阅读说明：本技术 一种底板隔水岩层稳定性计算方法 (Bottom plate water-resisting rock stratum stability calculation method ) 是由 李昂 段中会 李远谋 刘朝阳 马丽 王峰 杨增平 杨宇轩 丁学松 纪丙楠 周永根 于 2021-06-04 设计创作，主要内容包括：一种底板隔水岩层稳定性计算方法,S1：若煤岩层底板岩性相近,将岩煤开采层至承压开采层之间的部分简化为一种底板岩性结构的底板岩层,若煤岩层底板岩性存在明显的上下分层结构,将岩煤开采层至承压开采层之间的部分简化为两种底板岩性结构的底板岩层,建立力学模型,进行受力分析；S2：引入弹塑性破坏理论进行分析；S3：选取微分单元,建立微分平衡方程；S4：解微分方程,推导底板岩层能承受的最大极限水压力值或最小隔水岩层厚度安全阈值；S5：根据实际问题,判断隔水层厚度是否安全。该方法能推导出底板隔水岩层厚度安全阈值和最大极限水压力值,可科学合理的判断底板整体安全性,为高承压水体上开采煤岩层提供安全保障和理论指导。(A method for calculating the stability of a bottom plate water-resisting rock stratum is disclosed, S1: if the lithologic properties of the bottom plates of the coal rock strata are similar, simplifying the part between the rock coal mining layer and the pressure-bearing mining layer into the bottom plate rock strata with a bottom plate lithologic structure, if the lithologic properties of the bottom plates of the coal rock strata have obvious upper and lower layered structures, simplifying the part between the rock coal mining layer and the pressure-bearing mining layer into the bottom plate rock strata with two bottom plate lithologic structures, establishing a mechanical model, and carrying out stress analysis; s2: introducing an elastoplasticity destruction theory for analysis; s3: selecting a differential unit and establishing a differential balance equation; s4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum; s5: and judging whether the thickness of the water-resisting layer is safe or not according to the practical problem. The method can derive the safe threshold value of the thickness of the waterproof rock stratum of the bottom plate and the maximum limit water pressure value, can scientifically and reasonably judge the overall safety of the bottom plate, and provides safety guarantee and theoretical guidance for mining the coal rock stratum on the high-pressure water body.)

1. A bottom plate water-resisting rock stratum stability calculation method is characterized by comprising the following steps of;

if the lithology of the bottom plate of the coal rock stratum is similar, executing the step one; if the lithology of the bottom plate of the coal rock stratum has an obvious upper-lower layer layered structure, executing the second step;

the method comprises the following steps: the stability analysis is carried out by using the single lithologic structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

s1: establishing a mechanical model for stress analysis; the specific method comprises the following steps:

s10: simplifying the part from a rock coal mining layer to a pressure-bearing mining layer into a bottom plate rock layer with a bottom plate lithologic structure, and sequentially dividing the bottom plate lithologic structure into a bottom plate mining crack layer, an effective water-resisting layer and a bottom plate pressure-bearing water guiding and lifting crack layer from top to bottom;

s11: calculating the effective water-proof layer height h of the bottom plate according to the formula (1)₁；

h₁＝H₁-h₀-c (1)；

In the formula, H₁Is the thickness of the floor strata in m; h is₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

s12: calculating the equivalent water pressure q at the top of the pressure-bearing water lifting crack layer of the bottom plate according to the formula (2)₂(ii) a Calculating the equivalent load q of the caving gangue in the goaf according to a formula (3)₁；

q₂＝q₀-(h₁+h₀)·γ₁ (2)；

In the formula, q₀Water pressure for actual action of high confined water; gamma ray₁Is equivalent weight of the bottom rock layer, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

S2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

s20: simplifying the effective water-resisting layer and the bottom plate mining fracture layer into an ideal linear elastoplastomer, and enabling the deformation of the effective water-resisting layer to meet a formula (4) and the deformation of the bottom plate mining fracture layer to meet a formula (5);

σ_x＝k·σ_y+σ_n (4)；

in the formula (I), the compound is shown in the specification,σ_xthe horizontal stress of the microcell bodies in the bottom plate rock stratum in the x direction is unit MPa; sigma_yThe vertical stress of the microcell bodies in the bottom plate rock stratum in the y direction is unit MPa; sigma_nThe uniaxial compressive strength of the bottom rock stratum is unit MPa,or obtained by actual measurement; c. C_nThe cohesive force of the bottom plate rock stratum is unit MPa;is the internal friction angle of the floor strata in degrees;

is the residual strength of the bottom rock layer in MPa,or obtained by actual measurement;the residual cohesive force of the bottom plate rock stratum is unit MPa;the residual internal friction angle of the floor rock layer is unit degree; when the internal friction angle of the floor strata is constant during the elastic and residual phases, i.e. whenThen there is k^*＝k；

S3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of microcell body with the thickness of dy from the bottom plate isolation layer, and establishing a bottom plate rock stratum microcell body for stress analysis by taking the horizontal direction as an x axis and the vertical downward direction as a y axis, wherein d sigma_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; the stress balance equation of the microcell body in the y direction meets the formula (6); and according to formula (7)Calculating the frictional resistance tau on the contact surfaces of the microcell bodies and rock layers on two sides; establishing a stress balance equation in the y direction according to the formula (6) to obtain a formula (8);

∑F＝0 (6)；

τ＝f·σ_x+C (7)；

σ_y·L+2τ·dy-(σ_y+dσ_y)·L＝0 (8)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the effective water barrier h₁When C is equal to C_n(ii) a f is the friction coefficient of the contact surface of the micro unit body and the rock layers on two sides, and when the micro unit body is positioned on the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the effective water barrier h₁When the number of the carbon atoms is f,

s4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

s41: obtaining a formula (9) by simultaneous formula (6), formula (7) and formula (8), and solving the formula (9) to obtain a formula (10);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

s42: when y is 0, formula (11) is obtained; the formula (12) is obtained by combining the formula (3) and the formula (11); then deducing a formula (13);

s42: let y equal to h₀Obtaining a formula (14);

when the microcell bodies are positioned on the effective water-resisting layer, solving the problems as follows:

s43: obtaining a formula (15) by simultaneously establishing a formula (5), a formula (7) and a formula (8), and solving the formula (15) to obtain a formula (16);

in the formula, C₁Is an unknown quantity;

s44: first, let y be h₀+h₁Obtaining formula (17); the formula (18) is obtained by combining the formula (2) and the formula (17); then, simultaneously establishing a formula (16) and a formula (18) to obtain a formula (19);

s45: let y equal to h₀Obtaining a formula (20); when y is equal to h₀At the interface, the formula (20) is equal to the formula (14) to obtain a formula (21), and then the formula (21) is solved to obtain a formula (22);

s5: according to practical problems, whether the thickness of the water-resisting layer is safe or not is judged, and the specific process is as follows:

when the thickness H of the bottom plate water-resisting rock stratum₁When known, the extreme water pressure value that the bottom rock stratum can bear, the actual water pressure Q and the actual water pressure Q are given by a formula (22)₀There is a relationship in equation (23): when the water pressure value of the bottom plate water-resisting rock stratum is known, the formula (22) is solved to obtain the bottom plate rock stratumMinimum thickness value H_minActual thickness value H of floor strata₁With a minimum thickness value H_minThere is a relationship in equation (24):

step two: the stability analysis is carried out by using the double lithology structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

a1: establishing a mechanical model for stress analysis; the specific method comprises the following steps:

a10: simplifying the part between a rock coal mining layer and a pressure-bearing mining layer into bottom plate rock layers with two bottom plate lithologic structures, respectively marking the bottom plate rock layers with the two bottom plate lithologic structures as a bottom plate water-resisting rock layer A and a bottom plate water-resisting rock layer B from top to bottom, sequentially dividing the bottom plate water-resisting rock layer A into a bottom plate mining crack layer and an upper effective water-resisting layer from top to bottom, sequentially dividing the bottom plate water-resisting rock layer B into a lower effective water-resisting layer and a pressure-bearing water guiding crack layer from top to bottom, wherein the upper effective water-resisting layer and the lower effective water-resisting layer form a total effective water-resisting layer;

a11: calculating the total effective water-resisting layer height of the bottom plate according to a formula (25);

h₂+h₃＝H₂-h₀-c (25)；

in the formula, H₂When the actual thickness of the bottom plate water-resisting layer is determined to solve the maximum value of the pressure-bearing water pressure, H is the total thickness of the bottom plate rock layer in unit of m₂＝H_{Fruit of Chinese wolfberry}；h₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

a12: calculating the equivalent water pressure q at the top of the confined water lifting crack layer according to the formula (26)₃(ii) a Calculating the equivalent load q of the caving gangue in the goaf according to a formula (27)₁；

q₃＝q₀-(h₂+h₀)·γ₂-h₃·γ₃ (26)；

In the formula, q₀Water pressure for actual action of high confined water; h is₂Is the height of the upper effective water barrier; h is₀The height of a mining crack layer of the bottom plate; h is₃Is the height of the lower effective water barrier; gamma ray₂Is equivalent weight of the bottom plate water-resisting rock stratum A, unit KN/m³；γ₃Is equivalent weight of the bottom plate water-resisting rock stratum B, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

A2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

a20: simplifying the total effective water-resisting layer and the bottom plate mining fracture layer into an ideal linear elastoplast body, and enabling the deformation of the upper effective water-resisting layer in the bottom plate water-resisting rock layer A to meet a formula (27) and the deformation of the lower effective water-resisting layer in the bottom plate water-resisting rock layer B to meet a formula (28); enabling the deformation of the mining crack layer of the bottom plate to meet the formula (29);

σ_2x＝k₂·σ_2y+σ_2n (27)；

σ_3x＝k₃·σ_3y+σ_3n (28)；

in the formula (I), the compound is shown in the specification,σ_2xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum A in the x direction is in unit MPa; sigma_2yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum A in the y direction is in unit MPa; sigma_2nThe uniaxial compressive strength of the bottom plate water-resisting rock stratum A is unit MPa;or obtained by actual measurement; c. C_2nThe cohesive force of a bottom plate water-resisting rock stratum A is expressed in unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum A is unit degree;

σ_3xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum B in the x direction is in unit MPa; sigma_3yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum B in the y direction is in unit MPa; sigma_3mThe uniaxial compressive strength of the bottom plate water-resisting rock stratum B is unit MPa;or obtained by actual measurement; sigma_3nThe cohesive force of a bottom plate water-resisting rock stratum B is unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum B is unit degree;

is the residual strength of the top rock stratum A of the bottom plate water-resisting layer in unit MPa,or obtained by actual measurement;the residual cohesive force of a rock stratum A at the top of the water-resisting layer is unit MPa;the residual internal friction angle of the rock stratum A at the top of the water-resisting layer is unit degree; the internal friction angle of the top layer A of the water barrier in the elastic and residual phase is not changed, i.e.Then there is k^*＝k；

A3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of micro unit body with the thickness of dy from the bottom plate isolation layer, and establishing a bottom plate water-resisting layer micro unit body for stress analysis by taking the horizontal direction as an x axis and the vertical downward direction as a y axis, wherein da_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; the equilibrium equation of the stress of the microcells in the y direction of the microcells meets the formula (30); calculating the frictional resistance tau on the contact surfaces of the microcell bodies and rock layers on two sides according to a formula (31); establishing a y-direction stress balance equation according to the equation (31) to obtain an equation (32);

∑F＝0 (30)；

τ＝f·σ_x+C (31)；

σ_y·L+2τ·dy-(σ_y+dσ_y)·L＝0 (32)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the upper effective water barrier h₂When C is equal to C_2n(ii) a When the microcell is under the lower effective water barrier, C ═ C_3n(ii) a f is the friction coefficient of the contact surface of the micro unit body and the rock layers on two sides, and when the micro unit body is positioned on the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the upper effective water barrier h₂Always is f₂，When the microcells are in the upper effective water barrier h₃When is f₃，

A4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

a41: obtaining a formula (33) by a simultaneous formula (29), a formula (31) and a formula (32), and solving the formula (33) to obtain a formula (34);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

a42: when y is made 0, formula (35) is obtained; the formula (36) is obtained by combining the formula (27) and the formula (35); then deducing a formula (37);

a42: let y equal to h₀Obtaining a formula (38);

when the microcells are in the upper effective water barrier h₂Then, the solution is carried out according to the following method:

a43: obtaining a formula (39) by simultaneous formula (27), formula (31) and formula (32), and solving the formula (39) to obtain a formula (40);

in the formula, C₂Is an unknown quantity;

a44: let y equal to h₀Obtaining a formula (41); when y is equal to h₀At the interface, the formula (38) is equal to the formula (41) to obtain a formula (42), and the formula (42) and the formula (40) are simultaneously connected to obtain a formula (43);

a45: changing y to h₀+h₂Substituting the formula (43) to obtain a formula (44);

when the microcells are in the lower effective water-resisting layer h₃Then, the solution is carried out according to the following method:

a46: substituting the formula (28) and the formula (31) into the formula (32) to obtain a formula (45); solving the formula (45) to obtain a formula (46);

in the formula, C₃Is an unknown quantity;

a47: let y equal to h₀+h₂+h₃Obtaining a formula (47); the formula (24) and the formula (47) are combined to obtain a formula (48), and the formula (28) and the formula (46) are combined to obtain a formula (49);

a48: when y is equal to h₀+h₂At the interface, the formula (44) is equal to the formula (49) to obtain a formula (50), and then the formula (50) is solved to obtain a formula (51);

a5: according to practical problems, the thickness of the water-resisting layer is judged to be safe, and the specific process is as follows:

total thickness H of water-proof rock layer of bottom plate₂When known, the limit water pressure value that the soleplate water-proof layer can bear, the actual water pressure Q and the actual water pressure Q are given by a formula (51)₀There is a relationship in equation (52): when the water pressure value of the bottom plate waterproof rock stratum is known, solving the formula (51) to obtain the minimum thickness value H of the bottom plate waterproof rock stratum_minActual thickness value H of water-resisting layer of bottom plate₂With a minimum thickness value H_minThere is a relationship in equation (53):

2. the method for calculating the stability of the water-resisting rock stratum of the base plate according to claim 1, wherein in the step one, the heights of the mining crack layer and the confined water lifting crack layer of the base plate are calculated by field measurement or related theories.

3. The method for calculating the stability of the water-resisting rock stratum of the base plate according to claim 1, wherein in the second step, the heights of the mining crack layer and the confined water lifting crack layer of the base plate are calculated by field measurement or related theories.

Technical Field

The invention belongs to the technical field of rock and soil disasters, and particularly relates to a bottom plate water-resisting rock stratum stability calculation method.

Background

The development of coal plays a very important role in economic construction, and plays a middle and strong role in national economy and people's life. At present, a lot of coal is uniformly distributed near an underground water layer, and a lot of coal resources are seriously threatened by water damage. In recent years, water inrush accidents of coal strata bottom plates occur, the water inrush hidden danger of the coal strata bottom plates caused by confined water of limestone is particularly prominent, and the reasonable and scientific investigation of the water inrush hidden danger of the bottom plates in advance and the reduction and even elimination of the threat of water inrush of the bottom plates are very important.

In the prior art, no systematic theoretical solution method exists in the aspect of the stability of the bottom plate water-resisting layer, meanwhile, the double influences of the mining damage depth and the pressure bearing water lifting height of the bottom plate are not considered in the evaluation method of the safety of the bottom plate water-resisting rock layer, and the minimum water-resisting layer thickness and the maximum limit water pressure value are not obtained in the existing method. In addition, at the present stage, the site actual judgment of the safety of the bottom plate is still carried out by referring to a water inrush coefficient method, the water inrush coefficient method is an empirical result obtained by adopting a statistical induction method, no existing theoretical solution method exists for the safety evaluation of the stability of a specific coal mine or mining face bottom plate, theoretical support is lacked, the mechanical property of the bottom plate rock is not considered, and a systematic theoretical solution method is not available, so that scientific guidance cannot be brought to engineering practitioners in the actual operation process.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a method for calculating the stability of a bottom plate water-resisting rock stratum, which can derive a safety threshold value and a maximum limit water pressure value of the thickness of the bottom plate water-resisting rock stratum, can scientifically and reasonably judge the overall safety of the bottom plate and provide safety guarantee and theoretical guidance for mining coal rock strata on high-pressure water.

In order to achieve the purpose, the invention provides a method for calculating the stability of a bottom plate water-resisting rock stratum, wherein if the lithology of the bottom plate of a coal rock stratum is similar, a first step is executed; if the lithology of the bottom plate of the coal rock stratum has an obvious upper-lower layer layered structure, executing the second step;

the method comprises the following steps: the stability analysis is carried out by using the single lithologic structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

s1: establishing a mechanical model for stress analysis; the specific method comprises the following steps:

s10: simplifying the part from a rock coal mining layer to a pressure-bearing mining layer into a bottom plate rock layer with a bottom plate lithologic structure, and sequentially dividing the bottom plate lithologic structure into a bottom plate mining crack layer, an effective water-resisting layer and a bottom plate pressure-bearing water guiding and lifting crack layer from top to bottom;

s11: calculating the effective water-proof layer height h of the bottom plate according to the formula (1)₁；

h₁＝H₁-h₀-c (1)；

In the formula, H₁Is the thickness of the floor strata in m; h is₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

s12: calculating the equivalent water pressure q at the top of the pressure-bearing water lifting crack layer of the bottom plate according to the formula (2)₂(ii) a Calculating the equivalent load q of the caving gangue in the goaf according to a formula (3)₁；

q₂＝q₀-(h₁+h₀)·γ₁ (2)

In the formula, q₀Water pressure for actual action of high confined water; gamma ray₁Is equivalent weight of the bottom rock layer, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

S2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

s20: simplifying the effective water-resisting layer and the bottom plate mining fracture layer into an ideal linear elastoplastomer, and enabling the deformation of the effective water-resisting layer to meet a formula (4) and the deformation of the bottom plate mining fracture layer to meet a formula (5);

σ_x＝k·σ_y+σ_n (4)；

in the formula (I), the compound is shown in the specification,σ_xthe horizontal stress of the microcell bodies in the bottom plate rock stratum in the x direction is unit MPa; sigma_yThe vertical stress of the microcell bodies in the bottom plate rock stratum in the y direction is unit MPa; sigma_nThe uniaxial compressive strength of the bottom rock stratum is unit MPa,or obtained by actual measurement; c. C_nThe cohesive force of the bottom plate rock stratum is unit MPa;is the internal friction angle of the floor strata in degrees;

is the residual strength of the bottom rock layer in MPa,or obtained by actual measurement;of the floor strataResidual cohesion in MPa;the residual internal friction angle of the floor rock layer is unit degree; when the internal friction angle of the floor strata is constant during the elastic and residual phases, i.e. whenThen there is k^*＝k；

S3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of microcell body with the thickness of dy from the bottom plate isolation layer, and establishing a bottom plate rock stratum microcell body for stress analysis by taking the horizontal direction as an x axis and the vertical downward direction as a y axis, wherein d sigma_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; the stress balance equation of the microcell body in the y direction meets the formula (6); calculating the frictional resistance tau on the contact surfaces of the microcell bodies and rock layers on two sides according to a formula (7); establishing a stress balance equation in the y direction according to the formula (6) to obtain a formula (8);

∑F＝0 (6)；

τ＝f·σ_x+C (7)；

σ_y·L+2τ·dy-(σ_y+dσσ_y)·L＝0 (8)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the effective water barrier h₁When C is equal to C_n(ii) a f is the friction coefficient of the contact surface of the micro unit body and the rock layers on two sides, and when the micro unit body is positioned on the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the effective water barrier h₁When the number of the carbon atoms is f,

s4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

s41: obtaining a formula (9) by simultaneous formula (6), formula (7) and formula (8), and solving the formula (9) to obtain a formula (10);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

s42: when y is 0, formula (11) is obtained; the formula (12) is obtained by combining the formula (3) and the formula (11); then deducing a formula (13);

s42: let y equal to h₀Obtaining a formula (14);

when the microcell bodies are positioned on the effective water-resisting layer, solving the problems as follows:

s43: obtaining a formula (15) by simultaneously establishing a formula (5), a formula (7) and a formula (8), and solving the formula (15) to obtain a formula (16);

in the formula, C₁Is an unknown quantity;

s44: first, let y be h₀+h₁Obtaining formula (17); the formula (18) is obtained by combining the formula (2) and the formula (17); then, simultaneously establishing a formula (16) and a formula (18) to obtain a formula (19);

s45: let y equal to h₀Obtaining a formula (20); when y is equal to h₀At the interface, the formula (20) is equal to the formula (14) to obtain a formula (21), and then the formula (21) is solved to obtain a formula (22);

s5: according to practical problems, whether the thickness of the water-resisting layer is safe or not is judged, and the specific process is as follows:

when the thickness H of the bottom plate water-resisting rock stratum₁When known, the extreme water pressure value that the bottom rock stratum can bear, the actual water pressure Q and the actual water pressure Q are given by a formula (22)₀There is a relationship in equation (23): when the water pressure value of the bottom plate water-resisting rock stratum is known, solving the formula (22) to obtain a minimum thickness value H of the bottom plate rock stratum_minActual thickness value H of floor strata₁With a minimum thickness value H_minThere is a relationship in equation (24):

step two: the stability analysis is carried out by using the double lithology structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

a1: establishing a mechanical model for stress analysis; the specific method comprises the following steps:

a10: simplifying the part between a rock coal mining layer and a pressure-bearing mining layer into bottom plate rock layers with two bottom plate lithologic structures, respectively marking the bottom plate rock layers with the two bottom plate lithologic structures as a bottom plate water-resisting rock layer A and a bottom plate water-resisting rock layer B from top to bottom, sequentially dividing the bottom plate water-resisting rock layer A into a bottom plate mining crack layer and an upper effective water-resisting layer from top to bottom, sequentially dividing the bottom plate water-resisting rock layer B into a lower effective water-resisting layer and a pressure-bearing water guiding crack layer from top to bottom, wherein the upper effective water-resisting layer and the lower effective water-resisting layer form a total effective water-resisting layer;

a11: calculating the total effective water-resisting layer height of the bottom plate according to a formula (25);

h₂+h₃＝H₂-h₀-c (25)；

in the formula, H₂When the actual thickness of the bottom plate water-resisting layer is determined to solve the maximum value of the pressure-bearing water pressure, H is the total thickness of the bottom plate rock layer in unit of m₂＝H_{Fruit of Chinese wolfberry}；h₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

a12: calculating the equivalent water pressure q at the top of the confined water lifting crack layer according to the formula (26)₃(ii) a Calculating the equivalent load q of the caving gangue in the goaf according to a formula (27)₁；

q₃＝q₀-(h₂+h₀)·γ₂-h₃·y₃ (26)；

In the formula, q₀Water pressure for actual action of high confined water; h is₂Is the height of the upper effective water barrier; h is₀The height of a mining crack layer of the bottom plate; h is₃Is the height of the lower effective water barrier; gamma ray₂Is equivalent weight of the bottom plate water-resisting rock stratum A, unit KN/m³；γ₃Is equivalent weight of the bottom plate water-resisting rock stratum B, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

A2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

a20: simplifying the total effective water-resisting layer and the bottom plate mining fracture layer into an ideal linear elastoplast body, and enabling the deformation of the upper effective water-resisting layer in the bottom plate water-resisting rock layer A to meet a formula (27) and the deformation of the lower effective water-resisting layer in the bottom plate water-resisting rock layer B to meet a formula (28); enabling the deformation of the mining crack layer of the bottom plate to meet the formula (29);

σ_2x＝k₂·σ_2y+σ_2n (27)；

σ_3x＝k₃·σ_3y+σ_3n （28)；

in the formula (I), the compound is shown in the specification,σ_2xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum A in the x direction is in unit MPa; sigma_2yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum A in the y direction is in unit MPa; sigma_2nThe uniaxial compressive strength of the bottom plate water-resisting rock stratum A is unit MPa;or obtained by actual measurement; c. C_2nThe cohesive force of a bottom plate water-resisting rock stratum A is expressed in unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum A is unit degree;

σ_3xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum B in the x direction is in unit MPa; sigma_3yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum B in the y direction is in unit MPa; sigma_3nThe uniaxial compressive strength of the bottom plate water-resisting rock stratum B is unit MPa;or obtained by actual measurement; sigma_3nThe cohesive force of a bottom plate water-resisting rock stratum B is unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum B is unit degree;

is the residual strength of the top rock stratum A of the bottom plate water-resisting layer in unit MPa,or obtained by actual measurement;the residual cohesive force of a rock stratum A at the top of the water-resisting layer is unit MPa;the residual internal friction angle of the rock stratum A at the top of the water-resisting layer is unit degree; the internal friction angle of the top layer A of the water barrier in the elastic and residual phase is not changed, i.e.Then there is k^*＝k；

A3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of micro unit body with the thickness of dy from the bottom plate isolation layer, and establishing the bottom plate water-resisting layer micro unit body by taking the horizontal direction as an x axis and the vertical downward direction as a y axis for stress analysis, wherein d sigma_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; the equilibrium equation of the stress of the microcells in the y direction of the microcells meets the formula (30); calculating the frictional resistance tau on the contact surfaces of the microcell bodies and rock layers on two sides according to a formula (31); establishing a y-direction stress balance equation according to the equation (31) to obtain an equation (32);

∑F＝0 (30)；

τ＝f·σ_x+C (31)；

σ_y·L+2τ·dy-(σ_y+dσ_y)·L＝0 (32)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the upper effective water barrier h₂When C is equal to C_2n(ii) a When the microcell is under the lower effective water barrier, C ═ C_3n(ii) a f is the friction coefficient of the contact surface of the micro unit body and the rock layers on two sides, and when the micro unit body is positioned on the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the upper effective water barrier h₂Always is f₂，When the microcells are in the upper effective water barrier h₃When is f₃，

A4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

a41: obtaining a formula (33) by a simultaneous formula (29), a formula (31) and a formula (32), and solving the formula (33) to obtain a formula (34);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

a42: when y is made 0, formula (35) is obtained; the formula (36) is obtained by combining the formula (27) and the formula (35); then deducing a formula (37);

a42: let y equal to h₀Obtaining a formula (38);

when the microcells are in the upper effective water barrier h₂Then, the solution is carried out according to the following method:

a43: obtaining a formula (39) by simultaneous formula (27), formula (31) and formula (32), and solving the formula (39) to obtain a formula (40);

in the formula, C₂Is an unknown quantity;

a44: let y equal to h₀Obtaining a formula (41); when y is equal to h₀At the interface, the formula (38) is equal to the formula (41) to obtain a formula (42), and the formula (42) and the formula (40) are simultaneously connected to obtain a formula (43);

a45: changing y to h₀+h₂Substituting the formula (43) to obtain a formula (44);

when the microcells are in the lower effective water-resisting layer h₃Then, the solution is carried out according to the following method:

a46: substituting the formula (28) and the formula (31) into the formula (32) to obtain a formula (45); solving the formula (45) to obtain a formula (46);

in the formula, C₃Is an unknown quantity;

a47: let y equal to h₀+h₂+h₃Obtaining a formula (47); the formula (24) and the formula (47) are combined to obtain a formula (48), and the formula (28) and the formula (46) are combined to obtain a formula (49);

a48: when y is equal to h₀+h₂At the interface, the formula (44) is equal to the formula (49) to obtain a formula (50), and then the formula (50) is solved to obtain a formula (51);

a5: according to practical problems, whether the thickness of the water-resisting layer is safe or not is judged, and the specific process is as follows:

total thickness H of water-proof rock layer of bottom plate₂When known, the limit water pressure value that the soleplate water-proof layer can bear, the actual water pressure Q and the actual water pressure Q are given by a formula (51)₀There is a relationship in equation (52): when the water pressure value of the bottom plate waterproof rock stratum is known, solving the formula (51) to obtain the minimum thickness value H of the bottom plate waterproof rock stratum_minActual thickness value H of water-resisting layer of bottom plate₂With a minimum thickness value H_minThere is a relationship in equation (53):

in the first step, the heights of the mining crack layer and the pressure-bearing water lifting guide crack layer of the bottom plate are calculated by field actual measurement or related theories.

In the second step, the heights of the mining crack layer and the pressure-bearing water lifting guide crack layer of the bottom plate are calculated by field actual measurement or related theories.

According to the method, the method for judging the stability of the bottom plate water-resisting layer is provided by solving, and the safety threshold value and the maximum limit water pressure value of the thickness of the bottom plate water-resisting rock layer are obtained by deduction, so that the overall safety of the bottom plate can be judged scientifically and reasonably, and safety guarantee and theoretical guidance are provided for coal mining on a high-pressure water body. By constructing a mechanical model of the overall stability of the bottom plate water-resisting rock stratum between a coal rock stratum mining layer and a confined aquifer, a theoretical calculation method of the coupling effect of the bearing limit bearing water pressure and the mining stress of the bottom plate water-resisting rock stratum is established, and a theoretical solution of the limit water pressure and the minimum water-resisting stratum thickness threshold value of the bottom plate water-resisting rock stratum is given, so that technical guarantee is provided for researching and judging the safety and stability of the bottom plate and the water inrush risk.

Compared with other traditional bottom plate damage depth analysis theories, the method is more practical, novel in analysis angle and obvious in advantage. The method can derive the critical water pressure which can be borne by the single-layer coal rock layer bottom plate and the double-layer coal rock layer bottom plate, and can be popularized to the maximum limit water pressure and the minimum bottom plate safety thickness threshold which can be borne by the multi-layer coal rock layer bottom plate; furthermore, the method can be used for calculating the stability of the single-layer and double-layer structure bottom plate water-resisting rock stratum, and can be popularized to the checking calculation of the stability of the multilayer bottom plate structure. The method is suitable for all mining conditions of fully mechanized mining faces, fully mechanized caving faces, blasting mining faces, continuous mining faces and the like, is suitable for AoBu water prevention and control, Han grey water prevention and control and Tai grey water prevention and control in coal seam mining and rock protective layer mining, and is also suitable for all underground engineering such as rock layer mining, metal ore mining, semi-coal seam mining, roadway excavation, tunnel excavation, subway excavation and the like. Meanwhile, the method is also suitable for solving all mine disaster prevention and control fields such as water prevention and control of coal mines related to roadway floor safety thickness and the like.

Drawings

FIG. 1 is a cross-sectional stress analysis diagram of a water-resisting layer of a bottom plate under the action of pressure bearing water pressure in the invention;

FIG. 2 is a stress analysis diagram of a water-resisting layer unit body of a bottom plate in the invention;

FIG. 3 is a cross-sectional stress analysis diagram of a dual lithology structure bottom plate water-resisting layer under the action of pressure of confined water in the invention;

FIG. 4 is a stress analysis diagram of a double lithology structure bottom plate water-resisting layer unit body in the invention;

FIG. 5 is a curve of limiting water pressure of a dual lithology structural bottom plate according to the degree of propulsion of a working face.

Detailed Description

The invention will be further explained with reference to the drawings.

The invention provides a method for calculating the stability of a bottom plate water-resisting rock stratum, wherein if the lithology of the bottom plate of a coal rock stratum is similar, a first step is executed; if the lithology of the bottom plate of the coal rock stratum has an obvious upper-lower layer layered structure, executing the second step;

the method comprises the following steps: the stability analysis is carried out by using the single lithologic structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

s1: considering that the stope face adopts a fully mechanized mining or fully mechanized caving process, the mining width is large, the stope face can be treated as a plane strain problem along the stope direction of the face, a section is made along the stope direction, a mechanical model is established, and then a mechanical model diagram of a bottom plate water-resisting layer is shown in figure 1 to carry out stress analysis; the specific method comprises the following steps:

s10: simplifying the part from a rock coal mining layer to a pressure-bearing mining layer into a bottom plate rock layer with a bottom plate lithologic structure, and sequentially dividing the bottom plate lithologic structure into a bottom plate mining crack layer, an effective water-resisting layer and a bottom plate pressure-bearing water guiding and lifting crack layer from top to bottom;

s11: calculating the effective water-proof layer height h of the bottom plate according to the formula (1)₁；

h₁＝H₁-h₀-c (1)；

In the formula, H₁The thickness of a bottom plate rock layer between a bottom plate of a mining layer and the top of the limestone of the Hanwu system is unit m; when the actual thickness of the bottom plate water-resisting layer is determined to solve the maximum value of the pressure-bearing water pressure, H₁＝H_{Fruit of Chinese wolfberry}；h₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

s12: considering the existence of the pressure-bearing water lifting-guiding crack, the pressure-bearing water develops to the bottom of the effective water-resisting layer along the lifting-guiding crack, and the equivalent water pressure q at the top of the pressure-bearing water lifting-guiding crack layer of the bottom plate is calculated according to the formula (2)₂(ii) a Calculating the equivalent load q of the caving gangue in the goaf according to a formula (3)₁；

q₂＝q₀-(h₁+h₀)·γ₁ (2)；

In the formula, q₀Water pressure for actual action of high confined water; gamma ray₁Is equivalent weight of the bottom rock layer, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

S2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

s20: the effective water-resisting layer and the bottom plate mining-induced fracture layer are actually acted by the pressure-bearing water pressure in the water-resisting layer, and the effective water-resisting layer and the bottom plate mining-induced fracture layer can be simplified into an ideal linear elastoplastomer; the actual pressure bearing pressure in the water-resisting rock stratum acts as an effective water-resisting rock stratum and a bottom plate mining fracture layer, and the effective water-resisting rock stratum and the bottom plate mining fracture layer can be simplified into an ideal linear elastoplastomer. The deformation of the effective water-resisting layer conforms to Hooke's law, the Mohr-Coulomb criterion is met during yielding, and the deformation of the effective water-resisting layer meets the formula (4); the mining crack layer of the bottom plate is in a plastic failure stage, the strength value is reduced to the residual strength, the yield condition still meets the Mohr-Coulomb criterion, and the deformation of the mining crack layer of the bottom plate meets the formula (5);

σ_x＝k·σ_y+σ_n (4)；

in the formula (I), the compound is shown in the specification,σ_xthe horizontal stress of the microcell bodies in the bottom plate rock stratum in the x direction is unit MPa; sigma_yThe vertical stress of the microcell bodies in the bottom plate rock stratum in the y direction is unit MPa; sigma_nFor floor rock uniaxial resistanceThe compressive strength, in units of MPa,or obtained by actual measurement; c. C_nThe cohesive force of the bottom plate rock stratum is unit MPa;is the internal friction angle of the floor strata in degrees;

is the residual strength of the bottom rock layer in MPa,or obtained by actual measurement;the residual cohesive force of the bottom plate rock stratum is unit MPa;the residual internal friction angle of the floor rock layer is unit degree; when the internal friction angle of the floor strata is constant during the elastic and residual phases, i.e. whenThen there is k^*＝k；

S3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of the microcell body with the thickness of dy from the bottom plate isolation layer, establishing a stress analysis of the bottom plate water-resisting layer microcell body, and establishing a bottom plate rock stratum microcell body for the stress analysis by taking the O point of fig. 2 as an original point, taking the horizontal direction as an x axis and taking the vertical downward direction as a y axis as shown in fig. 2, wherein d sigma is_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; if the base plate water-resisting layer is kept stable, the balance equation of the stress of the microcell body of the microcell in the y direction meets the Mohr-Coulomb criterion, namely the formula (6) is met; and calculating according to the formula (7)The frictional resistance tau on the contact surfaces of the microcell bodies and rock layers on two sides; establishing a stress balance equation in the y direction according to the formula (6) to obtain a formula (8);

∑F＝0 (6)；

τ＝f·σ_x+C (7)；

σ_y·L+2τ·dy-(σ_y+dσ_y)·L＝0 (8)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the effective water barrier h₁When C is equal to C_n(ii) a f is the friction coefficient of the contact surface of the micro unit body and the rock layers on two sides, and when the micro unit body is positioned on the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the effective water barrier h₁When the number of the carbon atoms is f,

s4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

s41: obtaining a formula (9) by simultaneous formula (6), formula (7) and formula (8), and solving the formula (9) to obtain a formula (10);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

s42: when y is 0, formula (11) is obtained; the formula (12) is obtained by combining the formula (3) and the formula (11); then deducing a formula (13);

s42: let y equal to h₀Obtaining a formula (14);

when the microcell bodies are positioned on the effective water-resisting layer, solving the problems as follows:

s43: obtaining a formula (15) by simultaneously establishing a formula (5), a formula (7) and a formula (8), and solving the formula (15) to obtain a formula (16);

in the formula, C₁Is an unknown quantity;

s44: first, let y be h₀+h₁Obtaining formula (17); the formula (18) is obtained by combining the formula (2) and the formula (17); then, simultaneously establishing a formula (16) and a formula (18) to obtain a formula (19);

s45: let y equal to h₀Obtaining a formula (20); when y is equal to h₀At the interface, the formula (20) is equal to the formula (14) to obtain a formula (21), and then the formula (21) is solved to obtain a formula (22);

s5: according to practical problems, whether the thickness of the water-resisting layer is safe or not is judged, and the specific process is as follows:

when the thickness H of the bottom plate water-resisting rock stratum₁When known, the extreme water pressure value that the bottom rock stratum can bear, the actual water pressure Q and the actual water pressure Q are given by a formula (22)₀There is a relationship in equation (23): when the water pressure value of the bottom plate water-resisting rock stratum is known, solving the formula (22) to obtain a minimum thickness value H of the bottom plate rock stratum_minActual thickness value H of floor strata₁With a minimum thickness value H_minThere is a relationship in equation (24):

step two: the stability analysis is carried out by using the double lithology structure bottom plate water-resisting rock stratum, and the specific method comprises the following steps:

a1: establishing a mechanical model for stress analysis; the specific method comprises the following steps:

a10: as shown in fig. 3, the part between the rock coal mining layer and the pressure-bearing mining layer is simplified into two bottom plate rock layers with bottom plate lithologic structures, the bottom plate rock layers with the two bottom plate lithologic structures are respectively marked as a bottom plate water-resisting rock layer a and a bottom plate water-resisting rock layer B from top to bottom, the bottom plate water-resisting rock layer a is sequentially divided into a bottom plate mining fracture layer and an upper effective water-resisting layer from top to bottom, the bottom plate water-resisting rock layer B is sequentially divided into a lower effective water-resisting layer and a pressure-bearing water guiding fracture layer from top to bottom, and the upper effective water-resisting layer and the lower effective water-resisting layer form a total effective water-resisting layer;

a11: calculating the total effective water-resisting layer height of the bottom plate according to a formula (25);

h₂+h₃＝H₂-h₀-c (25)；

in the formula, H₂When the actual thickness of the bottom plate water-resisting layer is determined to solve the maximum value of the pressure-bearing water pressure, H is the total thickness of the bottom plate rock layer in unit of m₂＝H_{Fruit of Chinese wolfberry}；h₀The height of a mining crack layer of the bottom plate; c is the height of the pressure-bearing water lifting crack layer of the bottom plate;

a12: calculating the equivalent water pressure q3 at the top of the confined water lifting crack layer according to the formula (26); calculating the equivalent load q of the caving gangue in the goaf according to a formula (27)₁；

q₃＝q₀-(h₂+h₀)·γ₂-h₃·γ₃ (26)；

In the formula, q₀Water pressure for actual action of high confined water; h is₂Is the height of the upper effective water barrier; h is₀The height of a mining crack layer of the bottom plate; h is₃Is the height of the lower effective water barrier; gamma ray₂Is equivalent weight of the bottom plate water-resisting rock stratum A, unit KN/m³；γ₃Is equivalent weight of the bottom plate water-resisting rock stratum B, unit KN/m³(ii) a L is the length of the goaf along the trend; gamma is equivalent weight of caving gangue in goaf, unit KN/m³；

A2: introducing an elastoplasticity destruction theory for analysis; the specific method comprises the following steps:

a20: the actual pressure of the bearing water in the bottom plate water-resisting layer acts on the effective water-resisting rock layer and the bottom plate mining fracture layer, the total effective water-resisting layer and the bottom plate mining fracture layer can be simplified into an ideal linear elastoplastomer, the deformation of the total effective water-resisting rock layer meets Hooke's law, the Mohr-Coulomb criterion is met during yielding, the deformation of the upper effective water-resisting layer in the bottom plate water-resisting rock layer A meets the formula (27), and the deformation of the lower effective water-resisting layer in the bottom plate water-resisting rock layer B meets the formula (28); the mining crack layer of the bottom plate is in a plastic failure stage, the strength value is reduced to the residual strength, the yield condition still meets the Mohr-Coulomb criterion, and the deformation of the mining crack layer of the bottom plate meets the formula (29);

σ_2x＝k₂·σ_2y+σ_2n (27)；

σ_3x＝k₃·σ_3y+σ_3n (28)；

in the formula (I), the compound is shown in the specification,σ_2xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum A in the x direction is in unit MPa; sigma_2yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum A in the y direction is in unit MPa; sigma_2nThe uniaxial compressive strength of the bottom plate water-resisting rock stratum A is unit MPa;or obtained by actual measurement; c. C_2nThe cohesive force of a bottom plate water-resisting rock stratum A is expressed in unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum A is unit degree;

σ_3xthe horizontal stress of the micro unit body in the bottom plate water-resisting rock stratum B in the x direction is in unit MPa; sigma_3yThe vertical stress of the micro unit body in the bottom plate water-resisting rock stratum B in the y direction is in unit MPa; sigma_3nThe uniaxial compressive strength of the bottom plate water-resisting rock stratum B is unit MPa;or obtained by actual measurement; sigma_3nThe cohesive force of a bottom plate water-resisting rock stratum B is unit MPa;the internal friction angle of the bottom plate water-resisting rock stratum B is unit degree;

is the residual strength of the top rock stratum A of the bottom plate water-resisting layer in unit MPa,or obtained by actual measurement;the residual cohesive force of a rock stratum A at the top of the water-resisting layer is unit MPa;is a water barrier layerResidual internal friction angle of top rock stratum a, in degrees; the internal friction angle of the top layer A of the water barrier in the elastic and residual phase is not changed, i.e.Then there is k^*＝k；

A3: selecting a differential unit and establishing a differential balance equation; the specific method comprises the following steps:

selecting a section of the micro unit body with the thickness of dy from the bottom plate isolation layer, establishing a stress analysis of the bottom plate water-resisting layer micro unit body, and establishing the bottom plate water-resisting layer micro unit body for the stress analysis by taking the horizontal direction as an x axis and the vertical downward direction as a y axis as shown in figure 4, wherein d sigma is_y、dσ_xThe main stresses of the micro unit bodies in the vertical direction and the horizontal direction are respectively; the equilibrium equation of the stress of the microcells in the y direction of the microcells meets the formula (30); if the base plate water-resisting layer is kept stable, the balance equation of the stress of the micro unit body of the micro unit in the y direction meets the Mohr-Coulomb criterion, the frictional resistance tau of the contact surface of the micro unit body and rock strata on two sides is calculated according to the formula (31), and the stress balance equation in the y direction is established according to the formula (31) to obtain a formula (32);

∑F＝0 (30)；

τ＝f·σ_x+C (31)；

σ_y·L+2τ·dy-(σ_y+dσ_y)·L＝0 (32)；

wherein C is cohesive force of the contact surface of the microcell bodies and rock strata on two sides, and the unit is MPa, when the microcell bodies are positioned in the mining crack layer h of the bottom plate₀When the temperature of the water is higher than the set temperature,when the microcells are in the upper effective water barrier h₂When C is equal to C_2n(ii) a When the microcell is under the lower effective water barrier, C ═ C_3n(ii) a The friction coefficient of the contact surface of the microcells and rock layers on two sides is shown, when the microcells are positioned in the mining crack layer h of the bottom plate₀When the parameter is f^*，When the microcells are in the upper effective water barrier h₂Always is f₂，When the microcells are in the upper effective water barrier h₃When is f₃，

A4: solving a differential equation, and deducing a maximum limit water pressure value or a minimum water-resisting rock stratum thickness safety threshold value which can be borne by the bottom plate rock stratum;

when the microcell bodies are positioned in the mining crack layer of the bottom plate, the solution is carried out according to the following method:

a41: obtaining a formula (33) by a simultaneous formula (29), a formula (31) and a formula (32), and solving the formula (33) to obtain a formula (34);

in the formula (I), the compound is shown in the specification,is an unknown quantity;

a42: when y is made 0, formula (35) is obtained; the formula (36) is obtained by combining the formula (27) and the formula (35); then deducing a formula (37);

a42: let y equal to h₀Obtaining a formula (38);

when the microcells are in the upper effective water barrier h₂Then, the solution is carried out according to the following method:

a43: obtaining a formula (39) by simultaneous formula (27), formula (31) and formula (32), and solving the formula (39) to obtain a formula (40);

in the formula, C₂Is an unknown quantity;

a44: let y equal to h₀Obtaining a formula (41); when y is equal to h₀At the interface, the formula (38) is equal to the formula (41) to obtain a formula (42), and the formula (42) and the formula (40) are simultaneously connected to obtain a formula (43);

a45: changing y to h₀+h₂Substituting the formula (43) to obtain a formula (44);

when the microcells are in the lower effective water-resisting layer h₃Then, the solution is carried out according to the following method:

a46: substituting the formula (28) and the formula (31) into the formula (32) to obtain a formula (45); solving the formula (45) to obtain a formula (46);

in the formula, C₃Is an unknown quantity;

a47: let y equal to h₀+h₂+h₃Obtaining a formula (47); the formula (24) and the formula (47) are combined to obtain a formula (48), and the formula (28) and the formula (46) are combined to obtain a formula (49);

a48: when y is equal to h₀+h₂At the interface, the formula (44) is equal to the formula (49) to obtain a formula (50), and then the formula (50) is solved to obtain a formula (51);

a5: according to practical problems, whether the thickness of the water-resisting layer is safe or not is judged, and the specific process is as follows:

total thickness H of water-proof rock layer of bottom plate₂(H₂＝h₀+h₂+h₃+ c) when known, the extreme water pressure value that the soleplate water-proof layer can bear, the actual water pressure Q and Q are given by a formula (51)₀There is a relationship in equation (52): when the water pressure value of the bottom plate waterproof rock stratum is known, solving the formula (51) to obtain the minimum thickness value H of the bottom plate waterproof rock stratum_minActual thickness value H of water-resisting layer of bottom plate₂With a minimum thickness value H_minThere is a relationship in equation (53):

in the first step, the heights of the mining crack layer and the pressure-bearing water lifting guide crack layer of the bottom plate are calculated by field actual measurement or related theories.

In the second step, the heights of the mining crack layer and the pressure-bearing water lifting guide crack layer of the bottom plate are calculated by field actual measurement or related theories.

Firstly, on the basis of a high rock mechanics theory, a single-structure bottom plate water-resisting rock layer and double-lithology structure bottom plate water-resisting layer mechanical model is established, and a bottom plate water-resisting rock layer analytic formula of a key layer position (effective water-resisting layer) is obtained through solving; selecting differential units, establishing a soleplate infinitesimal differential balance equation under the coupling action of mining stress and confined water pressure by combining Mohr-Coulomb criterion and a plastic failure strength theory, and deducing to obtain the maximum limit water pressure and the minimum water-resisting layer thickness of the soleplate water-resisting rock stratumThe theoretical solution can derive the maximum limit water pressure and the minimum water-resisting layer thickness safety threshold value which can be borne by the water-resisting rock layer of the bottom plate, can scientifically and reasonably judge the overall safety of the bottom plate, provides safety guarantee and theoretical guidance for coal mining on high-pressure water, and provides feasible theoretical guidance for coal mine safety mining. At the same time, the actual thickness (H) of the coal stratum bottom plate is combined_{Fruit of Chinese wolfberry}) Pressure of the pressurized water (P)_{Fruit of Chinese wolfberry}) Obtaining the ultimate water pressure value p which can be born by the water-resisting layer of the bottom plate according to known parameters such as the damage depth of the bottom plate, the pressure-bearing water lifting height, the rock volume weight gamma and the like₀Or the minimum thickness value Hmin of the bottom plate water-resisting layer is solved by using scientific calculation software, and if the water inrush disaster does not happen on site, the basic conditions that P is less than or equal to Pmax or H is greater than or equal to Hmin need to be met.

Example (b):

the thickness and physical and mechanical parameters (table 1) of each rock stratum of the bottom plate of the pressure bearing mining working face of a certain mine in North China are combined, the whole water-resisting layer of the bottom plate is divided into two layers which are more in line with the reality for analysis, and the thickness of the upper layer is 56m and is mainly formed by mutually staggering limestone and sandy mudstone; the thickness of the lower layer is 8m, and the main lithology is aluminum mudstone. Physical and mechanical parameters of each layer of rock are calculated according to the field geological condition, the maximum limit water pressure borne under the condition that the bottom plate is composed of two different lithologies is solved, the stability and the water inrush danger of the current bottom plate water-resisting layer are judged, and the parameter values are shown in table 1.

TABLE 1 composite floor base parameters

And c is 1m for the height of the confined water lifting crack zone. Substituting the parameters into an equation (52) to obtain a curve (figure 5) of the variation of the limiting water pressure of the dual lithology structural bottom plate along with the propelling degree of the working face. As can be seen from fig. 5: the ultimate water pressure q that the bottom plate can bear at the early stage of face mining₀The ultimate water pressure born by the bottom plate is gradually reduced along with the propulsion of the working face because the stress balance state of the bottom plate rock stratum is changed after the coal rock stratum is mined out and the bottom plate rock stratum isThe disappearance of the partial load reduces the ultimate water pressure that it can withstand. However, within the range of 0-50 m, the ultimate water pressure q0 which can be borne by the bottom plate is greater than 8.5MPa and is greater than the water pressure value corresponding to the water bursting coefficient in the regulation, which indicates that the exposed area of the bottom plate of the goaf is smaller in the initial mining stage, and from the structural mechanics perspective, the bending moment of the effective water-proof layer rock beam is smaller, and the borne water pressure is larger, so that the water-proof layer structure of the bottom plate in the initial mining stage has stronger stability and is most likely to have water bursting accidents under the condition of certain water pressure.

The mining length L of the pressure bearing mining working face of the mine is 155.9m, and the maximum limit water pressure q0 which can be borne by an effective water-resisting layer is determined to be 3.46 MPa. In combination with the geological conditions of the mine site engineering, the pressure of the pressure-bearing water at the lower part of the working surface is 1.8MPa and is less than the limit water pressure which can be borne by the bottom plate by 3.46MPa (figure 5), and the water inrush from the bottom plate is known to be good in stability and free from water inrush from the water-resisting rock layer of the bottom plate according to a discrimination formula (53). Therefore, in the working face extraction process, the bottom plate can keep safe and stable without meeting the condition of a larger structure.