CN111598355B - Hierarchical prediction method for ore pressure of multi-layer hard rock stratum - Google Patents
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Abstract
The invention relates to a hierarchical prediction method for the rock pressure of a multi-layer hard rock, which comprises structural feature analysis of the multi-layer hard rock, primary instability scale calculation of the multi-layer hard rock, periodic instability scale calculation of the multi-layer hard rock and prediction of the rock pressure of the multi-layer hard rock. The invention provides a method for predicting mining pressure of a near-horizontal super-thick coal seam under the condition of a multi-layer hard rock stratum based on plate shell mechanics and plastic mechanics, which scientifically analyzes the control function of different layer hard rock strata on the development of the mining pressure, realizes the hierarchical prediction of the mining pressure, has higher prediction accuracy, and opens up a new way for the hierarchical prediction of the mining pressure of a coal mine.
Description
Technical Field
The invention belongs to the technical field of coal mining, and particularly relates to a multi-layer hard rock stratum ore pressure grading prediction method for ultra-thick coal seam mine mining.
Background
The hard rock stratum has the characteristics of high strength, large thickness, strong integrity and the like, so the hard rock stratum is not easy to be unstable. When a hard rock stratum exists above the working surface, the step distance can reach hundreds of meters, and particularly when a plurality of layers of hard rock stratum exist in the overlying strata, the problem of displaying the mine pressure is more complex, the roof can be pressed in a large area when the roof is unstable, underground storm can be caused, secondary disasters such as gas, water and the like can be induced when the roof is seriously unstable, and the safety of underground personnel is threatened. Aiming at the mine, the accurate mine pressure grading prediction is the basis of mine pressure prevention and control and rock stratum control, and is beneficial to safe and efficient production of the mine.
Disclosure of Invention
The invention provides a multi-layer hard rock stratum ore pressure grading prediction method, which aims to cope with mine disasters caused by hard rock stratum overburden instability and improve safe and efficient production of mines.
A method for hierarchical prediction of the mine pressure of a multi-level hard rock formation, the method comprising the steps of:
step 1, calculating and determining the number and positions of hard rock layers from bottom to top according to a mine drilling histogram until the position of the uppermost hard rock layer is determined, wherein the following judgment criteria are met in the calculation process:
(1): assuming that the 1 st formation is a hard formation, its control range reaches the n-th formation, then the n+1-th layer is the next hard formation, at which time the formation load satisfies: q n+1 <q n
Wherein: q n+1 -calculating the load to the (n+1) th rock formation, the (1) st rock formation;
q n -calculating the load to the 1 st formation when it reaches the nth formation;
(2): assuming that the hard formations in the overburden that meet condition (1) have k layers in total, the strength condition of the hard formations should also be met: b j+1 <b j
Wherein: b j+1 -primary destabilization scale of the j+1th formation;
b j -the primary destabilization scale of the jth formation;
and 2, carrying out structural feature analysis on the multi-layer hard rock stratum, determining the structural form of control of each hard rock stratum, and predicting the structural instability step of the hard rock stratum, wherein the method comprises the following specific steps of:
step 2-1: establishing a multi-layer hard rock stratum system model of a progressive and compound unsteady motion plate type structure from a low-position hard rock stratum cantilever structure, a middle-position hard rock stratum masonry structure to a high-position hard rock stratum pressure arch structure;
step 2-2: respectively determining the period instability scale of a control structure of the low-level hard rock stratum, the medium-level hard rock stratum and the high-level hard rock stratum, and calculating the advancing distance of the corresponding stope face of the structure instability;
step 3: and predicting the ore pressure appearance, and carrying out grading prediction on the ore pressure appearance according to the primary instability scale, the period instability scale, the free space height below the rock stratum before the instability and the working face pushing distance of the low-level hard rock stratum, the medium-level hard rock stratum and the high-level hard rock stratum. The prediction shows that the primary instability of the low-level hard rock stratum controls the primary pressure of the working surface, the periodic instability of the low-level hard rock stratum controls the small-period pressure of the working surface, the large-period pressure of the working surface is controlled by the instability of the medium-level hard rock stratum, the high-level hard rock stratum can form a large-scale pressure arch structure in a space range, and when the space structure is unstable, the dynamic appearance is easy to induce.
Further, the calculation formulas adopted for the hard rock stratum load calculation and the primary instability scale in the step 1 are respectively as follows:
wherein: (q) n ) 1 -load of the nth layer of strata on the 1 st layer of strata, MPa;
E n -the elastic modulus of the nth layer of rock formation, GPa;
μ n poisson's ratio of the nth layer of rock formation;
γ n -the volume weight, kN/m, of the nth layer of rock formation 3 ；
h n -the thickness of the nth layer of rock formation, m;
wherein: a mode:b mode: />
Wherein: b 1i -primary destabilization scale of hard rock formation, m;
a i -the length of the hard rock layer in the direction of the working surface is suspended, m;
q i -load on the hard rock formation, MPa;
M si -a bending moment at the limit of the hard formation,N·m；
h i -hard formation thickness, m;
σ si -tensile strength of the hard rock formation, MPa;
x i -a hard formation destabilization geometry in the primary destabilization a mode of the hard formation;
y i -geometrical parameters of destabilization of the hard formation in the primary destabilization b mode of the hard formation.
Further, the periodic instability scale calculation method in the step 2-2 is as follows:
after the primary destabilization of the low-level hard rock stratum, the period destabilization of the low-level hard rock stratum is caused as the stope working surface continues to advance, and the period destabilization scale of the low-level hard rock stratum is solved as follows:
wherein: a mode:b mode: />
Wherein: x is x i -rock stratum destabilization geometrical parameters in low-order hard rock stratum periodic destabilization mode b mode;
y i -a rock stratum destabilization geometrical parameter in a low-order hard rock stratum periodic destabilization mode a mode;
the working face is continuously pushed, the low-level hard rock stratum is subjected to periodic instability, the middle-level hard rock stratum can reach the primary instability scale, the calculation method is as above, periodic instability is generated after the middle-level hard rock stratum is subjected to primary instability, and the high-level hard rock stratum can also generate primary instability and periodic instability in the same way; the periodic instability scale of the middle hard rock stratum and the high hard rock stratum is solved as follows:
wherein: b mode:
a mode:
a mode:
x i -hard formation destabilization geometry in b mode;
y 1i -a hard formation destabilization geometry in mode;
y 2i -hard formation destabilization geometry in a mode.
Further, the relation between the working face advancing distance and the instability scale is as follows:
L i ＝2H i ×cotδ+b i (5)
wherein L is i Step distance is pressed for the working surface;
H i spacing the hard formation from the coal seam;
the delta formation collapses at an angle.
The beneficial effects are that: the invention provides a method for predicting mining pressure classification of a near-horizontal super-thick coal seam under a multi-layer hard rock stratum condition based on plate shell mechanics and plastic mechanics, which is used for revealing the overlying strata structure characteristics of a hard rock stratum stope, determining the instability scale of the hard rock stratum structure under different conditions, clarifying the instability movement rule of the overlying strata structure, reasonably explaining the mining pressure phenomenon generated by mining the super-thick coal seam under the hard rock stratum condition, and comprises the following steps: the low-level hard rock stratum is unstable for the first time, and the pressure strength is medium; the low-level hard rock stratum is unstable periodically, and the pressure intensity is weak; the medium-position hard rock stratum is unstable, and the pressure intensity is medium; the high-position hard instability has strong pressure intensity, realizes relatively accurate prediction of the instability movement of the hard rock stratum overlying strata, and provides technical support for safe and efficient production of coal mines.
Drawings
FIG. 1 is a flow chart of a method for hierarchical prediction of the mine pressure of a multi-level hard rock according to one embodiment of the present invention;
FIG. 2 is a schematic illustration of a primary destabilizing fracture line of a low level hard rock formation according to one embodiment of the present invention;
FIG. 3 is a schematic view of a low level hard formation periodic instability fracture line according to one embodiment of the present invention;
FIG. 4 is a schematic view of the initial destabilizing fracture lines of the medium hard rock formation I according to one embodiment of the invention;
FIG. 5 is a schematic illustration of a periodic destabilizing fracture line of a medium hard formation I according to one embodiment of the invention;
FIG. 6 is a schematic illustration of the initial destabilizing fracture line of the medium hard rock formation II according to one embodiment of the invention;
FIG. 7 is a schematic illustration of a median hard formation II cycle destabilizing fracture line according to one embodiment of the invention;
FIG. 8 is a schematic view of a primary destabilizing fracture line of an upper hard rock formation according to one embodiment of the invention;
FIG. 9 is a schematic view of a high-level hard formation periodic instability fracture line according to an embodiment of the present invention;
FIG. 10 is a cross-sectional view of a low level hard rock formation primary destabilization according to one embodiment of the invention;
FIG. 11 is a cross-sectional view of a first cycle of destabilization of a low level hard rock formation according to one embodiment of the invention;
FIG. 12 is a cross-sectional view of a primary destabilization of the medium hard rock formation I according to one embodiment of the invention;
FIG. 13 is a cross-sectional view of a primary destabilization of the medium hard rock formation II according to an embodiment of the invention;
FIG. 14 is a cross-sectional view of an initial destabilization of an upper hard rock formation according to an embodiment of the present invention.
In the figure, 1, high hard rock, 2, medium hard rock, II,3, medium hard rock, I,4, and low hard rock.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention.
The invention is described in further detail below with reference to fig. 1-14 using a hard rock mine in a large mine area as an example:
according to the drilling column and data of the coal mine working face, according to the hard rock stratum collaborative deformation load calculation formula and the hard rock stratum primary instability calculation formula, calculating the load of each overburden stratum layer by layer from bottom to top, wherein the calculation result is as follows: step 1: hard rock layer determination:
q 1 ＝γ 1 h 1 ＝68.4kPa
calculating the effect of layer 2 on layer 1, then q 2/1 The method comprises the following steps:
it follows that layer 3, 13.1m thick sandy mudstone, is the first hard formation; similarly, the above process is continued based on the layer 3 formation:
q 3 ＝γ 3 h 3 ＝340.6kPa
q 6/3 ＝547.3kPa
q 7/3 ＝620.3kPa
q 8/3 ＝638.3kPa
q 9/3 ＝658.5kPa
q 10/3 ＝707.9kPa
q 11/3 ＝735.8kPa
q 12/3 ＝777.4kPa
q 13/3 ＝792.7kPa
q 14/3 ＝810.7kPa
q 15/3 ＝866.4kPa
q 16/3 ＝903.9kPa
q 17/3 ＝939.9kPa
q 18/3 ＝972.5kPa
q 19/3 ＝994.7kPa
q 20/3 ＝586.1kPa<q 19/3
it follows that the 20 th layer of 14.4m thick siltstone is the second hard rock layer;
q 20 ＝γ 20 h 20 ＝364.3kPa
q 22/20 ＝520.4kPa
q 23/20 ＝607.2kPa
q 24/20 ＝674.7kPa
q 25/20 ＝518.6kPa<q 24/20
from this, the 25 th layer of 14.2m thick K4 sandstone is the third hard rock layer;
q 25 ＝γ 25 h 25 ＝369.2kPa
q 27/25 ＝507.9kPa
q 28/25 ＝550.5kPa
q 29/25 ＝633.1kPa
q 30/25 ＝729.5kPa
q 31/25 ＝573.2kPa<q 30/25
from this, it can be seen that layer 31, 15.9m thick, of K5 sandstone is the fourth hard formation;
q 31 ＝γ 31 h 31 ＝413.4kPa
q 33/31 ＝671.7kPa
q 34/31 ＝749.1kPa
q 35/31 ＝786.1kPa
q 36/31 ＝818.3kPa
q 37/31 ＝559.7kPa<q 36/31
from this, it can be seen that layer 37, 20.5m thick, of K8 sandstone is the fifth layer of hard rock;
a total of five layers of hard rock layers in the overburden are determined through calculation, wherein the five layers of hard rock layers are respectively Y3, Y20, Y25, Y31 and Y37.
And 2, calculating the primary instability scale of the hard rock stratum. And (3) respectively bringing the physical and mechanical parameters of the first to fourth hard rock layers into a formula (2), and calculating the primary instability scale of each hard rock layer:
b 120 ＝110.4m
b 125 ＝115.1m
b 131 ＝115.3m
from b 131 ＞b 125 ＞b 120 ＞b 13 Then the Y3 formation is a lower hard formation, the Y20 formation is a median hard formation I3, the Y25 formation is a median hard formation II2, and the Y31 is an upper hard formation.
And 3, calculating the period instability scale of the hard rock stratum.
(1) Low-order hard rock stratum 4 period instability scale calculation
The primary instability scale calculation of the low-level rock stratum is the same as that of the upper section, b 13 =56.6m, i.e. the low-level hard rock is unstable by 56.6m, the low-level hard rock is suspended along the length direction of the working surface by a distance a 3 For 224.6m, substituting the calculation of the geometrical parameter of the destabilization of the hard rock stratum in the low-order hard rock stratum a mode to obtain the calculation:
at this time satisfy 2x 3 ≤a 3 The primary destabilization mode of the lower hard rock follows the hard rock destabilization mode a.
Solving the period instability scale of the low-level hard rock stratum and the geometrical parameter y of the hard rock stratum according to the period instability mode a of the low-level hard rock stratum:
b 23 ＝20.5m
y 3 ＝30.0m
obviously b 23 ＜y 3 The mode application condition is not satisfied. Thus, the period instability mode of the low-order hard rock stratum is converted into a mode b, and the low-order hard rock stratum is recalculatedHard formation period destabilization scale and destabilization geometry parameters x:
b 23 ＝22.7m
at this time satisfy 2x 3 ≤a 3 The low hard formation period destabilization mode follows the low hard formation period destabilization mode b.
In summary, the low-level hard rock stratum is sandy mudstone with the thickness of 13.1m, the primary instability scale of the sandy mudstone is 56.6m, and the period instability scale of the sandy mudstone is 22.7m.
(2) Medium hard formation I3 destabilization scale calculation
The primary instability scale calculation of the median rock stratum 1 is the same as that of b 120 =110.4m, i.e. the primary destabilization scale of the median hard rock layer I3 is 110.4m, when the median hard rock layer I3 is suspended along the length direction of the working surface by a distance a 20 For 166.0m, the median hard formation destabilization geometry x was calculated to be:
at this time satisfy 2x 20 ≤a 20 The medium hard formation I3 primary destabilization mode follows the medium high hard formation primary destabilization mode a. The median hard rock layer I3 period destabilization scale and median hard rock layer destabilization geometric parameter x:
at this time satisfy 2x 20 ≤a 20 The medium hard formation period destabilization mode follows the medium high hard formation period destabilization mode a.
In summary, the median hard formation I3 is siltstone 14.4m thick, with a primary destabilization scale of 110.4m and a periodic destabilization scale of 92.8m.
(3) Median hard formation II2 destabilization scale calculation
The primary destabilization scale calculation of the medium hard rock layer II is the same as that of b 125 115.1m, i.e. the primary destabilization scale of the median hard rock layer II is 115.1m, at which time the median hard rock layer II is suspended along the length of the working surface by a distance a 25 For 140.3m, the hard formation destabilization geometry x was calculated to be:
at this time satisfy 2x 25 ≤a 25 The median hard formation II primary destabilization mode follows the hard formation destabilization mode a. Median hard formation II cycle destabilization scale and hard formation destabilization geometry parameter x:
at this time satisfy 2x 25 ≤a 25 The medium hard formation II cycle destabilization follows the medium high hard formation destabilization mode a.
In summary, the median hard rock layer II2 is a K4 sandstone 14.2m thick, with a primary destabilization scale of 115.1m and a period destabilization scale of 96.9m.
(4) High-order hard rock stratum 1 instability scale calculation
The primary instability scale calculation of the high-order hard rock stratum 1 is the same as that of b 131 115.3m, i.e. the high-order hard rock is unstable to a dimension of 115.3m, the high-order hard rock is suspended along the length direction of the working surface by a distance a 31 For 111.7m, the calculation of the hard formation primary destabilization geometry y can be obtained:
at this time satisfy 2y 31 ≤b 31 The high hard formation primary destabilization mode follows the hard formation primary destabilization mode b. High-order hard rock stratum period instability scale and hard rock stratum instability geometric parameter x:
at this time do not satisfy 2x 31 ≤a 31 The high-order hard rock layer period instability mode is converted into a mode b, and the mode b comprises the following steps:
y 131 ＝k·y 222 ＝41.0m
at this time satisfy y 131 +y 131 ≤b 331 The formation period destabilization follows the medium and high hard formation period destabilization mode b.
In summary, the high-order hard rock layer is fine-grained sandstone 15.9m thick, the primary instability scale is 115.3m, and the period instability scale is 104.4m.
And 4, analyzing the ore pressure appearance prediction process.
According to a similar simulation result, the stratum collapse angle delta is 65 degrees, the broken expansion coefficient of the fractured zone stratum is 1.15, and the broken expansion coefficient of the fractured zone stratum is 1.05. The structural instability evolution law of the hard rock stratum is described as follows:
(1) Low-level hard destabilization analysis: the working face is pushed to 62.0m, the low-level hard rock stratum reaches the primary instability scale 56.6m, the free space height delta below the rock stratum before instability is 16.5m, the low-level hard rock stratum is subjected to primary instability, the primary instability of the low-level hard rock stratum leads to the primary pressure coming from the working face, and the primary pressure coming step distance is 62.0m.
The period instability scale of the low-level hard rock stratum is 22.7m, and the working surface is pushed to 84.7m for the first period to come and press. At this time, the mine pressure is more gentle, if the destabilization scale of the middle hard rock layer I is close to the destabilization scale of the middle hard rock layer II2, the two hard rock layers can generate compound destabilization manifestation, and stronger mine pressure manifestation occurs at this time.
(2) Medium hard formation I destabilization analysis: the primary instability scale of the rock stratum is 110.4m, the free space height delta below the rock stratum before instability is 3.9m, the working face is pushed to 174.4m, the primary instability of the middle hard rock stratum I occurs, the primary instability is only 1.1m different from the fifth period instability of the low hard rock stratum, the composite instability occurs to the middle and low hard rock stratum, and the secondary pressure is severe.
The period instability scale of the middle hard rock layer I3 is 92.8m, and when the working surface is pushed to 267.2m, the middle hard rock layer I3 is subjected to period instability for the first time, so that the working surface is subjected to large period pressure. At this time, the mine pressure appears more severe.
(3) Median hard formation II2 destabilization analysis: the primary instability scale of the rock stratum is 115.1m, the free space height delta below the rock stratum before instability is 0.9m, the working face is pushed to 204.8m, the primary instability of the medium-hard rock stratum II2 occurs, and the secondary pressure is more intense.
The period instability scale of the middle hard rock layer II2 is 96.9m, and when the working surface is pushed to 301.7m, the middle hard rock layer II2 is subjected to period instability for the first time, so that the working surface is subjected to large period pressure. At this time, the mine pressure appears more severe.
(4) High-order hard rock layer instability analysis: the rock stratum is mainly made of fine sandstone, the strength is high, the primary instability scale is 115.3m, the working face is pushed to 233.6m, the space above the stope is formed by taking the high-position hard rock stratum as the top, and a pressure arch structure is formed to bear the weight of the overlying rock stratum. Thus, it results in the working face still being affected by the development of the mine pressure in the region 200m behind it. As the working surface continues to advance beyond its limit dimensions, the high-lying hard rock formations will destabilize because there is still about 0.8m free space below it. The destabilization of the high-level hard rock layer causes the overlying rock to move in a large range, releases a large amount of elastic energy and can induce the appearance of strong mine pressure. After the high-level hard rock stratum is first destabilized, the working surface is pushed 104.4m again, and the high-level hard rock stratum is periodically destabilized, so that the circulation is performed.
After destabilization of the high hard rock, when the controlled overburden fracture height is developed to about 168m, the goaf is filled up due to the broken expansion of the coal rock, and the rock is only bent above the range and no destabilization occurs.
From the theoretical calculation, the primary pressure step distance of the working surface is 62.0m, the small-period pressure step distance is 7.7-28.8 m, the large-period pressure step distance is 30.4-62.4 m, the high-level hard rock stratum pressure arch structure dimension is 222.7-233.6 m, and the structural influence is exerted in the range of about 200-250 m behind the goaf.
The results of the step size is summarized in the range of 400m for face prediction and field measurement mining, as shown in Table 1. Theoretical prediction is carried out for 18 times, 3 future pressures exist in numerical simulation, and 1 future pressure exists in field actual measurement; the error between the theoretical prediction incoming pressure position and the actual measurement result in the field is 0-13.8 m, the maximum error of the incoming pressure step distance is 14.4%, and the error has higher coincidence degree with the actual measurement in the field.
Table 1 8218 working face field measured tap position
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (4)
1. A method for hierarchical prediction of the mine pressure of a multi-level hard rock stratum, the method comprising the steps of:
step 1, calculating and determining the number and positions of hard rock layers from bottom to top according to a mine drilling histogram until the position of the uppermost hard rock layer is determined, wherein the following judgment criteria are met in the calculation process:
(1): assuming that the 1 st formation is a hard formation, its control range reaches the n-th formation, then the n+1-th layer is the next hard formation, at which time the formation load satisfies: q n+1 <q n
Wherein: q n+1 -calculating the load to the (n+1) th rock formation, the (1) st rock formation;
q n -calculating the load to the 1 st formation when it reaches the nth formation;
(2): assuming that the hard formations in the overburden that meet condition (1) have k layers in total, the strength condition of the hard formations should also be met: b j+1 <b j
Wherein: b j+1 -primary destabilization scale of the j+1th formation;
b j -the primary destabilization scale of the jth formation;
and 2, carrying out structural feature analysis on the multi-layer hard rock stratum, determining the structural form of control of each hard rock stratum, and predicting the structural instability step of the hard rock stratum, wherein the method comprises the following specific steps of:
step 2-1: establishing a multi-layer hard rock stratum system model of a progressive and compound unsteady motion plate type structure from a low-position hard rock stratum cantilever structure, a middle-position hard rock stratum masonry structure to a high-position hard rock stratum pressure arch structure;
step 2-2: respectively determining the period instability scale of a control structure of the low-level hard rock stratum, the medium-level hard rock stratum and the high-level hard rock stratum, and calculating the advancing distance of the corresponding stope face of the structure instability;
step 3: and predicting the ore pressure appearance, and carrying out grading prediction on the ore pressure appearance according to the primary instability scale, the period instability scale, the free space height below the rock stratum before the instability and the working face pushing distance of the low-level hard rock stratum, the medium-level hard rock stratum and the high-level hard rock stratum.
2. The method for predicting the ore pressure of a multi-layer hard rock according to claim 1, wherein the calculation formulas adopted in the calculation of the load of the hard rock and the primary instability in the step 1 are respectively:
wherein: (q) n ) 1 -load of the nth layer of strata on the 1 st layer of strata, MPa;
E n -the elastic modulus of the nth layer of rock formation, GPa;
μ n poisson's ratio of the nth layer of rock formation;
γ n -the volume weight, kN/m, of the nth layer of rock formation 3 ；
h n -the thickness of the nth layer of rock formation, m;
wherein: a mode:b mode: />
Wherein: b 1i -primary destabilization scale of hard rock formation, m;
a i -the length of the hard rock layer in the direction of the working surface is suspended, m;
q i -load on the hard rock formation, MPa;
M si -ultimate bending moment of hard rock stratum, M si ＝σ si ·h i 2 /6，N·m；
h i -hard formation thickness, m;
σ si -tensile strength of the hard rock formation, MPa;
x i -a hard formation destabilization geometry in the primary destabilization a mode of the hard formation;
y i -geometrical parameters of destabilization of the hard formation in the primary destabilization b mode of the hard formation.
3. The method for predicting the ore pressure of the multi-layer hard rock stratum according to claim 2, wherein the method for calculating the period instability scale in the step 2-2 is as follows:
the period instability scale of the low-order hard rock stratum is solved as follows:
wherein: a mode:b mode: />
Wherein: x is x i -rock stratum destabilization geometrical parameters in low-order hard rock stratum periodic destabilization mode b mode;
y i -a rock stratum destabilization geometrical parameter in a low-order hard rock stratum periodic destabilization mode a mode;
a i -the length of the hard rock layer in the direction of the working surface is suspended, m;
q i -load on the hard rock formation, MPa;
M si -a bending moment at the limit of the hard formation,N·m；
the periodic instability scale of the middle hard rock stratum and the high hard rock stratum is solved as follows:
wherein: b mode:
a mode:
a mode:
x′ i -hard formation destabilization geometry in b mode;
y 1i -a hard formation destabilization geometry in mode;
y 2i -a hard formation destabilization geometry in mode;
a i -the length of the hard rock layer in the direction of the working surface is suspended, m;
q i -load on the hard rock formation, MPa;
M si -a bending moment at the limit of the hard formation,N·m。
4. the method for predicting the ore pressure of a multi-layer hard rock stratum according to claim 1, wherein the relation between the advancing distance of a working surface and the instability scale is as follows:
L i ＝2H i ×cotδ+b i (5)
wherein: l (L) i Step distance is pressed for the working surface;
H i spacing the hard formation from the coal seam;
the delta formation collapses at an angle.
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