A Matlab-based system for calculating the critical water pressure of a non-uniform layered structure base plate during water inrush.

Abstract

This invention relates to the field of coal mining technology and discloses a Matlab-based system for calculating the critical water pressure for water inrush in non-uniform layered coal seam floor structures. The system includes the following modules: a menu bar module with "Start" and "Help" buttons; clicking the "Start" button allows for data import and export, while clicking the "Help" button displays software-related information; a parameter value module for displaying and modifying user-imported data; a range value module for user input of parameters such as the number of layers, the angle θ1 between the fracture surface and the horizontal plane, the angle β between the fault plane and the horizontal plane, the length of the goaf, and the height of the failure zone; and a display module for showing the relationship between the critical water pressure below layer i and the fracture angle θ1. This invention, through its proposed system for calculating the critical water pressure for water inrush in non-uniform layered coal seam floor structures, provides theoretical and data support for subsequent evaluation of coal seam floor water inrush and is of significant importance for the prevention and control of coal seam floor water inrush.

Description

Technical Field

[0001] This invention relates to the field of coal mining technology, and in particular to a Matlab-based system for calculating the critical water pressure of a non-uniform layered structure floor slab prone to water inrush. Background Technology

[0002] Currently, the problem of coal seam floor water inrush caused by high-pressure water beneath the mine floor is becoming increasingly serious and urgently needs to be solved. Therefore, how to solve the problem of floor water inrush and how to mine coal resources quickly and healthily are the focus of contemporary coal mine researchers. The core issue and key point is the prediction of the ultimate water pressure value of coal seam floor water inrush. Therefore, how to achieve economical, safe and rational coal mining, how to more accurately and efficiently evaluate the degree of danger of coal seam floor water inrush under high water pressure, and how to reasonably propose prevention and control measures to curb the occurrence of disasters are urgent problems that researchers need to solve.

[0003] MATLAB, a combination of "matrix" and "laboratory," is a high-tech computing environment primarily designed for scientific computing, visualization, and interactive programming. It integrates powerful functions such as numerical analysis, matrix computation, scientific data visualization, and modeling and simulation of nonlinear dynamic systems into an easy-to-use graphical environment. This provides a comprehensive solution for scientific research, engineering design, and numerous scientific fields requiring effective numerical computation, largely eliminating the need for traditional non-interactive programming languages ​​(such as C and Fortran) in their editing modes. Therefore, it is necessary to research and develop software based on the MATLAB R2021b platform to calculate the critical water pressure of a non-uniform layered structure floor slab during water inrush. This is of great significance for improving the understanding and mastery of critical water pressure during safe coal mining by both professional geologists and non-professionals, and for providing data and software support for the evaluation of safe coal mining. Summary of the Invention

[0004] To address the technical problems mentioned in the background section, this invention provides a Matlab-based system for calculating the critical water pressure of a non-uniform layered structure base plate during water inrush.

[0005] This invention is achieved using the following technical solution: a Matlab-based critical water pressure calculation system for non-uniform layered structure bottom plate, comprising the following modules:

[0006] The menu bar module includes "Start" and "Help" buttons. Clicking the "Start" button allows you to import and export data, while clicking the "Help" button displays software-related information.

[0007] The parameter value retrieval module is used to display and modify user-imported data;

[0008] The range value module is used for users to input the following parameters: number of layers, angle θ1 between the rupture surface and the horizontal plane, angle β between the fault plane and the horizontal plane, length of the goaf, and height of the failure zone.

[0009] The display module is used to display the relationship between the critical water pressure below layer i and the rupture angle θ1; specifically, the parameters are obtained through the parameter value module and the range value module.

[0010] The backend system receives data from the parameter value module, the range value module, and the display module. It can perform calculations on the frontend data and plot the relationship between the critical water pressure and the rupture angle θ1 below layer i, which is then fed back to the display module on the frontend interface.

[0011] The button operation module includes "Calculate", "Save", "Modify", "Exit", and "Graphic Window" buttons, allowing users to perform different operations by manipulating these buttons.

[0012] Preferably, the data in the parameter value module includes, but is not limited to, the thickness h of each waterproof layer. i Angle of friction within each soil layer Cohesion C within each layer of the fracture surface 1i internal friction angles of each layer of the fracture surface Cohesion C within each layer of the fault plane 2i internal friction angles of each layer of the fault plane and the unit weight γ of each soil layer i .

[0013] Preferably, the data is saved to an Excel file for import.

[0014] This invention also proposes a calculation method for a system for calculating the critical water pressure of a uniformly layered structure bottom plate, comprising the following steps:

[0015] Step 1: A mechanical model for water inrush during mining of a fault in a working face above a confined aquifer was established. This model focuses on the ultimate water pressure that the floor strata of the stope can withstand when a fault occurs at the working face, as well as its influencing factors and susceptibility. In the model, it is assumed that there are i layers of aquitard protection zone, L is the range of the suspended goaf behind the working face, and the thickness of the i-th layer is h. i Severe γ i The internal friction angle is The cohesive force is C 1i The i-th rock layer is assumed to have a fracture surface with an angle of θ with the horizontal plane. i The cohesion within the fracture surface is C. 2i The internal friction angle is ;

[0016] Step 2: Establish a rectangular coordinate system, with the coordinate axes set at the boundary of the overhanging goaf behind the working face. Simultaneously, set the x-axis at the interface between the mining-induced failure zone and the protective zone of the floor strata, pointing in the same direction as the working face movement, to analyze the influence of the lithology of the floor protective zone on water inrush from the mining fault in the working face. Considering the shape of the trapezoidal differential unit, the z-axis is set at the interface of the assumed fracture surface, pointing downwards and perpendicular to the floor strata. The origin o is the intersection of the x-axis and y-axis.

[0017] Step 3: Based on the limit equilibrium theory of rock mass, the force analysis of the trapezoidal differential element with thickness dz was determined;

[0018] Stress σ in the strata of the protected area 1i and shear strength τ 1i The vertical stress σ affects the left end face of the infinitesimal element. z The shear strength τ of the fracture surface is affected by dw and the increment σz+dσz on the upper and lower surfaces. 2i and normal stress σ 2i The right end face is affected. A bidirectional trapezoidal differential element with thickness dz along the x and z directions satisfies the following formula.

[0019] σ 1i ·dz+τ 1i ·cotθ1·dz=σ 2i ·dz+τ 2i ·cotβ1·dzσ 1i ·cotθ1·dz+σ 2i ·cotβ1·dz+dσ z [Lh(cotθ+cotβ)-z(cotθ1+cotβ1)-dz(cotθ1+cotβ1)]=τ 1i ·dz+τ 2i ·dz+σ z ·cotθ1·dz+σ z ·cotβ1·dz+γ1·[Lh·(cotθ+cotβ)-z·(cotθ1+cotβ1)]·dz (1)

[0020] Step 4: According to the rock mass limit equilibrium theory, during fault activation and water inrush, the trapezoidal differential unit will slide upward along the fault plane. During this process, the left end face of the trapezoidal differential unit will be subjected to the horizontal stress σ of the strata in the protected area. 1i and shear strength τ 1i Due to the influence of the trapezoidal differential unit band, the right-hand inclined surface will be subjected to the normal stress σ of the fault plane. 2i and shear strength τ 2i The influence of the Mohr-Coulomb yield criterion on the shear strength τ of the protected area strata. 1i Shear strength σ1i and the shear strength τ of the fault plane 2i Shear strength σ 2i Each satisfies

[0021] (2)

[0022] (3)

[0023] According to the Mohr-Coulomb yield criterion, the limit equilibrium condition for rock mass failure is:

[0024] (4)

[0025] Equations (2), (3), and (4) above utilize previous formulas in order to substitute them into (1) and finally obtain the desired relationship between the variable and the dependent variable. By combining the various equations, the second-order differential component dydσ is omitted. z Dividing by dz, we get:

[0026] (5)

[0027] in:

[0028]

[0029]

[0030]

[0031]

[0032] From the above formula, we can obtain:

[0033] (6)

[0034] In the formula,

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where c1 is the integration constant to be determined, and σ is the constant when Z=0. z =γh, where h is the depth of the mining-induced failure zone and γ is the weight of the soil in the mining-induced failure zone.

[0041]

[0042] We can obtain:

[0043] (7)

[0044] From the above formula, we can see that

[0045] When z=h1, σ z =p-γh

[0046] (8)

[0047] It can be concluded that when there is i layers of rock,

[0048] (9)

[0049] The above formula represents the breakage angles θ1, θ2, ... θ i The rupture angles are functions of the slope, but these rupture angles are not independent of each other. When the retaining wall moves forward or rotates around its base, the soil behind the wall slides downward at the same sliding velocity V. Assuming the soil follows the Mohr-Coulomb yield criterion and obeys the associated flow laws, the rupture angle θ in the (i-1)th layer of fill is... i-1 The rupture angle θ of the overlying fill i The following relationships exist between them.

[0050] (10)

[0051] This ensures that the multi-layered soil and rock slides obliquely at the same sliding velocity V, thus naturally satisfying the deformation coordination conditions of the multi-layered soil and rock.

[0052] Therefore, the limiting water pressure p and the rupture angle θ can be obtained. i The relation is the relation obtained by combining formula (9) and formula (10).

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] Based on data such as the thickness of each impermeable layer, the internal friction angle of the soil layer, the angle between the fracture surface and the horizontal plane, and the unit weight of the soil layer, this invention establishes a software for calculating the critical water pressure of water inrush on the bottom plate of a non-uniform layered structure using the Matlab R2021b software platform. This enables rapid simulation analysis and evaluation of safe mining of coal resources in the study area, providing reliable information services and auxiliary decision-making basis for safe mining and development of coal resources, and also providing theoretical and data support for subsequent demonstration projects of coal resource development and utilization.

[0055] The critical water pressure calculation system for water inrush in non-uniform layered structure floor proposed in this invention provides theoretical and data support for subsequent evaluation of water inrush in coal seam floor, and is of great significance for the prevention and control of water inrush in coal seam floor. Attached Figure Description

[0056] Figure 1 This is a framework diagram of the critical water pressure calculation system for a uniform layered structure base plate proposed in this invention.

[0057] Figure 2 This is a schematic diagram illustrating the failure of the bottom plate during mining in confined water.

[0058] Figure 3 A mechanical model for water inrush during mining of a fault above a confined aquifer, constructed based on the theories of ground pressure and rock strata control;

[0059] Figure 4 Based on the limit equilibrium theory of rock mass, the stress analysis of a trapezoidal differential element with thickness dz was determined, and the stress diagram of the protective layer element was drawn.

[0060] Figure 5 The movement of fill soil to comply with relevant flow laws. Detailed Implementation

[0061] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0062] Example 1:

[0063] A Matlab-based system is provided for calculating the critical water pressure of a non-uniform layered structure base plate during water inrush.

[0064] This invention is achieved using the following technical solution: a Matlab-based critical water pressure calculation system for non-uniform layered structure bottom plate, comprising the following modules:

[0065] The menu bar module includes "Start" and "Help" buttons. Clicking the "Start" button allows you to import and export data, while clicking the "Help" button displays software-related information.

[0066] The parameter value retrieval module is used to display and modify user-imported data;

[0067] The range value module is used for users to input the following parameters: number of layers, angle θ1 between the rupture surface and the horizontal plane, angle β between the fault plane and the horizontal plane, length of the goaf, and height of the failure zone.

[0068] The display module is used to display the relationship between the critical water pressure below layer i and the rupture angle θ1; specifically, the parameters are obtained through the parameter value module and the range value module.

[0069] The backend system receives data from the parameter value module, the range value module, and the display module. It can perform calculations on the frontend data and plot the relationship between the critical water pressure and the rupture angle θ1 below layer i, which is then fed back to the display module on the frontend interface.

[0070] The button operation module includes "Calculate", "Save", "Modify", "Exit", and "Graphic Window" buttons, allowing users to perform different operations by manipulating these buttons.

[0071] Preferably, the data in the parameter value module includes, but is not limited to: the thickness hi of each impermeable layer and the internal friction angle of each soil layer. Cohesion C within each layer of the fracture surface 1i internal friction angles of each layer of the fracture surface Cohesion C within each layer of the fault plane 2i internal friction angles of each layer of the fault plane and the unit weight γ of each soil layer i .

[0072] Preferably, the data is saved to an Excel file for import.

[0073] This invention utilizes Matlab R2021 b software to establish a software for calculating the critical water pressure of a non-uniform layered structure bottom plate. This software can safely, accurately, and quickly simulate and evaluate coal resource mining, thereby providing reliable information services and auxiliary decision-making basis for coal resource development and utilization. Based on the Matlab R2021 b software platform, a human-computer interaction interface is established, and the main interface of the software is designed to facilitate operation for each user.

[0074] This invention also proposes a calculation method for a system for calculating the critical water pressure of a uniformly layered structure bottom plate, comprising the following steps:

[0075] Step 1: A mechanical model for water inrush during mining of a fault in a working face above a confined aquifer was established. This model focuses on the ultimate water pressure that the floor strata of the stope can withstand when a fault occurs at the working face, as well as its influencing factors and susceptibility. In the model, it is assumed that there are i layers of aquitard protection zone, L is the range of the suspended goaf behind the working face, and the thickness of the i-th layer is h. i Severe γ i The internal friction angle is The cohesive force is C 1i The i-th rock layer is assumed to have a fracture surface with an angle of θ with the horizontal plane. i The cohesion within the fracture surface is C. 2i The internal friction angle is ;

[0076] Step 2: Establish a rectangular coordinate system, with the coordinate axes set at the boundary of the overhanging goaf behind the working face. Simultaneously, set the x-axis at the interface between the mining-induced failure zone and the protective zone of the floor strata, pointing in the same direction as the working face movement, to analyze the influence of the lithology of the floor protective zone on water inrush from the mining fault in the working face. Considering the shape of the trapezoidal differential unit, the z-axis is set at the interface of the assumed fracture surface, pointing downwards and perpendicular to the floor strata. The origin o is the intersection of the x-axis and y-axis.

[0077] Step 3: Based on the limit equilibrium theory of rock mass, the force analysis of the trapezoidal differential element with thickness dz was determined;

[0078] Stress σ in the strata of the protected area 1i and shear strength τ 1i The vertical stress σ affects the left end face of the infinitesimal element. z dw and increment σ z +dσ z The shear strength τ of the upper and lower surfaces and the fracture surface is affected. 2i and normal stress σ 2i The right end face is affected. A bidirectional trapezoidal differential element with thickness dz along the x and z directions satisfies the following formula.

[0079] σ 1i ·dz+τ 1i ·cotθ1·dz=σ 2i ·dz+τ 2i ·cotβ1·dzσ 1i ·cotθ1·dz+σ 2i ·cotβ1·dz+dσ z [Lh(cotθ+cotβ)-z(cotθ1+cotβ1)-dz(cotθ1+cotβ1)]=τ 1i ·dz+τ 2i ·dz+σ z ·cotθ1·dz+σ z ·cotβ1·dz+γ1·[Lh·(cotθ+cotβ)-z·(cotθ1+cotβ1)]·dz(1)

[0080] Step 4: According to the rock mass limit equilibrium theory, during fault activation and water inrush, the trapezoidal differential unit will slide upwards along the fault plane, as shown below. Figure 3 As shown, during this process, the left end face of the trapezoidal differential unit will be subjected to the horizontal stress σ of the protected stratum. 1i and shear strength τ 1i Due to the influence of the trapezoidal differential unit band, the right-hand inclined surface will be subjected to the normal stress σ of the fault plane. 2i and shear strength τ 2iThe influence of the Mohr-Coulomb yield criterion on the shear strength τ of the protected area strata. 1i Shear strength σ 1i and the shear strength τ of the fault plane 2i Shear strength σ 2i Each satisfies

[0081] (2)

[0082] (3)

[0083] According to the Mohr-Coulomb yield criterion, the limit equilibrium condition for rock mass failure is:

[0084] (4)

[0085] Equations (2), (3), and (4) above utilize previous formulas in order to substitute them into (1) and finally obtain the desired relationship between the variable and the dependent variable. By combining the various equations, the second-order differential component dydσ is omitted. z Dividing by dz, we get:

[0086] (5)

[0087] in:

[0088]

[0089]

[0090]

[0091]

[0092] From the above formula, we can obtain:

[0093] (6)

[0094] In the formula,

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] Where c1 is the integration constant to be determined, and σ is the constant when Z=0. Z=γh, where h is the depth of the mining-induced failure zone and γ is the weight of the soil in the mining-induced failure zone.

[0101]

[0102] We can obtain:

[0103] (7)

[0104] From the above formula, we can see that

[0105] When z = h1, σz = p - γh

[0106] (8)

[0107] It can be concluded that when there is i layers of rock,

[0108] (9)

[0109] The above formula represents the breakage angles θ1, θ2, ... θ i The function is , but these breakage angles are not independent of each other, such as Figure 5 As shown, when the retaining wall moves forward or rotates around its base, the soil behind the wall slides obliquely downward at the same sliding velocity V. Assuming the soil follows the Mohr-Coulomb yield criterion and obeys the associated flow laws, the rupture angle θ in the (i-1)th layer of fill is... i-1 The rupture angle θ of the overlying fill i The following relationships exist between them.

[0110] (10)

[0111] This ensures that the multi-layered soil and rock slides obliquely at the same sliding velocity V, thus naturally satisfying the deformation coordination conditions of the multi-layered soil and rock.

[0112] Therefore, the limiting water pressure p and the rupture angle θ can be obtained. i The relation is the relation obtained by combining formula (9) and formula (10).

[0113] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A Matlab-based system for calculating the critical water pressure of a non-uniform layered structure base plate during water inrush, characterized in that: Includes the following modules: The menu bar module includes "Start" and "Help" buttons. Clicking the "Start" button allows you to import and export data, while clicking the "Help" button displays relevant software information. The parameter value retrieval module is used to display and modify user-imported data; The range value module is used for users to input the following parameters: number of layers, angle θ1 between the rupture surface and the horizontal plane, angle β between the fault plane and the horizontal plane, length of the goaf, and height of the failure zone. The display module is used to display the relationship between the critical water pressure below layer i and the rupture angle θ1; specifically, the parameters are obtained through the parameter value module and the range value module. The backend system receives data from the parameter value module, the range value module, and the display module. It can perform calculations on the frontend data and plot the relationship between the critical water pressure and the rupture angle θ1 below layer i, which is then fed back to the display module on the frontend interface. The button operation module includes "Calculate", "Save", "Modify", "Exit", and "Graph" buttons, allowing users to perform different operations by manipulating the buttons in this module. The computing system performs the following steps: Step 1: A mechanical model for water inrush during mining of a fault in a working face above a confined aquifer was established. This model focuses on the ultimate water pressure that the floor strata of the stope can withstand when a fault occurs at the working face, as well as its influencing factors and susceptibility. In the model, it is assumed that there are i layers of aquitard protection zone, L is the range of the suspended goaf behind the working face, the thickness of the i-th layer is hi, and the unit weight is γ. i The internal friction angle is The cohesive force is C 1i The i-th rock layer is assumed to have a fracture surface with an angle of θ with the horizontal plane. i The cohesion within the fracture surface is C. 2i The internal friction angle is ; Step 2: Establish a rectangular coordinate system, with the coordinate axes set at the boundary of the suspended goaf behind the working face. Simultaneously, set the x-axis at the interface between the bottom plate mining failure zone and the protection zone, and in the same direction as the working face movement. Analyze the influence of the lithology of the bottom plate protection zone on the water inrush of the mining fault in the working face. Considering the shape of the trapezoidal differential unit, the z-axis is set at the interface of the assumed fracture surface, downward and perpendicular to the bottom plate strata. The origin o is the intersection of the x-axis and y-axis. Step 3: Based on the limit equilibrium theory of rock mass, the force analysis of the trapezoidal differential element with thickness dz was determined; Stress σ in the strata of the protected area 1i and shear strength τ 1i The vertical stress σ affects the left end face of the infinitesimal element. z d w and increment σ z +dσ z The shear strength τ2 of the upper and lower surfaces and the fracture surface is affected. i and normal stress σ 2i A bidirectional trapezoidal differential element with thickness dz along the x and z directions, affecting the right end face, satisfies the following formula. s 1i ·dz+t 1i ·cotθ1·dz=σ 2i ·dz+t 2i ·cotβ1·dzσ 1i ·cotθ1·dz+σ 2i ·cotβ1·dz+dσ z [Lh(cotθ+cotβ)-z(cotθ1+cotβ1)-dz(cotθ1+cotβ1)]=τ 1i ·dz+t 2i ·dz+σ z ·cotθ1·dz+σ z ·cotβ1·dz+γ1·[Lh·(cotθ+cotβ)-z·(cotθ1+cotβ1)]·dz(1); Step 4: According to the rock mass limit equilibrium theory, during the fault activation and water inrush process, the trapezoidal differential unit will slide upward along the fault plane. The left end face of the trapezoidal differential unit will be subjected to the horizontal stress σ of the strata in the protected area. 1i and shear strength τ 1i Due to the influence of the trapezoidal differential unit band, the right-hand inclined surface will be subjected to the normal stress σ of the fault plane. 2i and shear strength τ 2i The impact.

2. The critical water pressure calculation system for non-uniform layered structure bottom plate based on Matlab as described in claim 1, characterized in that, The data in the parameter value module includes, but is not limited to: the thickness h of each waterproof layer. i Angle of friction within each soil layer Cohesion C within each layer of the fracture surface 1i internal friction angles of each layer of the fracture surface Cohesion C within each layer of the fault plane 2i internal friction angles of each layer of the fault plane and the unit weight γ of each soil layer i .

3. The critical water pressure calculation system for non-uniform layered structure bottom plate based on Matlab as described in claim 1, characterized in that, Save the data to an Excel file for import.

4. The critical water pressure calculation system for non-uniform layered structure bottom plate based on Matlab as described in any one of claims 1-3, characterized in that, According to the Mohr-Coulomb yield criterion, the shear strength τ of the strata in the protected area is... 1i Shear strength σ 1i and the shear strength τ of the fault plane 2i Shear strength σ 2i Each satisfies （2）； （3）； According to the Mohr-Coulomb yield criterion, the limit equilibrium condition for rock mass failure is: （4）； Equations (2), (3), and (4) above utilize previous formulas in order to substitute them into (1) and finally obtain the desired relationship between the variable and the dependent variable. By combining the various equations, the second-order differential component dydσ is omitted. z Dividing by dz, we get: （5） ； in: ； ； ； ； From the above formula, we can obtain: （6）； In the formula, ； ； ； ； ； Where c1 is the integration constant to be determined, and σ is the constant when Z=0. z =γh, where h is the depth of the mining-induced failure zone and γ is the weight of the soil in the mining-induced failure zone; ； We can obtain: （7）； From the above formula, we can see that When z=h1, σ z =p-γh （8）； It can be determined when there is i layers of rock; （9）； The above formula represents the breakage angles θ1, θ2, ... θ i The rupture angles are functions of the slope, but these rupture angles are not independent of each other. When the retaining wall moves forward or rotates around its base, the soil behind the wall slides downward at the same sliding velocity V. Assuming the soil follows the Mohr-Coulomb yield criterion and obeys the associated flow laws, the rupture angle θ in the (i-1)th layer of fill is... i-1 The rupture angle θ of the overlying fill i The following relationships exist between them. （10）； This ensures that the multi-layered soil and rock slides obliquely at the same sliding speed V, thus naturally satisfying the deformation coordination conditions of the multi-layered soil and rock. Therefore, the limiting water pressure p and the rupture angle θ can be obtained. i The relational expression.

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