A method for predicting water inrush volume of edge water-filled karst collapse column

Abstract

The application discloses a kind of edge water-filled karst collapse column water inrush quantity prediction methods, belong to coal mine water disaster prevention technical field.The prediction method is: coupling groundwater dynamics and fluid mechanics related theory, to karst collapse column passage form, three-dimensional space, flow state, supply condition make basic assumption, and using calculus method, in column coordinate system, by defining annular passage inner radius, outer radius, water passageway height geometric parameter, contact head difference, fluid density, viscous coefficient hydraulic parameter, based on Navier-Stokes equation deduces the water inrush quantity prediction theory equation considering flow velocity variation and along the way head loss.The application reasonably simplifies passage form, deduces and establishes edge type collapse column water inrush quantity theoretical prediction model;Compared with traditional method, the geometric characteristics and laminar flow mechanism of annular passage are considered in the model, the physical meaning is clear, the prediction result is more accurate and reliable, and theoretical support is provided for mine water disaster prevention.

Description

Technical Field

[0001] This invention belongs to the field of coal mine water hazard prevention and control technology, and relates to a method for predicting the water inrush volume of edge-filled karst collapse columns. Background Technology

[0002] When soluble rocks such as carbonate rocks beneath coal seams are dissolved by groundwater, forming cavities, the resulting collapse of the overlying strata creates columnar subsidence bodies. These subsidence bodies, disturbed by mining, become a significant component of the dominant water-conducting channels for limestone water to surge from the floor into the mining area. The concealed presence and manifestation of these karst subsidence columns lead to the stagnation of substantial coal resources, hindering the safe and efficient development of the energy industry.

[0003] Based on past incidents of water inrush from collapse columns, it has been concluded that water inrushes caused by collapse columns are characterized by suddenness, large water volume, severe economic losses, and significant difficulty in handling. With the continuous increase in the depth of coal mining in my country, hydrogeological conditions are becoming increasingly complex, especially the water inrush problem of "marginally water-filled" karst collapse columns. These collapse columns are located in a dynamic transition zone between water-filled and non-water-filled areas, and their hydrogeological characteristics change significantly with time and mining disturbances, making traditional prediction methods inadequate for practical needs. Therefore, research on prediction models for water inrush volumes from marginally water-filled karst collapse columns has significant theoretical value and engineering practical implications.

[0004] Existing methods for predicting water inrush volume are mostly based on empirical formulas or simplified models, failing to fully consider channel morphology and hydrodynamic characteristics, resulting in low prediction accuracy and poor applicability to water inrush volume prediction in marginal karst collapse columns. Therefore, there is an urgent need for a water inrush volume prediction method based on theoretical derivation, with clearly defined parameters, high calculation accuracy, and small error. Summary of the Invention

[0005] This invention aims to provide a method for predicting the water inrush volume of edge-filled karst collapse columns. Through theoretical modeling and mathematical derivation, a theoretical equation for predicting the water inrush volume is derived, taking into account changes in flow velocity distribution and head loss along the flow path, thereby achieving quantitative prediction of the water inrush volume.

[0006] This invention provides a method for predicting the inrush volume of edge-filled karst collapse columns. By coupling relevant theories of groundwater dynamics and fluid mechanics, it makes basic assumptions about the channel morphology, three-dimensional space, flow regime, and recharge conditions of the karst collapse column. Using calculus methods in cylindrical coordinates, it defines the geometric parameters of the inner radius, outer radius, and water-conducting channel height of the annular channel, and connects the hydraulic parameters of head difference, fluid density, and viscosity coefficient. Based on the Navier-Stokes equations, it derives a theoretical equation for predicting the inrush volume, considering velocity changes and head loss along the flow path.

[0007] The parameters required for the model can be obtained through geological exploration, hydrological observation, or geophysical exploration. The source of the parameters is clear and they are easy to measure.

[0008] Furthermore, the irregular edge water-conducting channel is generalized into a vertical annular water-conducting channel. The rationale for this generalization lies in the fact that the distribution of water-conducting media (such as fracture zones and fissure zones) at the edge of actual collapse columns often forms a ring around the column core, and its water-conducting capacity is significantly higher than that of the dense core area and the surrounding intact rock strata. Using the annular channel model not only reflects this main water-conducting characteristic but also avoids the mathematical difficulties caused by complex and irregular morphologies.

[0009] Furthermore, the entire water-conducting height from the top of the Ordovician limestone seam to the bottom of the coal seam is generalized into a vertical, cylindrical space of uniform thickness.

[0010] Furthermore, we assume that the Ordos limestone water flow is a steady, incompressible laminar flow, and neglect lateral recharge of the regional groundwater flow field. The basis and rationale for this are as follows:

[0011] (1) Assuming that the flow of Ordovician limestone water is a steady flow: During a specific period of mining (such as the instantaneous water inrush or short-term strong water inrush stage), the changes in the aquifer head and boundary conditions are relatively slow and can be approximated as a steady state, which is consistent with the common simplification in most water inrush dynamics analyses.

[0012] (2) Assuming the water flow is an incompressible fluid: the volume change of groundwater under normal temperature and pressure and general mining pressure is very small, which is consistent with the assumption of an incompressible fluid.

[0013] (3) Assuming the water flow is laminar: Based on the characteristics that the edge water-conducting ring is usually narrow and the water flow velocity is controlled by rock mass fissures, the Reynolds number is usually low and the water flow is mostly in a laminar state. This assumption applies to most non-extreme turbulent situations.

[0014] (4) Ignore the lateral recharge of the regional groundwater flow field: For the problem of concentrated water inrush in the collapsed column, the water inrush volume is mainly driven by the vertical head difference and flows out through the columnar channel. In the short term, the lateral recharge volume is relatively small compared with the concentrated water inrush volume and can be ignored to simplify the model.

[0015] Furthermore, in cylindrical coordinate system Below, define the inner radius. The outer boundary of the dense core region of the column; outer radius This is the contact boundary between the collapse column and the intact surrounding rock; the water-conducting height is... ; Ring width ( () represents the width of the effective water-conducting ring. Wherein The axis coincides with the central axis of the collapse column.

[0016] Furthermore, assuming the flow is axisymmetric under conditions free from significant asymmetric external forces or boundary conditions, and without the influence of obvious asymmetric external forces or boundary conditions, we assume the flow is axisymmetric, meaning that in cylindrical coordinates, the flow velocity depends only on the radial coordinates. and axial coordinates , and azimuth Irrelevant. That is to say, at the same altitude. At any point, along any The velocity distribution in all directions is the same, and the radial velocity... and tangential velocity All values ​​are 0, only the axial velocity exists. That is, velocity vector .

[0017] Furthermore, from arrive An integral equation for predicting water inrush volume was established, and water in the Ordovician limestone only occurs in... arrive Flowing within the range, where This is the interface between the Ordovician limestone aquifer and the collapse column. This is a water inrush point on the bottom of the coal seam, where Ordovician limestone water rushes to the bottom of the coal seam under high water pressure.

[0018] Furthermore, under the aforementioned assumptions, the z-direction components of the Navier-Stokes equations in cylindrical coordinates can be simplified as follows:

[0019] (1)

[0020] Where: P is pressure, Pa; μ is the dynamic viscosity of water, Pa·s; r is a variable describing the radial position of the water particle in the annular channel, m; ρ is the density of water, kg / m³. 3 g is the acceleration due to gravity, in m / s². 2 ; It is the flow velocity in the z-direction, in m / s.

[0021] Furthermore, from the Ordovician limestone aquifer ( ) to the water inlet ( Bernoulli's equation is expressed as:

[0022] (2)

[0023] Where: P1 is the water pressure in the Ordovician limestone aquifer; v1 is the average flow velocity of the Ordovician limestone water flowing from the aquifer into the annular water-conducting channel of the collapse column; P2 is the water pressure at the coal seam water inrush point; v2 is the average flow velocity of the water gushing out at the water inrush point; z1 is the Ordovician limestone water level elevation; z2 is the coal seam water level elevation; h f This refers to head loss along the route.

[0024] Furthermore, neglecting the kinetic energy term, equation (2) simplifies to:

[0025] (3)

[0026] Define the total head difference H as:

[0027] (4)

[0028] Combination ,get:

[0029] (5)

[0030] Furthermore, in a vertical pipe, the pressure gradient is determined by both the hydrostatic pressure and the driving pressure:

[0031] (6)

[0032] in, The change in hydrostatic pressure per unit height (gravity term); The net pressure gradient required to drive the flow, The driving pressure difference required to overcome viscous resistance.

[0033] Furthermore, in the vertical pipes, from the Ordovician limestone aquifer ( ) to the water inlet ( Total pressure difference It consists of two parts: the hydrostatic pressure difference required to overcome gravity. The net driving pressure difference required to overcome flow resistance ,Right now: .

[0034] The pressure gradient is obtained after sorting: (7)

[0035] Substituting the pressure gradient expression (7) back into equation (1), we get:

[0036] (8)

[0037] The core governing equations are obtained by reorganization: (9)

[0038] Furthermore, the second integral yields the velocity distribution formula:

[0039] (10)

[0040] Furthermore, the inner boundary of the channel ( ) and outer boundary ( () is considered a fixed boundary, and no-slip boundary conditions are applied: when hour, ;when hour, .

[0041] Substituting into equation (10), we get: (11)

[0042] Furthermore, by solving for the integration constants C1 and C2, we obtain:

[0043] (12)

[0044] The final velocity distribution formula is obtained as follows:

[0045] (13)

[0046] Furthermore, the integral of the flow velocity over the annular cross-sectional area is the total flow rate Q:

[0047] (14)

[0048] Substituting the velocity distribution formula (13) into the equation, we get:

[0049] (15)

[0050] Furthermore, the three integral results of equation (15) are combined to obtain:

[0051] (16)

[0052] Substituting the integral result (16) back into the expression (14) for the flow rate Q, we get:

[0053] (17)

[0054] This equation establishes the relationship between the water inrush rate Q and geometric parameters. and hydraulic parameters The quantitative relationship between them.

[0055] Furthermore, equation (17) is simplified using a first-order approximation to facilitate its application in engineering.

[0056] The final approximation result, i.e., the theoretical formula for predicting water inrush volume, is as follows:

[0057]

[0058] In the formula, Q is the water inrush volume, μ is the dynamic viscosity coefficient of water (Pa·s), and ρ is the density of water (kg / m³). 3 g is the acceleration due to gravity, in m / s². 2 H is the total head difference, L is the water-conducting height, r1 is the inner radius, i.e. the outer boundary of the dense core area of ​​the column, and d is the width of the effective water-conducting ring.

[0059] The beneficial effects of this invention are:

[0060] (1) Based on the Navier-Stokes equations, this invention reasonably simplifies the channel morphology and derives a theoretical prediction model for the water inrush volume of edge-type collapse columns. Compared with traditional methods, this model considers the geometric characteristics and laminar flow mechanism of the annular channel, has clear physical meaning, and provides more accurate and reliable prediction results, thus providing theoretical support for mine water hazard prevention and control.

[0061] (2) The parameters required by the model can be obtained through geological exploration, hydrological observation or geophysical exploration. The parameters are clear in origin and easy to measure, making them easy to promote and apply on site. They are suitable for actual scenarios with complex hydrogeological conditions in coal mines.

[0062] (3) The water inrush volume prediction formula provided by the present invention is an analytical expression, which does not require complex numerical simulation or iterative calculation. The parameters can be directly substituted for quick estimation, further improving the calculation efficiency.

[0063] (4) This model can be used in conjunction with other hydrogeological models or monitoring systems to provide theoretical support for water inrush risk assessment, waterproof coal pillar design, and drainage system selection.

[0064] (5) By accurately predicting the amount of water inrush, this invention helps mines to formulate reasonable water prevention and control strategies, such as determining the amount of water to be drained, setting early warning thresholds, and assessing the risk level of water inrush, thereby improving the pertinence and effectiveness of mine water hazard prevention and control and ensuring safe production in coal mines. Attached Figure Description

[0065] Figure 1 This is a schematic diagram illustrating the generalization process of the annular water guiding channel in the present invention.

[0066] Figure 2 The model of this invention assumes a three-dimensional diagram of a vertical annular channel;

[0067] Figure 3 This is a schematic diagram of the cylindrical coordinate system used in the mathematical derivation of the model of this invention;

[0068] Figure 4 This is a cross-sectional view of the annular channel of the model of the present invention. Detailed Implementation

[0069] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0070] This invention provides a method for predicting the water inrush volume of edge-filled karst collapse columns. By coupling relevant theories of groundwater dynamics and fluid mechanics, basic assumptions are made about the channel morphology, three-dimensional space, flow regime, and recharge conditions of the karst collapse column. Using calculus methods in cylindrical coordinates, geometric parameters such as the inner radius, outer radius, and height of the annular channel are defined. Hydraulic parameters such as head difference, fluid density, and viscosity coefficient are considered. Based on the Navier-Stokes equations, a theoretical equation for predicting the water inrush volume is derived, taking into account velocity changes and head loss along the flow path.

[0071] The parameters required for the model can be obtained through geological exploration, hydrological observation, or geophysical exploration. The source of the parameters is clear and they are easy to measure.

[0072] like Figure 1 The present invention generalizes an actual irregular edge-type water-conducting channel into a vertical annular water-conducting channel. The left figure is a schematic cross-sectional view of an actual irregular edge-type sinkhole, and the right figure is a schematic cross-sectional view of the generalized vertical annular water-conducting channel. Figure 2 The entire vertical water-conducting height from the top of the Ordovician limestone seam to the bottom of the coal seam is generalized as a vertical, uniformly thick cylindrical shell-like space; it is assumed that the Ordovician limestone water flow is a steady, incompressible laminar flow, and the lateral recharge of the regional groundwater flow field is ignored; as shown... Figure 3 As shown, in cylindrical coordinates, the governing equations are established, where The axis coincides with the central axis of the collapse column. For example... Figure 4 The inner radius is defined as shown. ) is the outer boundary of the dense core region of the column; outer radius ( ) is the contact boundary between the collapse column and the intact surrounding rock; the water-conducting height ( ); Ring width ( () represents the width of the effective water-guiding ring.

[0073] Furthermore, assuming the flow rate is The direction is symmetrical, and the velocity component is in the axial direction ( The radial and tangential velocities are both zero (direction). That is, the velocity vector... .from arrive An integral equation for predicting water inrush volume is established. Water in the Ordovician limestone only occurs in… arrive Flowing within a certain range. Among them, in... This is the interface between the Ordovician limestone aquifer and the collapse column. This is a water inrush point on the coal seam floor. Ordovician limestone water inrushes to the coal seam floor under high water pressure.

[0074] Furthermore, the z-components of the Navier-Stokes equations can be simplified as follows:

[0075] (1)

[0076] Where: P is pressure, Pa; μ is the dynamic viscosity of water, Pa·s; r is a variable describing the radial position of the water particle in the annular channel, m; ρ is the density of water, kg / m³. 3 g is the acceleration due to gravity, in m / s². 2 ; It is the flow velocity in the z-direction, in m / s.

[0077] Furthermore, from the Ordovician limestone aquifer (z=0) to the water inrush point (z=L), the Bernoulli equation is expressed as follows:

[0078] (2)

[0079] Where: P1 is the water pressure in the Ordovician limestone aquifer; v1 is the average flow velocity of the Ordovician limestone water flowing from the aquifer into the annular water-conducting channel of the collapse column; P2 is the water pressure at the coal seam water inrush point; v2 is the average flow velocity of the water gushing out at the water inrush point; z1 is the Ordovician limestone water level elevation; z2 is the coal seam water level elevation; h f This refers to head loss along the route.

[0080] In the water-conducting channel of a karst collapse column, the kinetic energy term accounts for a very small proportion compared to the total head difference; and the cross-sectional area of ​​the annular water-conducting channel is large, so even if the flow rate is large, the flow velocity is still relatively small due to the large area; under laminar flow conditions, the head loss is mainly determined by viscous dissipation, and the kinetic energy accounts for a small proportion compared to the potential energy and pressure energy during the water inrush process, so the kinetic energy term can be ignored, and equation (2) simplifies to:

[0081] (3)

[0082] Define the total head difference H as:

[0083] (4)

[0084] Combining z1-z2=-L, we get:

[0085] (5)

[0086] Furthermore, in vertical pipes, the pressure gradient is determined by both hydrostatic pressure and driving pressure:

[0087] (6)

[0088] in, The change in hydrostatic pressure per unit height (gravity term); The net pressure gradient required to drive the flow, The driving pressure difference required to overcome viscous resistance.

[0089] Furthermore, in the vertical pipes, from the Ordovician limestone aquifer ( ) to the water inlet ( Total pressure difference It consists of two parts: the hydrostatic pressure difference required to overcome gravity. The net driving pressure difference required to overcome flow resistance ,Right now: .

[0090] The pressure gradient is obtained after sorting: (7)

[0091] Substituting the pressure gradient expression (7) back into equation (1), we get:

[0092] (8)

[0093] The core governing equations are obtained by reorganization: (9)

[0094] First point: (10)

[0095] get: (11)

[0096] Second integration: (12)

[0097] get: (13)

[0098] Boundary conditions: Set the boundary inside the channel ( ) and outer boundary ( () is considered a fixed boundary, and no-slip boundary conditions are applied: when hour, ;when hour, .

[0099] Substituting into equation (13), we get: (14)

[0100] Further solving for the integration constants C1 and C2, subtracting the two equations above and eliminating C2, yields:

[0101] (15)

[0102] The results were: (16)

[0103] Substitute C1 back into the first boundary condition equation to find C2: (17)

[0104] The final velocity distribution formula is obtained as follows:

[0105] (18)

[0106] Furthermore, the integral of the flow velocity over the annular cross-sectional area is the total flow rate Q:

[0107] (19)

[0108] Substituting the velocity distribution formula (18) into the equation, we get:

[0109] (20)

[0110] make The integral is then divided into three parts:

[0111] (twenty one)

[0112] Calculate the third integral, let ,but .when hour, ;when hour, .

[0113] (twenty two)

[0114] Using the integral formula ,get:

[0115] (twenty three)

[0116] therefore:

[0117] (twenty four)

[0118] Will Substituting into equation (24), we get:

[0119] (25)

[0120] Combining the three integral results:

[0121] (26)

[0122] Substituting the integral result (26) back into the expression (20) for the flow rate Q, we get:

[0123] (27)

[0124] This equation establishes the relationship between the water inrush rate Q and geometric parameters. and hydraulic parameters The quantitative relationship between them.

[0125] Furthermore, equation (27) is verified using dimensional analysis. In dimensional analysis, M, L, and T are general symbols for three basic physical quantities, represented as M: mass (kg); L: length (m); and T: time (s), respectively.

[0126] Molecular part In this context, π is a dimensionless number, and the dimension of density ρ is... The dimensions of gravitational acceleration g are The dimension of the head difference H is ,but The dimensions are .

[0127] denominator In this context, 8 is a dimensionless number, and the dimension of the dynamic viscosity coefficient μ is... The dimensions of the water guide height L are: ,but The dimensions are .

[0128] The part in parentheses The dimensions of the inner and outer radii r1 and r2 are both... , sorted out The dimensions are .

[0129] The overall dimensions of the right side of formula (27) are obtained by rearranging: The dimension of flow Q is: This verifies that the dimensions of the water inrush volume prediction equation conform to physical principles and can be applied to the theoretical prediction of water inrush volume.

[0130] Furthermore, equation (27) is simplified using a first-order approximation for easier engineering application. When the ring width... When the radius is much smaller than the inner radius r1, Taylor expansion can be performed.

[0131] make ,but .

[0132]

[0133] Expression within parentheses:

[0134] First-order approximate preservation The first-order term gives:

[0135]

[0136] Processing the fractional terms yields:

[0137]

[0138] When x is very small ,here ,so:

[0139] therefore:

[0140] Substituting into the equation, we get:

[0141] Finally, a first-order approximation result is obtained, namely the theoretical formula for predicting water inrush volume:

[0142]

[0143] Example: A method for predicting the water inrush volume of extra-large, edge-filled karst collapse columns.

[0144] 1. Project Background and Geological Conditions

[0145] During the excavation of the return airway of the No. 11 coal seam at Shanxi Shide Sunjiagou Coal Mine, a collapse column was discovered. The same collapse column was also discovered at the same location in the No. 13 coal seam. After underground drilling and intensified control, it was basically determined that the short axis (east-west) is about 47m long and the long axis (north-south) is about 60m long. The structure is dense and the filling material is yellow mud. The collapse column has certain water-bearing and water-conducting properties.

[0146] Based on the development morphology of the collapse column and the properties of the filling material in Sunjiagou Coal Mine, the collapse column is located in the Ordovician limestone zone under pressure mining area. The elevation of the coal seam floor near the collapse column is 765m, the elevation of the Ordovician limestone water level is 835m, and the thickness of the aquitard is 51m. The maximum depth of water head that the coal seam floor can withstand is calculated to be 121m (835-765+51=121m).

[0147] 2. Model Parameter Determination

[0148] Based on the results of geological drilling, hydrological observations, and geophysical exploration, the parameters required for the prediction model are determined as follows:

[0149] The apparent viscosity of mud slurry is much higher than that of water, and it varies with concentration and shear rate. An "equivalent dynamic viscosity coefficient μ" can be calculated based on the borehole water inflow conditions. eff ".

[0150] Back-calculation method: Based on the maximum water inflow of 15m³ in borehole ZT11-1 at Sunjiagou Coal Mine. 3 / h, assuming the borehole exposes a typical annular water-conducting channel, its "equivalent dynamic viscosity coefficient μ" can be derived using the formula. eff ".

[0151] This borehole represents a micro-annular channel: r1=0.1m, r2=0.15m, d=0.05m, L=51m, H=121m, Q=15m 3Substituting / h into formula (17) and solving for μ, we get μ. eff =15.4 Pa·s.

[0152] Considering that the actual water-conducting channel is composed of a discrete fracture network rather than a continuous uniform annular space, an effective water-conducting width reduction factor is introduced. (Take a value of 0.05~0.1). Reduce the original ring width d=2m to... .

[0153]

[0154] Note: Equivalent dynamic viscosity coefficient μ eff It was obtained by back-calculation based on water inflow data from similar water-conducting fractures that have been exposed in the mining area, reflecting the additional resistance that water flow experiences in the actual geological medium.

[0155] 3. Calculation of water inrush volume prediction

[0156] Substitute the above parameters into the formula:

[0157] .

[0158] 4. Effect Evaluation

[0159] (1) The calculated water inrush volume is 3793 m³. 3 / h, which falls under the category of extremely large water inrush volume, and is consistent with actual cases of water inrush from collapse columns in mines (such as Renlou Coal Mine and Luotuoshan Coal Mine, where water inrush volume >10000m³). 3 Compared to the previous prediction ( / h), this predicted value is within a reasonable range, indicating that the model can reflect the magnitude of the actual water inrush.

[0160] (2) The geometric parameters in the model are determined based on measured data such as geological boreholes and transient electromagnetic data; the hydraulic parameters are obtained through hydrological observation and inversion methods. In particular, the introduction of equivalent dynamic viscosity coefficient and effective water conduction width reduction coefficient enhances the model's adaptability to actual geological conditions.

[0161] (3) Specialized modeling for edge-filled collapse columns: The irregular water-conducting channel is generalized into an annular channel, which has a clear physical meaning. It simplifies the mathematical processing and retains the main water-conducting characteristics (annular fracture zone), overcoming the shortcomings of traditional methods in adapting to "edge-type" channels.

[0162] In summary, the model demonstrated good applicability and predictive ability in the case study of the Sunjiagou Mine, with prediction results possessing clear physical significance and engineering reference value. The model has a clear structure, well-defined parameter sources, and high computational efficiency, making it potential for widespread application in mining areas with similar hydrogeological conditions.

Claims

1. A method for predicting water inrush volume of edge water-filled karst collapse column, characterized in that, By coupling groundwater dynamics and fluid mechanics theories, basic assumptions are made about the morphology, three-dimensional space, flow regime, and recharge conditions of karst collapse column channels. Using calculus methods in cylindrical coordinates, geometric parameters such as the inner radius, outer radius, and height of the annular channel are defined, and hydraulic parameters such as head difference, fluid density, and viscosity coefficient are considered. Based on the Navier-Stokes equations, a theoretical equation for predicting water inrush volume considering velocity changes and head loss along the flow path is derived.

2. The method according to claim 1, wherein, The required parameters are obtained through geological exploration, hydrological observation, or geophysical exploration, and the source of the parameters is clear and easy to measure.

3. The method according to claim 1, characterized in that, The irregular edge water-conducting channel is generalized into a vertical annular water-conducting channel; the entire water-conducting height from the top of the Ordovician limestone seam to the bottom of the coal seam is generalized into a vertical cylindrical space of uniform thickness.

4. The method according to claim 1, wherein, Assuming the flow of Ordovician limestone water is a steady, incompressible laminar flow, and neglecting the lateral recharge of the regional groundwater flow field.

5. The method for predicting water inrush volume in edge-filled karst collapse columns according to claim 1, characterized in that, In cylindrical coordinate system Below, define the inner radius. The outer boundary of the dense core region of the column; outer radius This is the contact boundary between the collapse column and the intact surrounding rock; the water-conducting height is... Ring width Represents the width of the effective water-conducting ring; where The axis coincides with the central axis of the collapse column.

6. The method according to claim 5, wherein, When unaffected by significant asymmetric external forces or boundary conditions, and satisfying axisymmetric boundary conditions, assume the flow velocity is... Symmetrical in direction, the velocity components are zero in the axial, radial, and tangential directions, i.e., the velocity vector. .

7. The method according to claim 1, wherein, from arrive An integral equation for predicting water inrush volume was established, and water in the Ordovician limestone only occurs in... arrive Flowing within the range, where This is the interface between the Ordovician limestone aquifer and the collapse column. This is a water inrush point on the bottom of the coal seam, where Ordovician limestone water rushes to the bottom of the coal seam under high water pressure.

8. The method according to claim 1, wherein, The theoretical equation for predicting water inrush volume is: In the formula, Q is the water inrush volume, μ is the dynamic viscosity coefficient of water (Pa·s), and ρ is the density of water (kg / m³). 3 g is the acceleration due to gravity in m / s². 2 H is the total head difference, L is the water-conducting height, r1 is the inner radius, i.e. the outer boundary of the dense core area of ​​the column, and d is the width of the effective water-conducting ring.

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