CN115758046A - Working face ultimate mining width calculation method, readable storage medium and electronic device - Google Patents

Working face ultimate mining width calculation method, readable storage medium and electronic device Download PDF

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CN115758046A
CN115758046A CN202211429802.5A CN202211429802A CN115758046A CN 115758046 A CN115758046 A CN 115758046A CN 202211429802 A CN202211429802 A CN 202211429802A CN 115758046 A CN115758046 A CN 115758046A
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arch
hard rock
rock stratum
thick
stress
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CN115758046B (en
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李全生
阎跃观
朱元昊
郭俊廷
张琰君
李军
张村
滕腾
张成业
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China University of Mining and Technology Beijing CUMTB
National Institute of Clean and Low Carbon Energy
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China University of Mining and Technology Beijing CUMTB
National Institute of Clean and Low Carbon Energy
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Abstract

The invention discloses a working face ultimate mining width calculation method, a readable storage medium and electronic equipment, wherein the method comprises the following steps: A. determining a thick and hard rock stratum with a fixed component layer arch condition from the overlying strata according to a key layer theory; B. gradually advancing along with the working surface of the stress arch, and calculating the arch height of the stress arch under the thick hard rock stratum and under the condition that the stress arch spans the thick hard rock stratum without being broken or broken; C. setting the arch height of the stress arch to be equal to the total thickness H of the overlying strata 0 And calculating to obtain the working face limit mining width for the limit critical condition of the mining width. The method determines the thick hard rock stratum according to the rigidity condition discriminant and the strength condition discriminant, gradually advances along with the working face of the stress arch, judges whether the thick hard rock stratum is broken or not according to the empty-top distance condition and the thick hard rock stratum limit breaking distance condition, respectively calculates the arch height, further calculates the working face limit mining width of the arch, and provides the design for coal mining and the subsidence controlFor technical support.

Description

Working face ultimate mining width calculation method, readable storage medium and electronic equipment
Technical Field
The invention relates to the field of mining subsidence and safe mining, in particular to a working face ultimate mining width calculation method based on a layered arch concept, a readable storage medium and electronic equipment.
Background
Coal resources are main energy, the proportion of coal in primary energy consumption is over 50 percent, and the coal has important promotion effect on industrial and modern development. However, coal mining inevitably forms a large amount of mining space in the underground, which causes movement and destruction of rock strata, resulting in migration of underground water and gas, subsidence and even collapse of the earth surface, and ecological damage, which also pose serious challenges to the ecological civilization construction of mining areas. Relevant researches show that when the underground coal seam is used for mining rocks, the internal stress transmission path of overlying rocks deviates to form a stress arch structure, and the arch structure bears and transmits the load of the overlying rock-soil layer and plays a supporting role for mining the overlying rocks, so that the surface subsidence is controlled, and the surface damage is slowed down.
The stress arch is used as a macro bearing structure for mining overburden rocks, the span and height of the arch are continuously increased along with the increase of the mining size of a working face, and instability occurs when the height grows to the ground surface. However, the development process of the arch becomes more complex when the overburden lithology is heterogeneous and there is significant thick hard rock formation. The thick and hard rock stratum can influence the development of the stress arch, when the thick and hard rock stratum is in an unbroken state, the arch height of the stress arch below the hard rock stratum can be stopped at the bottom of the thick and hard rock stratum, the rock stratum can not be broken through, and the mining overlying rock above the hard rock stratum can be re-arched at the top of the thick and hard rock stratum to form a layered arch phenomenon. However, when the mining width is continuously increased, the thick hard rock layer is broken, and the layered arches are combined again to form a complete new arch. In recent years, relevant scholars have studied development process, structural morphology, stability and the like of the mining overburden arch structure by adopting methods such as numerical simulation, similarity simulation, theoretical analysis and the like, and have made certain progress. However, the problem of calculating the working face ultimate mining width under the condition of thick and hard rock layers in the overlying strata and critical instability of an arch structure still needs to be researched, and no related technical solution exists.
Disclosure of Invention
The invention aims to solve the technical problems pointed out by the background technology and provides a working face ultimate mining width calculation method, a readable storage medium and electronic equipment, wherein overlying strata in a target mining area are judged layer by layer according to a rigidity condition discriminant and an intensity condition discriminant so as to determine a thick hard stratum with a layered arch forming condition; and (3) gradually advancing along with the working face of the stress arch, judging whether the thick and hard rock stratum is broken or not according to the empty-top distance condition and the limit breaking distance condition of the thick and hard rock stratum, respectively calculating the unbroken and broken arch heights of the thick and hard rock stratum, further calculating to obtain the working face limit mining width of the arch containing the thick and hard rock stratum overburden rock, and providing technical support for coal mining design and subsidence control.
The purpose of the invention is realized by the following technical scheme:
a working face ultimate mining width calculation method comprises the following steps:
A. the method comprises the following steps that overlying strata are arranged above a coal seam, the overlying strata comprise n layers of rock strata, and thick and hard rock strata S forming layered arch conditions are determined from the n layers of rock strata according to a key layer theory;
B. a stress arch is constructed above a coal seam and is gradually pushed along with the working surface of the stress arch, and the arch height calculation method of the stress arch is as follows:
b1, if the stress arch is positioned below the thick hard rock stratum S, the arch height a of the stress arch 1 Is calculated by the method ofThe following:
a 1 ＝bK j wherein a is 1 Is arch height, b is arch span, K j The arch coefficient of the elliptical arch is represented by j, the stratum where the arch crown of the stress arch is located is represented by j, and j is more than 0 and less than or equal to n;
b2, if the stress arch spans the thick and hard rock stratum S, judging whether the thick and hard rock stratum is broken or not, and dividing the situation into two situations of not breaking the thick and hard rock stratum and breaking the thick and hard rock stratum according to the situation, wherein the two situations are as follows:
b21, the rock thick hard rock stratum is not broken, the stress arch comprises an upper stress arch and a lower stress arch, the upper stress arch is formed above the rock thick hard rock stratum, the lower stress arch is formed below the rock thick hard rock stratum, and the total arch height a of the upper stress arch and the lower stress arch is 2 Calculated according to the following formula:
a 2 ＝[L 1 -2H s cotψ+0.1(M-ε P H S +H S )(H 0 -H s )]K 2 +H s +h s wherein L is 1 For the mining width of the lower stress arch, H s Is the horizon height of the thick hard rock formation S,
Figure BDA0003941684480000021
h s the self-depth of the thick hard rock stratum S, M is the mining thickness, epsilon p To break the residual crushing-expansion coefficient of the rock formation, H 0 Total thickness of overburden, K 2 The camber coefficient of the upper stress arch is phi, and phi represents the fracture angle of the overlying strata;
b22, breaking rock thick hard rock stratum and arch height a of new stress arch broken by thick hard rock stratum 3 Calculated according to the following formula:
a 3 ＝(L 3 +0.1MH 0 )K 3 wherein L is 3 For the mining width of the new stress arch, M is the mining thickness, K 3 The arch coefficient of the new stress arch;
C. setting the arch height of the stress arch to be equal to the total thickness H of the overlying strata 0 Calculating the limit mining width of the working face for the limit critical condition of the mining width, wherein the method comprises the following steps:
c1, under the condition that the thick and hard rock stratum is not broken, the thickness is calculated by the following formula:
Figure BDA0003941684480000031
c2, under the condition of breaking the thick hard rock stratum, the steel is obtained by calculation through the following formula:
Figure BDA0003941684480000032
to better practice the invention, the arch factor (including K) of the stress arch 1 、K 2 、K 3 ) Obtained according to the following formula:
Figure BDA0003941684480000033
wherein C represents the Pythium hardness coefficient of the rock stratum lithology related to the stress arch, e is a mathematical constant, and A and B are coefficients determined according to numerical simulation inversion or field actual measurement data; the rock stress arch is positioned below the thick hard rock stratum S, then H k Value of H j (ii) a Under the condition that the rock thick hard rock layer is not broken, H k Value of H 0 -H s (ii) a Breaking condition of rock thick hard rock layer, H k Value of H 0 。
Preferably, the thick hard rock formation S of the present invention is determined by the following method:
a1, taking a rock stratum S1 as an assumed thick hard rock stratum, and judging the rock stratum S1 < n by using the following rigidity conditions and strength conditions respectively:
a11, the rigidity condition discriminant is as follows:
Figure BDA0003941684480000041
wherein E and gamma represent the elastic modulus and the gravity density of the rock formation respectively;
a12, the strength condition discriminant is as follows:
l s1 ＜l n+1 wherein l is s1 Is the breaking distance of the s1 st formation, l m+1 The breaking distance of the (m + 1) th stratum;
and A13, judging all rock strata of the overburden rock until a rigidity condition discriminant and a strength condition discriminant are simultaneously met, and determining that the rock stratum m +1 is a thick hard rock stratum.
Preferably, the method for judging whether the thick hard rock stratum is broken or not comprises the following steps:
b200, respectively judging according to the conditions of the empty top distance and the limit fracture distance of the thick hard rock stratum;
b201, the conditions of the space-head distance of the thick hard rock stratum are as follows:
M-(ε p -1)H k1 -W s if the thickness is larger than zero, a hollow top appears below the thick hard rock layer, wherein M is the mining thickness, and epsilon p In order to break the residual crushing-expansion coefficient of the rock formation, W s The maximum sinking amount of the earth surface;
b202, the conditions of the limit fracture distance of the thick hard formation are as follows:
Figure BDA0003941684480000042
wherein L is S The expression represents the lateral suspension length, R, of a thick hard rock formation T Tensile strength of thick hard rock formations, q s Representing the load borne by a thick hard rock formation;
b203, and simultaneously satisfies M- (epsilon) p -1)H k1 -W s ＞0、
Figure BDA0003941684480000043
And judging that the thick hard rock stratum is broken.
As another preferable technical scheme of the stiffness condition discriminant, the stiffness condition discriminant in the method a11 adopts the following formula;
q S1/m+1 ＜q S1/m s1 < m, wherein q S1/m Represents the load of the rock layer S1 calculated from the S1 th layer to the m 1 th layer, q S1/m+1 The load borne by the rock formation S1 is calculated from the S1 st zone to the (m + 1) th zone.
Preferably, if the method A1 cannot be simultaneously satisfied by the rigidity condition discriminant and the strength condition discriminant, the working face ultimate mining width in the method C is calculated by the following formula:
Figure BDA0003941684480000051
wherein b 'is arch springing offset, b' =0.05MH j J is the stratum where the vault of the stress arch is located, H j Is the horizon height of formation j.
A readable storage medium having stored thereon an executable program which, when executed by a processor, performs the steps of a face ultimate mining width calculation method.
An electronic device comprising a memory storing an executable program and a processor that when executed implements the steps of a face ultimate mining width calculation method.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) According to the method, the overlying rock stratum of the target mining area is judged layer by layer according to a rigidity condition discriminant and a strength condition discriminant so as to determine a thick hard rock stratum with a layered arch forming condition; and (3) gradually advancing along with the working face of the stress arch, judging whether the thick and hard rock stratum is broken or not according to the empty-top distance condition and the limit breaking distance condition of the thick and hard rock stratum, respectively calculating the unbroken arch height and the broken arch height of the thick and hard rock stratum, further calculating to obtain the limit mining width of the working face of the arch containing the thick and hard rock stratum overlying rocks, and providing technical support for coal mining design and subsidence control.
(2) The method can quantitatively calculate and obtain the ultimate mining width of the working face when the mining overburden stress arch loses the bearing capacity, is convenient for mining area mining research and guidance, and improves mining work and environmental safety.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating the limit mining width of a working face in an embodiment;
FIG. 2 is a schematic diagram of a formation horizon distribution of overburden rock in an example;
FIG. 3 is a schematic view of a stress arch axis in an embodiment;
FIG. 4 is a schematic view of the structural configuration of a stress arch under a thick hard rock layer in an embodiment;
FIG. 5 is a schematic diagram of a structure of a stress arch in an embodiment when the stress arch spans thick hard rock strata;
FIG. 6 is a schematic diagram of the combination of the upper and lower stress arches of the thick hard rock formation into a new stress arch in the embodiment.
Detailed Description
The present invention will be described in further detail with reference to the following examples:
examples
As shown in fig. 1 to 6, a method for calculating the limit mining width of a working face includes:
A. the method comprises the following steps that overlying rocks are arranged above a coal seam, the overlying rocks comprise n rock layers (as shown in figure 2, the overlying rocks are arranged from the coal seam to the ground surface, the n rock layers comprise rock layers 1 and 2 \8230, rock layers i \8230, rock layers n, rock layers 1 and 2 \8230, rock layers i \8230, the rock layers corresponding to the rock layers n are respectively h1 and h2 \8230, hi \8230hn, the rock layers S in figure 2 are thick and hard rock layers, thick and hard rock layers (namely key layers) in the overlying rocks play a control role in the movement of the overlying rocks, the rigidity and strength of the thick and hard rock layers are respectively greater than those of peripheral rock layers, arches can also be influenced by the thick and hard rock layers, when the development height of the arches reaches the level of the thick and hard rock layers, the mining overlying rocks above and below the hard rock layers respectively arch forming a ' layered arch ' phenomenon ', and the thick and hard rock layers S forming layered arch bar pieces are determined from the n rock layers according to the key layer theory;
B. as shown in fig. 3, as the working surface of the stress arch is gradually advanced (at this time, the advancing distance of the working surface is gradually increased), the arch height of the stress arch is calculated as follows:
b1, if the stress arch is positioned below the thick hard rock stratum S, as shown in FIG. 4, the arch height a of the stress arch 1 The calculation method of (2) is as follows:
a 1 ＝bK j wherein a is 1 Is the height of the arch, b is the span of the arch, K j J represents a rock stratum where the arch crown of the stress arch is located, and j is more than 0 and less than or equal to n; k j Obtained by the following formula:
Figure BDA0003941684480000061
C j the coefficient of Prussian hardness representing the lithology of the stress arch rock stratum, e is a numerical constant, A and B are coefficients determined according to numerical simulation inversion or field actual measurement data, H j For the horizon height of the formation j, i.e. the height of the formation j at the overburden position, the calculation formula is as follows:
Figure BDA0003941684480000071
H j is the sum of the own thicknesses of j-1 formations below formation j.
B2, if the stress arch spans the thick hard rock stratum S, judging whether the thick hard rock stratum is broken or not, and dividing the situation into two situations of not breaking the thick hard rock stratum and breaking the thick hard rock stratum according to the situation, wherein the two situations are as follows:
b21, if the thick hard rock stratum is not broken, as shown in figure 5, the stress arch comprises an upper stress arch and a lower stress arch, the upper stress arch is formed above the thick hard rock stratum, the lower stress arch is formed below the thick hard rock stratum, and the total arch height a of the upper stress arch and the lower stress arch is 2 Calculated according to the following formula:
a 2 ＝[L 1 -2H s cotψ+0.1(M-ε P H S +H S )(H 0 -H s )]K 2 +H s +h s wherein L is 1 For the mining width of the lower stress arch, H s For the horizon height of the thick hard formation S, the calculation formula is as follows:
Figure BDA0003941684480000072
H s is the sum of the self thicknesses of s-1 rock formations below the rock formation s; h is s Is the thickness of the thick hard rock stratum S, M is the mining thickness, epsilon P To break the residual crushing expansion coefficient of the rock formation, H 0 Total thickness of overburden, K 2 Psi represents the breaking angle of the overburden rock, which is the camber factor of the upper stress arch. K 2 Obtained by the following formula:
Figure BDA0003941684480000073
wherein C 2 The Pythiihardness coefficient of the lithology of the rock stratum involved in the upper stress arch is expressed, e is a mathematical constant, A and B are inverted according to numerical simulation or on siteCoefficient determined by measured data, H 2 The height of the upper stress arch relative to the layer height of the thick hard rock layer, namely the difference between the height of the vault of the upper stress arch and the height of the thick hard rock layer, is expressed as follows: h 2 ＝H 0 -H s . At this time, the thick and hard rock stratum suspension distance formed by the propulsion of the working face does not reach the limit fracture distance or the empty top appears under the thick and hard rock stratum, the key layer is in a complete deflection state, and the stress arch is in a layered arch structure form, as shown in fig. 5; and the left and right arch shoulder arch trace equations of the stress arch below the thick hard layer are shown, and the arch crown is a horizontal line. A stress arch is arranged above the thick and hard rock stratum, and the arch mainly comprises a rock stratum unloaded by a deflection separation layer; assuming that the camber trajectory also satisfies the axis equation at this time, unlike the lower camber state, the upper stress camber coefficient K2 is determined by the critical layer deflection w, the stress camber related to the thickness H2 of the rock formation and the lithology C2 thereof.
B22, breaking the rock thick hard rock stratum, and as shown in figure 6, the arch height a of the new stress arch of the broken rock thick hard rock stratum 3 Calculated according to the following formula:
a 3 ＝(L 3 +0.1MH 0 )K 3 wherein L is 3 For the mining width of the new stress arch, M is the mining thickness, K 3 The arch coefficient of the new stress arch; k 3 Obtained by the following formula:
Figure BDA0003941684480000081
wherein C is 3 The coefficient of the Pythiihardness of the rock stratum of the new stress arch is represented, e is a mathematical constant, and A and B are coefficients determined according to numerical simulation inversion or field actual measurement data. The thick and hard rock stratum is broken by dust, the upper stress arch and the lower stress arch are combined into a new arch as shown in figure 6, and the arch coefficient of the new stress arch is determined by the mining thickness, the integral overburden lithology and the thickness.
C. Setting the arch height of the stress arch to be equal to the total thickness H of the overlying strata 0 Critical condition for maintaining stable stress arch structure a = H for ultimate mining width (failure of load bearing capacity of stress arch is the moment when the height of arch dome develops to surface, at which time the corresponding working face advance distance is the ultimate mining width of working face 0 Respectively calculate the thicknessThe working face ultimate mining width under the two states of the hard rock layer not broken and the hard rock layer broken) is calculated to obtain the working face ultimate mining width, and the method comprises the following steps:
c1, under the condition that the thick and hard rock stratum is not broken, the thickness is calculated by the following formula:
Figure BDA0003941684480000082
c2, under the condition of breaking the thick hard rock stratum, the steel is obtained by calculation through the following formula:
Figure BDA0003941684480000083
the arch coefficient of the stress arch is obtained according to the following formula:
Figure BDA0003941684480000091
wherein C represents the Pythium hardness coefficient of the lithology of the rock stratum related to the stress arch, C is more than or equal to 8 when the rock stratum is hard, C is more than or equal to 3 and less than 8 when the rock stratum is hard, and C is less than 3 when the rock mass is weak; e is a mathematical constant, and A and B are coefficients determined according to numerical simulation inversion or field actual measurement data; the rock stress arch is positioned below the thick and hard rock stratum S, then H k Value of H j (ii) a Under the condition that the rock thick hard rock layer is not broken, H k Value of H 0 -H s (ii) a Breaking condition of rock thick hard rock stratum, namely H k Value of H 0 。
In some embodiments, if the method A1 cannot be satisfied by both the stiffness condition criterion and the strength condition criterion, the working face ultimate mining width in the method C is calculated by the following formula:
Figure BDA0003941684480000092
wherein b 'is arch springing offset, b' =0.05MH j J is the stratum in which the arch crown of the stress arch is located, H j Is the horizon height of formation j.
In some embodiments, the thick hard formation S of the present invention is determined by:
a1, calculating rock strata from an S1 th layer to an m +1 th layer by taking the rock stratum S1 as an assumed thick hard rock stratum, sequentially judging, wherein S1 is more than 0 and less than n, and respectively judging by the following rigidity conditions and strength conditions:
a11, the rigidity condition discriminant is as follows:
Figure BDA0003941684480000093
wherein i represents a rock formation, S1 < i < m, wherein E and gamma represent the elastic modulus and the gravity density of the rock formation, respectively, i.e. E m+1 Denotes the elastic modulus, γ, of the formation m +1 m+1 Denotes the gravity density, h, of the formation m +1 m+1 Denotes the thickness of the formation m +1 itself, h i Denotes the thickness of the formation i itself, gamma i Representing the gravity density of formation i.
In some embodiments, the stiffness condition criterion in method a11 may be determined using the following formula;
q S1/m+1 ＜q S1/m s1 < m, wherein q S1/m Represents the load of the rock layer S1 calculated from the S1 th layer to the m 1 th layer, q S1/m+1 The load to be borne by the rock formation S1 is calculated from the S1 st zone to the (m + 1) th zone.
A12, the strength condition discriminant is as follows:
l s1 ＜l m+1 wherein l is s1 Is the breaking distance of the s1 st rock formation, l m+1 The breaking distance of the (m + 1) th stratum; the breaking distance calculation formula is as follows:
Figure BDA0003941684480000101
wherein i represents a rock formation, l i Is the breaking distance of the i-th rock formation, h i Denotes the thickness of the formation i itself, R Ti Denotes the tensile strength of the i-th rock formation, q i Indicating the load experienced by the ith formation.
A13, judging all rock layers of the overlying strata until a rigidity condition discriminant and a strength condition are simultaneously metAnd determining that the rock stratum m +1 is the thick hard rock stratum S by the discriminant. The thick hard rock stratum S can also have multiple layers, preferably, the multiple layers of the thick hard rock stratum S can be combined and simplified into one layer, the thick hard rock stratum S can also be numbered as S1, S2 and 8230from bottom to top in sequence, and then h s ＝h s1 +h s2 + \8230thatthe height of thick and hard rock S layer is H s1 、H s2 823000, or H s ＝H s1 +H s2 + \8230, the present embodiment will be described in detail by taking the example of merging and simplifying the multiple layers of thick and hard rock S into one layer.
Taking a single-layer thick hard rock layer in the overburden as an example, the working face is pushed to a certain distance, the arch height develops to the position of the thick hard rock layer, and the stress arch height can be stopped below the thick hard rock layer and does not increase due to the existence of the thick hard rock layer. The working face continues to be pushed, and the thick and hard rock stratum has two states: (1) the thick and hard rock stratum is not broken, the shape of the lower arch is gradually flattened at the moment, and the overlying rock above the thick and hard rock stratum arches again; (2) if the thick and hard rock stratum is broken, the upper and lower stress arches are combined into a new arch, and in some embodiments, the method for judging whether the thick and hard rock stratum is broken or not is as follows:
b200, respectively judging according to the conditions of the empty top distance and the limit fracture distance of the thick hard rock stratum;
b201, the conditions of the space-head distance of the thick hard rock stratum are as follows:
M-(ε p -1)H k1 -W s if the thickness is larger than zero, a hollow top appears below the thick hard rock layer, wherein M is the mining thickness, and epsilon p In order to break the residual crushing expansion coefficient of the rock formation, W s The maximum subsidence of the earth surface;
b202, the conditions of the limit fracture distance of the thick hard formation are as follows:
Figure BDA0003941684480000111
wherein L is S The expression represents the lateral exposure length, R, of a thick hard rock formation T Tensile strength of thick hard rock formations, q s Representing the load borne by the thick and hard rock formation; the thick hard rock layer S is a multilayer, and the thick hard rock layer at the lowermost layer (i.e., the thick hard rock layer S1) is used for the determination.
B203, and simultaneously satisfies M- (epsilon) p -1)H k1 -W s ＞0、
Figure BDA0003941684480000112
And judging that the thick and hard rock stratum is broken, namely that the suspension distance of the thick and hard rock stratum caused by the mining of the working face reaches the limit breaking distance.
A readable storage medium having stored thereon an executable program which when executed by a processor implements the steps of a face ultimate mining width calculation method.
An electronic device comprising a memory storing an executable program and a processor that when executed implements the steps of a face ultimate mining width calculation method.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made herein without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims (8)

1. A working face ultimate mining width calculation method is characterized by comprising the following steps: the method comprises the following steps:
A. the method comprises the following steps that overlying strata are arranged above a coal seam, the overlying strata comprise n rock strata, and a thick and hard rock stratum S forming layered arch conditions is determined from the n rock strata according to a key layer theory;
B. a stress arch is constructed above a coal seam and is gradually pushed along with the working surface of the stress arch, and the arch height calculation method of the stress arch is as follows:
b1, if the stress arch is positioned below the thick hard rock stratum S, the arch height a of the stress arch 1 The calculation method (2) is as follows:
a 1 ＝bK j wherein a is 1 Is the height of the arch, b is the span of the arch, K j The arch coefficient of the elliptical arch is represented by j, the stratum where the arch crown of the stress arch is located is represented by j, and j is more than 0 and less than or equal to n;
b2, if the stress arch spans the thick hard rock stratum S, judging whether the thick hard rock stratum is broken or not, and dividing the situation into two situations of not breaking the thick hard rock stratum and breaking the thick hard rock stratum according to the situation, wherein the two situations are as follows:
b21, if the thick hard rock stratum is not broken, the stress arch comprises an upper stress arch and a lower stress arch, the upper stress arch is formed above the thick hard rock stratum, the lower stress arch is formed below the thick hard rock stratum, and the total arch height a of the upper stress arch and the lower stress arch is 2 Calculated according to the following formula:
a 2 ＝[L 1 -2H s cotψ+0.1(M-ε P H S +H S )(H 0 -H s )]K 2 +H s +h s
wherein L is 1 Width of mining for lower stress arches, H s Is the horizon height of the thick hard rock formation S,
Figure FDA0003941684470000011
h s is the thickness of the thick hard rock stratum S, M is the mining thickness, epsilon p To break the residual crushing expansion coefficient of the rock formation, H 0 Total thickness of overburden, K 2 The camber coefficient of the upper stress arch is phi, and phi represents the fracture angle of the overlying strata;
b22, if the thick hard rock stratum is broken, the arch height a of the new stress arch of the broken thick hard rock stratum 3 Calculated according to the following formula:
a 3 ＝(L 3 +0.1MH 0 )K 3 wherein L is 3 For the mining width of the new stress arch, M is the mining thickness, K 3 The arch coefficient of the new stress arch;
C. setting the arch height of the stress arch to be equal to the total thickness H of the overlying strata 0 And calculating to obtain the working face limit mining width for the limit critical condition of the mining width, wherein the method comprises the following steps:
c1, under the condition that the thick and hard rock stratum is not broken, the thickness is calculated by the following formula:
Figure FDA0003941684470000021
c2, under the condition of breaking the thick hard rock stratum, the steel plate is obtained by calculation through the following formula:
Figure FDA0003941684470000022
2. the face ultimate mining width calculation method of claim 1, wherein: the arch coefficient of the stress arch is obtained according to the following formula:
Figure FDA0003941684470000023
wherein C represents the Pythium hardness coefficient of the rock stratum lithology related to the stress arch, e is a mathematical constant, and A and B are coefficients determined according to numerical simulation inversion or field actual measurement data; h if the stress arch is located below the thick hard rock stratum S k Value of H j (ii) a If the thick hard rock formation is not in a broken condition, H k Value of H 0 -H s (ii) a If the thick and hard rock formation is broken, H k Value of H 0 。
3. The face ultimate mining width calculation method of claim 1, wherein: the thick hard rock formation S is determined by the following method:
a1, taking a rock stratum S1 as an assumed thick hard rock stratum, and judging the rock stratum S1 < n by using the following rigidity conditions and strength conditions respectively:
a11, the stiffness condition discriminant is as follows:
Figure FDA0003941684470000024
wherein E and gamma represent the elastic modulus and the gravity density of the rock stratum respectively;
a12, the strength condition discriminant is as follows:
l s1 ＜l m+1 wherein l is s1 Is the breaking distance of the s1 st rock formation, l m+1 Breaking distance of the (m + 1) th rock stratum;
and A13, judging all rock strata of the overburden rock until a rigidity condition discriminant and a strength condition discriminant are simultaneously met, and determining that the rock stratum m +1 is a thick and hard rock stratum.
4. The face ultimate mining width calculation method of claim 1, wherein: the method for judging the breakage of the thick and hard rock stratum comprises the following steps:
b200, respectively judging according to the conditions of the space-head distance and the ultimate breaking distance of the thick hard rock stratum ；
B201, the conditions of the space-head distance of the thick hard rock stratum are as follows:
M-(ε p -1)H k1 -W s if the thickness is larger than zero, a hollow top appears below the thick hard rock layer, wherein M is the mining thickness, and epsilon p In order to break the residual crushing-expansion coefficient of the rock formation, W s The maximum subsidence of the earth surface;
b202, the conditions of the limit fracture distance of the thick hard rock stratum are as follows:
Figure FDA0003941684470000031
wherein L is S The expression represents the lateral exposure length, R, of a thick hard rock formation T Tensile strength of thick hard rock formations, q s Representing the load borne by a thick hard rock formation;
b203, and simultaneously satisfies M- (epsilon) p -1)H k1 -W s ＞0、
Figure FDA0003941684470000032
And judging that the thick hard rock stratum is broken.
5. The face ultimate mining width calculation method of claim 3, wherein: the rigidity condition discriminant in the method A11 adopts the following formula;
q S1/m+1 ＜q Sl/m s1 < m, wherein q S1/m Represents the load of the rock layer S1 calculated from the S1 st layer to the m 1 th layer, q S1/m+1 The load borne by the rock formation S1 is calculated from the S1 st zone to the (m + 1) th zone.
6. The face ultimate mining width calculation method of claim 3, wherein: if the method A1 cannot satisfy the rigidity condition discriminant and the strength condition discriminant at the same time, the working face ultimate mining width in the method C is calculated by the following formula:
Figure FDA0003941684470000041
wherein b 'is arch springing offset, b' =0.05MH j J is the stratum in which the arch crown of the stress arch is located, H j Is the horizon height of formation j.
7. A readable storage medium having stored thereon an executable program, the executable program when executed by a processor implementing the steps of the face ultimate mining width calculation method of any one of claims 1 to 6.
8. An electronic device comprising a memory and a processor, the memory storing an executable program, wherein the processor when executing the executable program performs the steps of the face limit mining width calculation method of one of claims 1 to 6.
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