CN107103143A - The Forecasting Methodology of working face top covering rockmass permeability variation under the conditions of mining influence - Google Patents

Abstract

The invention discloses a method for predicting the permeability change of the overlying rock mass on the working face under the influence of mining. Using the rock layer movement model based on the influence function, the movement of each layered rock mass after coal seam mining is calculated, and then the response to the horizontal and vertical strain of the rock layer is obtained. By establishing the relationship between strain and permeability, a set of A complete "strain-porosity-permeability" relationship model to study the permeability distribution of mined overburden. The invention overcomes the defects existing in the traditional rock mass permeability change prediction method, and can further analyze problems such as gas drainage, stratum water flow and the like.

Description

Prediction method of permeability change of overlying rock mass on working face under the influence of mining

technical field

The invention belongs to the technical field of mining, and in particular relates to a method for predicting the permeability change of the overlying rock mass on the working face under the influence of mining.

Background technique

Mining mining leads to the subsidence and movement of the overlying rock strata and the surface, which has a huge impact on the environment, construction, production and other activities. Especially, the rock strata and surface movement caused by large-scale and high-intensity mining are the root causes of mining area subsidence disasters and regional deformation. Therefore, the qualitative and quantitative analysis of the subsidence of the surface and overlying rock is not only of great significance to the protection of the surface environment and the safety of buildings, but also the prediction of the deformation and movement characteristics inside the rock strata in advance is of great significance to the safe production of dangerous underground mines such as water damage and gas during mining. Factors to achieve early pre-control also have important value. Research workers at home and abroad have achieved rich results in the research on rock formation subsidence caused by mining, and have established various subsidence prediction models based on different theoretical foundations, such as theoretical analysis prediction models, empirical prediction models, and physical simulations. model etc.

The influence function method is a very effective method for predicting surface subsidence. Compared with other methods, this method is a method of transition from an empirical method to a theoretical model. Its theoretical basis is a distribution function, so it is also called an influence function. method. This method believes that every excavation of any unit point in the underground mine layer can cause subsidence of the surface within a certain range around it, and the farther away from this point, the smaller the surface subsidence. The final subsidence of a certain point on the surface is the superposition of the influence of all excavation unit points in the ore seam on the surface point.

After the coal seam is mined, it will cause the movement and fracture of the rock strata, and form separation layers and cracks in the overlying rock. Long-term theoretical research and production practice have shown that the movement of overlying strata is a very complicated process. Through on-site observation research and theoretical analysis of the transfer process of subsidence, it is found that there is an inevitable connection between surface subsidence and the movement of overlying strata, which is specifically manifested in the correspondence between the two in space and the continuity in time, and the influence function The method can be used to express the correspondence and continuity in the process of rock formation subsidence.

The principle that the influence function method is used to predict the movement and deformation of the surface is also applicable to the research on the movement and deformation of the formation. As shown in Fig. 1, for a certain rock layer on the subsurface working surface, the excavation of any unit body in the mining coal seam will cause the expected point in the rock layer to move to the excavation unit body. In the figure, the origin of the O-X global coordinate system is set at the junction of the left edge of the working face and the bottom of the coal seam roof. In the overlying rock at any height (h is the height above the coal seam), the closer the horizontal distance between the excavation unit and the predicted point, the greater the impact of excavation on the predicted point. When all the units in the working face are excavated one by one, the final displacement P(x,h) of the predicted point in the overlying rock is the superposition of the influences caused by these mining units at the predicted point.

The traditional rock mass permeability change prediction method mainly obtains the permeability by sampling coal (rock) samples on site, and then carrying out related experiments on special experimental equipment. Although this method has good accuracy, it has the following disadvantages: 1) The experimental conditions loaded in the laboratory may be inconsistent with the real situation on site, and the reliability of the obtained permeability change is low; It takes a long time to obtain samples from the core.

Contents of the invention

In order to solve the technical problems raised by the above-mentioned background technology, the present invention aims at the prediction method of the permeability change of the overlying rock mass on the working face under the influence of mining, overcomes the defects existing in the traditional rock mass permeability change prediction method, and improves the permeability change prediction reliability and real-time performance.

In order to realize above-mentioned technical purpose, technical scheme of the present invention is:

The method for predicting the permeability change of the overlying rock mass on the working face under the influence of mining includes the following steps:

(1) Divide the overlying strata into n layers according to the lithology of the strata, and carry out the layer numbers of 1, 2,..., n to each layer in sequence from the coal seam to the surface;

(2) Starting from the first layer of rock mass, calculate the influence function of the subsidence prediction and the influence function of the horizontal movement prediction of each layer layer by layer;

(3) Starting from the first layer of rock mass, the influence function is integrated layer by layer in the selected integration area to obtain the subsidence and horizontal movement of any point in each layer;

(4) Calculate the vertical strain of each point according to the subsidence of each point, calculate the horizontal strain of each point according to the horizontal movement of each point, and then calculate the surface strain of the overlying rock according to the vertical strain and horizontal strain of each point;

(5) Establish the relationship between the porosity of the coal-rock mass and the surface strain of the overlying rock, and establish the relationship between the permeability of the coal-rock mass and the porosity of the coal-rock mass, so as to obtain the relationship between the permeability change and the surface strain of the overlying rock, and use this relationship Characterize the prediction results of the permeability change of the overlying rock mass.

Further, in step (2), the influence function of subsidence prediction and the influence function of horizontal movement prediction of each layer are as follows:

In the above formula, f _s (x', _zi ) and f _u (x _' , _zi ) are the influence function of subsidence prediction and horizontal movement prediction respectively; The horizontal distance between mining unit points, S(x', z _i-1 ) represents the subsidence value of the i-1th layer rock mass at x', a _i represents the subsidence coefficient of the i-th layer rock mass, R _i represents the mining influence radius of the i-th rock mass, h represents the depth of the working face, z _i represents the height difference between the prediction point of the i-th rock mass and the coal seam working face; when i=1, S(x ', z _i-1 )=m, where m represents the mining height of the coal seam.

Further, in step (3), the amount of sinking and the amount of horizontal movement are as follows:

In the above formula, S(x,i) and U(x,i) are the subsidence and horizontal movement of a point in the i-th layer, respectively, and d _1i and d _2i are the inflection points on the left and right sides of the i-th layer rock mass Offset distance, the origin of the OX global coordinate system is set at the left edge of the coal seam working face, x represents the coordinates of the i-th rock mass prediction point in the OX global coordinate system, W represents the left edge and right edge of the OX global coordinate system The horizontal spacing between the side edges, the selected integration area is W _c =Wd _1i -d _2i .

Further, in step (4), the strain in the vertical direction and the strain in the horizontal direction are as follows:

In the above formula, ε _x (x, z), ε _z (x, z) are vertical strain and horizontal strain respectively, S and U are sinking amount and horizontal moving amount respectively, x and z represent horizontal direction and vertical direction.

Further, in step (4), the surface strain of the overlying rock is as follows:

ε _t = ε _x (x, z) + ε _z (x, z) + ε _x (x, y) ε _z (x, z).

Further, in step (5), the relationship between the porosity of the coal rock mass and the surface strain of the overlying rock is as follows:

In the above formula, φ is the porosity of coal and rock mass under the influence of mining, and φ ₀ is the original porosity of coal and rock mass.

Further, in step (5), the relationship between the permeability of coal rock mass and the porosity of coal rock mass is as follows:

In the above formula, K is the permeability of coal and rock mass, K _c is a constant, and ∑s is the surface area of pores in porous media per unit volume.

Further, in step (5), the relationship between the permeability change and the surface strain of the overlying rock is as follows:

In the above formula, K ₀ is the initial permeability of the coal-rock mass, and the ratio of the permeability of the coal-rock mass under the influence of mining to the initial permeability is used Characterize permeability changes.

The beneficial effect brought by adopting the above-mentioned technical scheme:

The present invention uses the stratum movement model based on the influence function to calculate the movement of each layered rock mass after the coal seam is mined, thereby obtains the strain in the horizontal and vertical directions of the stratum by calculating the derivative of the displacement, and establishes the relationship between the strain and the permeability, Obtained a complete set of "strain-porosity-permeability" relationship model, and obtained the permeability distribution of the mined overlying rock, with high reliability and good real-time performance. The prediction results are conducive to the analysis of gas migration and formation water flow the law.

Description of drawings

Fig. 1 is a schematic diagram of integral calculation for influence function method;

Fig. 2 is a basic flow chart of the present invention;

Fig. 3 is a schematic diagram of stratification of the overlying strata in the present invention.

detailed description

The technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings.

The prediction method of the permeability change of the overlying rock mass on the working face under the influence of mining is shown in Fig. 2, and the specific process is as follows.

Firstly, the overlying strata are divided evenly in a limited manner, and the overlying strata are numbered 1, 2, ..., n at the same time, as shown in Fig. 3 .

The movement influence function of the rock layer is defined in the order from the first layer of rock layer (direct roof) up to the nth layer of the ground surface. The influence function given in the background technology is still used to describe the deformation of the rock formation, but the calculation parameters need to be corrected, and the revised influence function formula for calculating the settlement of the rock formation is shown in the following formula:

In the above formula, x' represents the horizontal distance between the prediction point of the i-th layer rock mass and the underground mining unit point, S(x',z _i-1 ) represents the downfall of the i-1 layer rock mass at x' The subsidence value, a _i represents the subsidence coefficient of the rock mass in the i layer, R _i represents the mining influence radius of the rock mass in the i layer, h represents the buried depth of the working face, and z _i represents the prediction point of the rock mass in the i layer and the coal seam working The height difference between the planes; when i=1, S(x', z _i-1 )=m, where m represents the mining height of the coal seam.

The above formula actually expresses an idea of iterative calculation. When calculating the subsidence of the i-th layer, it is necessary to first obtain the calculation result of the subsidence of the i-1 layer, and then combine the characteristic parameters of this layer to obtain conduct. It should be noted that the calculation of the first layer (i.e. when i=1) is special, and the S(x', z _i-1 ) in the formula should be replaced by m to ensure the continuity of the calculation.

In the same way, calculate the influence function of the horizontal movement prediction of the i-th rock layer:

Integrate the movement influence function layer by layer in an appropriate range from the first rock layer up to the nth layer on the surface to obtain the deformation calculation results of each rock layer.

The selected integration area is still as shown in Figure 1, but it should be noted that the inflection point offsets of any rock formation i are different from each other. Therefore, record the inflection point offsets of the rock formations on the left and right sides as d _1i and d _2i , then Integrate the influence function to obtain the subsidence and horizontal movement at any point in the formation:

In the above formula, the origin of the OX global coordinate system is set at the left edge of the coal seam working face, x represents the coordinates of the i-th rock mass prediction point in the OX global coordinate system, and W represents the left edge and The horizontal spacing between the right edges, the selected integration area is W _c =Wd _1i -d _2i .

Due to the different subsidence value and horizontal displacement of each point on the surface under the influence of mining, there is a relative movement between points, which leads to deformation of the surface. In the traditional study of surface subsidence, surface deformation is divided into inclination, curvature, and horizontal strain. However, for the study of overlying rock subsidence, the distribution of overlying rock horizontal strain, vertical strain and surface strain is more meaningful for studying and dealing with engineering problems caused by overlying rock subsidence strain. The horizontal strain of the surface refers to the ratio of the difference between the horizontal movement of two adjacent points on the surface to the horizontal distance between the two points, reflecting the difference in the horizontal movement of two adjacent points per unit length. By definition, horizontal deformation can be viewed as the first derivative of horizontal movement. It is not difficult to understand that the principle of overburden deformation is the same as that of surface deformation, that is, the subsidence and horizontal displacement of each point in the overburden affected by mining are different, so that there is relative movement between points. This results in deformation of the overlying rock. Therefore, the horizontal strain at each point in the overlying rock is also the first derivative of the horizontal movement of the overlying rock with respect to x:

Similarly, the vertical strain of the overburden refers to the ratio of the difference between the subsidence values of two adjacent points in the vertical direction of the overlying rock to the vertical distance between the two points, reflecting the subsidence value per unit height between the upper and lower points. difference. Therefore, according to the definition, the vertical strain at each point in the overlying rock can be regarded as the first-order derivative of the overlying rock subsidence value to -h, so the vertical strain at each point in the overlying rock is:

According to the characteristics of the main section of the subsidence basin: the horizontal displacement is zero in the direction perpendicular to the main section, that is, there is no horizontal strain in the direction perpendicular to the main section. Therefore, in the two-dimensional case, the surface strain of the mining overlying rock can be seen as two-dimensional surface strain. According to the relationship between the surface strain and the horizontal strain and vertical strain, the formula of the overlying rock surface strain in the two-dimensional case is deduced as follows:

ε _t = ε _x (x,z)+ε _z (x,z)+ε _x (x,y)ε _z (x,z)

Coal and rock mass can be regarded as porous media, and a large number of studies have shown that its deformation is the sum of the deformation of the following two parts. The first part is the body deformation of the medium, that is, the deformation caused by the deformation of the skeleton particles of the coal and rock mass. This process is reversible and is an elastic deformation process; Deformation caused by misalignment, which is usually irreversible.

In the relationship between the porosity and surface strain of the coal-rock mass established below, the weak body deformation of the coal-rock mass is ignored, and the analysis is as follows on the basis of the following related literature research:

Use V _s to represent the solid skeleton volume of porous media, and ΔV _s to represent its change; use V _b to represent the apparent volume of porous media, and ΔV _b to represent its change; use V _p to represent the pore volume of porous media, and ΔV _p to represent its change.

Defined by porosity, it is assumed that the porosity of coal and rock mass in the initial transition state is:

When the coal rock mass changes from the initial state to a certain deformation state, its porosity is:

In the three-dimensional case, it is the volume strain, that is, the volume change per unit volume of the coal-rock mass during the deformation process. In the two-dimensional case, the surface strain of the coal-rock mass is taken as the surface strain, and the weak body deformation of the coal-rock mass is ignored. Let ΔV _s = 0, then the above formula becomes:

It can be seen from the above formula that the porosity of mining overlying coal rock mass can be regarded as a function of surface strain.

The permeability of coal and rock mass will change with the change of porosity, which will affect the flow of gas in coal and rock mass. Therefore, the relationship between permeability and porosity in the Kozeny-Carman equation can be used to obtain the relationship between permeability and surface strain . The Kozeny-Carman equation for the relationship between permeability and porosity of coal and rock mass is:

In the above formula, K _c is a constant, approximately 5; S _p is the surface area per unit pore volume in porous media, and ∑s is the pore surface area per unit volume in porous media.

Assuming that in the initial state, the permeability of coal and rock mass is:

The ratio of the new permeability under the influence of mining to the permeability under the original state is:

Considering that for a coal-rock mass with a specific structure, the total surface area of medium particles is approximately considered to be constant during the process of stress and strain, then ∑s=∑s ₀ , namely:

The relationship formula between permeability change and surface strain is obtained after sorting out:

The above formula is the characterization formula of the permeability change of coal and rock mass under the influence of mining, and it is a function of the surface strain of coal and rock mass.

The above embodiments are only to illustrate the technical ideas of the present invention, and can not limit the protection scope of the present invention with this. All technical ideas proposed in accordance with the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. Inside.

Claims (8)

1. the Forecasting Methodology of working face top covering rockmass permeability variation under the conditions of mining influence, it is characterised in that including following step Suddenly：

(1) overlying rock is divided into n-layer by the lithology situation on stratum, 1 is carried out successively to each layering from coal seam to ground apparent bearing, 2 ..., n level number；

(2) by the 1st layer of rock mass, successively calculate the influence function of the sinking prediction of each layering and move horizontally the influence of prediction Function；

(3) by the 1st layer of rock mass, successively influence function is integrated in selected integral domain, obtained in each layering The deflection and the amount of moving horizontally at any point；

(4) calculate each point vertical direction according to the deflection of each point to strain, each point level is calculated according to the amount of moving horizontally of each point Direction is strained, and is strained further according to each point vertical direction and the face of horizontal direction strain calculation overlying strata is strained；

(5) relation of the face strain of coal and rock porosity and overlying strata is set up, coal and rock permeability and coal and rock porosity is set up Relation, so as to obtain the relation of the face strain of permeability variation and overlying strata, overlying strata body permeability variation is characterized using the relation Predict the outcome.

2. according to claim 1 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (2), the influence function and the influence function for moving horizontally prediction for the sinking prediction being respectively layered are as follows：

<mrow> <msub> <mi>f</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>S</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> </mrow>

<mrow> <msub> <mi>f</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mrow> <mi>S</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>n</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>h</mi> </mrow> </mfrac> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> </mrow>

In above formula, f_s(x',z_i) and f_u(x',z_i) it is respectively sinking predicted impact function and the influence function for moving horizontally prediction； X' represents the horizontal range between i-th layer of rock mass future position and underground mining unit spot, S (x', z_i-1) represent the i-th -1 layer rock mass The sinking occurred at x', a_iRepresent the subsidence factor of i-th layer of rock mass, R_iRepresent the mining influence radius of i-th layer of rock mass, h tables Show working face buried depth, z_iRepresent the difference in height between i-th layer of rock mass future position and working face of coal seam；As i=1, S (x', z_i-1) =m, m represent seam mining height.

3. according to claim 2 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (3), the deflection and the amount of moving horizontally are as follows：

<mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <msub> <mi>d</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> <mrow> <mi>W</mi> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> </msubsup> <msub> <mi>f</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>dx</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfrac> <msub> <mi>a</mi> <mi>i</mi> </msub> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mrow> <msub> <mi>d</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> <mrow> <mi>W</mi> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> </msubsup> <mi>S</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> <msup> <mi>dx</mi> <mo>&amp;prime;</mo> </msup> </mrow>

<mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <msub> <mi>d</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> <mrow> <mi>W</mi> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> </msubsup> <msub> <mi>f</mi> <mi>u</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>dx</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>n</mi> </mrow> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>h</mi> </mrow> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mrow> <msub> <mi>d</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> <mrow> <mi>W</mi> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>x</mi> </mrow> </msubsup> <mi>S</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>&amp;pi;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>R</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> <msup> <mi>dx</mi> <mo>&amp;prime;</mo> </msup> </mrow>

In above formula, S (x, i) and U (x, i) are respectively the deflection and the amount of moving horizontally, d of i-th layer of certain point_1iAnd d_2iRespectively i-th The flex point offset distance of the layer rock mass left and right sides, the origin of O-X global coordinate systems is arranged at working face of coal seam left side edge, and x is represented The coordinate of i-th layer of rock mass future position in O-X global coordinate systems, W represents left side edge and right edge in O-X global coordinate systems Level interval between edge, selected integral domain is W_c=W-d_1i-d_2i。

4. according to claim 1 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (4), the vertical direction strain and horizontal direction strain are as follows：

<mrow> <msub> <mi>&amp;epsiv;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>S</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow>

<mrow> <msub> <mi>&amp;epsiv;</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>U</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>z</mi> </mrow> </mfrac> </mrow>

In above formula, ε_x(x,z)、ε_z(x, z) is respectively vertical direction strain and horizontal direction strain, and S, U are respectively deflection and water Momentum is translated, x, z are represented horizontally and vertically respectively.

5. according to claim 4 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (4), the face strain of the overlying strata is as follows：

ε_t=ε_x(x,z)+ε_z(x,z)+ε_x(x,y)ε_z(x,z)。

6. according to claim 5 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (5), the relation of the face strain of coal and rock porosity and overlying strata is as follows：

<mrow> <mi>&amp;phi;</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mi>t</mi> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mi>t</mi> </msub> </mrow> </mfrac> </mrow>

In above formula, φ is the coal and rock porosity under mining influence, φ₀For the original porosity of coal and rock.

7. according to claim 6 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (5), the relation of coal and rock permeability and coal and rock porosity is as follows：

<mrow> <mi>K</mi> <mo>=</mo> <mfrac> <msup> <mi>&amp;phi;</mi> <mn>3</mn> </msup> <mrow> <msub> <mi>K</mi> <mi>c</mi> </msub> <msup> <mi>&amp;Sigma;s</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>

In above formula, K is coal and rock permeability, K_cFor constant, ∑ s is the porous media mesopore surface area of unit volume.

8. according to claim 7 under the conditions of mining influence working face top covering rockmass permeability variation Forecasting Methodology, it is special Levy and be, in step (5), the relation of the face strain of permeability variation and overlying strata is as follows：

<mrow> <mfrac> <mi>K</mi> <msub> <mi>K</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>&amp;epsiv;</mi> <mi>t</mi> </msub> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>&amp;epsiv;</mi> <mi>t</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow>

In above formula, K₀For the original permeability of coal and rock, using the ratio of coal and rock permeability and original permeability under mining influenceCharacterize permeability variation.