stress of the suspended arch top plate. Based on the basic condition that "when the maximum tensile stress of the suspended arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the suspended arch top plate collapses", calculate the ultimate stable thickness within the stress arch bearing area, that is, the safe thickness of the suspended arch top plate h s .

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

[0066] δ 11 X1+Δ 1p =0

[0067] Where: 11 is the horizontal displacement coefficient; X1 is the horizontal thrust of the support; Δ 1p It is the displacement along the X1 direction generated when the basic structure is acted upon by the load alone and 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 ordinate of any section; M p is the bending moment of the cantilevered arch slab under the overlying load; l is the length of the cantilevered arch slab; I c and A c are the moment of inertia of the arch section and the cross-sectional area of ​​the arch ring, 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 suspended 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 the 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 suspended arch top slab, respectively, and f is the arch height.

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

[0080]

[0081] 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. Without considering the blasting load, the safe thickness h of the suspended arch top plate is calculated based on the primary statically indeterminate structure of the arch. s :

[0082]

[0083] Where: k is the safety factor.

[0084] Step 3: The blasting load is equivalent to a uniformly distributed load, acting on the ground surface with a preset safety thickness of the suspended arch top slab. The dynamic tensile strength is used instead of the static tensile strength to calculate the critical load of blasting collapse and determine the damage criterion of the suspended arch top slab.

[0085] Since the tensile strength under blasting load is much greater than the static tensile strength, the dynamic tensile strength of the cantilevered arch top plate [σ] is used. d,max Static tensile strength of the alternative suspended 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 collapse is d for

[0086]

[0087] According to the relationship between the tensile stress and tensile strength of the suspended 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 suspended 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 suspended arch top slab, q1 is the additional load on the suspended arch top slab.

[0088] Step 4: Under the condition that the uniformly distributed load of the suspended arch top slab blasting is equal to the blasting peak equivalent pressure under the maximum dynamic tensile strength, determine the optimal solution of 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, 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 blasthole diameter; ρ e V is the density of blasting explosive; VOD is the blast hole volume.

[0092] Among them, when explosives explode, pressure waves are generated, and the pressure changes with time. There is a maximum pressure value, which is the blasting peak pressure. The complex explosion pressure wave is represented by an equivalent constant pressure, and this constant pressure is the blasting peak equivalent pressure. The blasting peak equivalent pressure has the same effect as the actual blasting peak pressure in some 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 be other values, such as the blasting peak equivalent pressure is less than the blasting peak pressure.

[0093] In some embodiments of the present invention, a blasthole spacing determination system for treating an arched suspended roof goaf in open-pit deep hole blasting is also provided, which is used to implement the above method. The system includes the following modules:

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

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

[0096] A roof failure criterion determination module is used to convert the blasting load into a uniformly distributed load, acting on the ground surface with a preset safety thickness of the suspended arch roof, and replace the static tensile strength of the suspended arch roof with the dynamic tensile strength of the suspended arch roof to calculate the critical load of blasting collapse, and determine the failure criterion of the suspended arch roof based on the maximum tensile stress and dynamic tensile strength of the suspended arch 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 top plate 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 top arch structure management model for suspended roof goaf areas, 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, reduce the probability of secondary accidents such as collapse of the suspended arch roof, impact earthquakes, overburden sliding, and surface collapse, eliminates the hidden dangers of the suspended roof, and can facilitate 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, it 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 protection scope of the present invention.

Claims

1. A method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground reform, characterized in that: The following steps are involved: The safe thickness of the suspended arch roof is reserved, and the suspended arch roof is simplified into a two-hinged arch to construct a model for the management of the suspended goaf roof arch structure. Based on the two-hinged arch theory, the bending moment and maximum tensile stress of the suspended arch top plate are calculated. Based on the basic condition that "when the maximum tensile stress of the suspended arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the suspended arch top plate collapses", the ultimate stable thickness within the stress arch bearing area, i.e., the safe thickness h of the suspended arch top plate, 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 suspended arch top plate, and the dynamic tensile strength of the suspended arch top plate is used instead of the static tensile strength of the suspended arch top plate to calculate the critical load of blasting collapse, and the failure criterion of the suspended arch top plate is determined based on the maximum tensile stress and dynamic tensile strength of the suspended arch top plate. 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.

2. The method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground modification according to claim 1 is characterized in that: When constructing the arch structure management model of the suspended goaf area, 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.

3. The method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground modification according to claim 1 is characterized in that: Based on the two-hinged arch theory, the bending moment of the cantilever arch top plate is calculated, including: The two-hinged arch is calculated based on the parabolic curve arch axis equation, and the equation is listed as follows with a simply supported curved beam as the basic structure: d 11 X1+D 1p =0 Where: 11 is the horizontal displacement coefficient; X1 is the horizontal thrust of the support; Δ 1p It is the displacement along the X1 direction generated when the basic structure is subjected to the load alone, which is regarded as a free term; When calculating the coefficients and free terms, the influence of axial pressure and shear force on the mid-span section is ignored. Therefore, the horizontal thrust X1 of the support is: Where: y is the ordinate of any section; M p is the bending moment of the cantilevered arch slab under the overlying load; l is the length of the cantilevered arch slab; 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 suspended arch top slab respectively; f is the arch height.

4. The method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground modification according to claim 1 is characterized in that: Maximum tensile stress of cantilever arch top plateσ t,max The expression is: Where: b is the span of the suspended roof goaf, and h is the thickness of the suspended arch roof.

5. The method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground modification according to claim 4 is characterized in that: 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. Without considering the blasting load, the safe thickness h of the suspended arch top plate is calculated based on the primary 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 borne by the cantilever arch top plate, and f is the arch height.

6. The method for determining the blasthole spacing based on the treatment of the remaining suspended roof in the ground modification according to claim 1 is characterized in that: Since the tensile strength under blasting load is much greater than the static tensile strength, the dynamic tensile strength of the cantilevered arch top plate [σ] is used. d,max Static tensile strength of the alternative suspended 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 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 of the suspended arch roof σ t,max Less than dynamic tensile strength [σ] d,max , that is, q1<q d At that time, the blasting load failed to collapse the suspended arch roof.

7. A method for determining blasthole spacing based on ground modification and exposed residual suspended roof management according to any one of claims 1 to 6, characterized in that: The expression of the blasthole distance a is: Where: d c is the blasting charge diameter; d b is the blasthole diameter; e V is the density of blasting explosive; 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 slab.

8. A system for determining the blasthole spacing for treating arched suspended roof goaf with open-pit deep hole blasting, characterized in that: For implementing the method according to any one of claims 1 to 7, the system comprises the following modules: The model building module is used to reserve the safe thickness of the suspended arch roof. On the basis of simplifying the suspended arch roof into a two-hinged arch, a model for the management of the suspended arch structure in the goaf area is constructed. The tensile stress and safety thickness determination module is used to calculate the bending moment and maximum tensile stress of the suspended arch top plate based on the two-hinged arch theory, and calculate the ultimate stable thickness within the stress arch bearing area, i.e., the safety thickness h of the suspended arch top plate, based on the basic condition that "when the maximum tensile stress of the suspended arch top plate exceeds the tensile stress threshold that the stress arch bearing area can withstand, the suspended arch top plate collapses". s ; A roof failure criterion determination module is used to convert the blasting load into a uniformly distributed load, acting on the ground surface with a preset safety thickness of the suspended arch roof, and replace the static tensile strength of the suspended arch roof with the dynamic tensile strength of the suspended arch roof to calculate the critical load of blasting collapse, and determine the failure criterion of the suspended arch roof based on the maximum tensile stress and dynamic tensile strength of the suspended arch 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 top plate blasting is equal to the blasting peak equivalent pressure under the maximum dynamic tensile strength.

9. A device, characterized in that: The device comprises 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 any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, and when the instructions are executed on a device, the device executes the steps of the method according to any one of claims 1 to 7.

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