Prediction method for coal mine goaf directional drilling grouting slurry diffusion distance

Abstract

The invention provides a coal mine goaf directional drilling grouting slurry diffusion distance prediction method, which comprises the steps of defining a global coordinate system for an operation scene of a goaf, establishing a goaf three-dimensional numerical model, and performing grid division on the goaf and a grouting drilling area by adopting a hybrid grid division strategy; based on an O-shaped ring theory and a key layer theory, establishing a three-dimensional space distribution model of porosity and permeability of the goaf; introducing a free medium and porous medium flow coupled slurry-water two-phase flow theory and a level set method, and establishing a slurry diffusion distance prediction model; the grouting pressure, the grout dynamic viscosity and the porous medium permeability are used as influence factors, the grout diffusion volume is used as a response variable, a three-factor and three-level response surface test is designed, and the optimal parameter combination of all the influence factors and the corresponding prediction result of the goaf grouting grout volume fraction are obtained. The method provides theoretical basis and engineering support for goaf grouting process parameter optimization and goaf water disaster prevention and control.

Description

Technical Field

[0001] This application belongs to the field of mine water hazard prevention technology, and in particular relates to a method for predicting the diffusion distance of grout from directional drilling in coal mine goaf. Background Technology

[0002] During the closure of coal mines, numerous operating mines remain around abandoned mines. These abandoned mines not only significantly impact the regional groundwater system, but their old workings also pose a potential threat of water inrush to neighboring operating mines. Simultaneously, the collapse of the goaf roof leads to the subsidence of the overlying strata, which gradually propagates to the surface, causing land subsidence. During subsidence, uneven stress on the strata creates numerous cracks. These cracks become channels for groundwater flow. Aquifers that were originally blocked by rock strata connect with the goaf, making it easier for groundwater to flow into the goaf, increasing the risk of water inrush, and potentially triggering regional environmental problems, even threatening the safety of surface buildings and infrastructure. Statistical analysis of coal mine safety accidents over the past 20 years shows that water hazards, as one of the "five major disasters" in coal mines, have become the second leading cause of disaster after gas accidents, seriously threatening coal mine safety and the lives of workers.

[0003] Despite significant progress in coal mine water hazard prevention and control in recent years, water-related accidents continue to occur, with an increasing proportion of disasters caused by water in old workings. This indicates weaknesses in the current methods of exploring, managing, and monitoring water in old workings. Therefore, grouting is commonly used in mining engineering to displace water from aquifers, transforming them into relatively impermeable layers, and sealing and reinforcing water-conducting channels such as primary fractures, faults, and collapse columns in the strata to achieve water hazard control and strata stability. However, the migration and diffusion range and patterns of grout in horizontal boreholes are difficult to standardize or accurately predict under different operating conditions, leading to a reliance on field experience in engineering practice, which carries a degree of uncertainty.

[0004] Scholars have conducted extensive theoretical, modeling, and experimental research on the laws and characteristics of grout diffusion, achieving fruitful results. However, existing research mainly focuses on the diffusion mechanism of grout in karst fractured aquifers such as Ordovician limestone and under intact rock mass conditions of coal seam floor. In contrast, research results on the migration and diffusion characteristics of directional drilling grout in the highly heterogeneous and strongly anisotropic fractured medium of goaf formed by mining are still limited. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method for predicting the diffusion distance of grout in directional drilling in coal mine goaf areas, which can provide theoretical basis and engineering support for optimizing grouting process parameters in goaf areas and preventing water hazards in old goaf areas.

[0006] This application provides a method for predicting the diffusion distance of grout from directional drilling in coal mine goaf areas. S1. Define a global coordinate system for the working scenario of the goaf and establish a three-dimensional numerical model of the goaf. At the same time, adopt a hybrid meshing strategy to divide the goaf and the grouting borehole area into meshes. S2. Based on the "O"-shaped ring theory and the key layer theory, a three-dimensional spatial distribution model of porosity and permeability in the goaf is established. S3. Introduce the two-phase flow theory of slurry water coupling between free medium and porous medium and the horizontal collection method to establish a slurry diffusion distance prediction model to simulate the displacement process of groundwater by slurry from directional drilling grouting in goaf areas. S4. Using grouting pressure, grout dynamic viscosity, and porous media permeability as influencing factors, and grout diffusion volume as the response variable, a three-factor, three-level response surface experiment was designed to obtain the optimal parameter combination for each influencing factor and the corresponding predicted results of the grout volume fraction in the goaf.

[0007] 2. The method as described in claim 1, wherein step S1 specifically includes: S11. Take the intersection of the middle part of the goaf and the longwall face and the top plane of the bottom plate as the origin of the coordinate system. Let the direction along the strike and pointing to the depth of the goaf be the positive x-axis, the direction along the dip and pointing to the return air side be the positive y-axis, and the direction perpendicular to the top plane of the bottom plate and pointing upwards be the positive z-axis, thus defining the global coordinate system. S12. Set the strike length, dip width, and vertical height of the three-dimensional numerical model of the goaf; S13. In order to describe the distribution characteristics of the "O"-shaped rings, which are "relatively dense in the middle and have developed fissures around the edges", two concentric and coaxial elliptical boundaries are established in the xy plane and stretched along the z-axis to form an elliptical cylindrical surface, thereby dividing the goaf into a compaction stability zone, a load-affected zone and a natural accumulation zone from the inside to the outside. S14. A short-distance feather-shaped branch hole pattern is adopted. A horizontal main hole is laid out along the strike in the middle of the goaf. Branch holes are arranged sequentially along the strike at equal intervals of 50m from its starting point. The left and right sides are staggered. Each branch hole maintains a small angle with the main hole and points to the roadways on both sides. The main hole and the branch holes are explicitly modeled in the model as cylindrical channels with a radius of 0.074m. S15. The main body of the goaf adopts a free tetrahedral grid, while the grouting borehole area generates regular hexahedral units by mapping the inlet circular surface and sweeping along the axial direction. A boundary layer grid is set at the borehole wall to refine the near-wall flow field.

[0008] The method for predicting the diffusion distance of grout in directional drilling in coal mine goaf provided in this application has the following beneficial effects: 1) Based on the "O"-shaped ring theory and the key layer theory, a three-dimensional spatial distribution model of porosity and permeability in the goaf was established. The slurry two-phase flow theory and the level set method, which couple free and porous media flow, were introduced to simulate the displacement process of groundwater by directional drilling grout in the highly heterogeneous and strongly anisotropic fractured medium of the goaf in a relatively realistic way.

[0009] 2) This model reveals the asymmetric diffusion law of grout diffusion distance, which is "longer at the top and shorter at the bottom, and farther laterally". It also quantitatively gives the diffusion distance of grout in the horizontal, vertical upward and vertical downward directions. In engineering, it solves the technical problems of the difficulty in accurately predicting the diffusion pattern and diffusion distance of grout in goaf grouting in traditional grouting methods, and the high dependence of borehole layout and grouting parameters on experience.

[0010] 3) Building upon this foundation, a high-precision grout diffusion volume prediction model was established by combining two-level fractional factorial design, steepest ramp test, and response surface methodology. This model elucidated the influence of factors such as porous media permeability, grouting pressure, and grout dynamic viscosity on the grout diffusion distance, enabling quantitative optimization and rational selection of key process parameters such as grouting pressure, grout dynamic viscosity, and hole spacing. Engineering application results demonstrate that, while ensuring treatment effectiveness, this method can significantly improve the targeting and reliability of grouting design, reduce the blind spots in design and construction, and lower treatment costs, exhibiting good engineering applicability and promising prospects for wider application. Attached Figure Description

[0011] Figure 1 A flowchart is shown below illustrating a method for predicting the diffusion distance of grout in directional drilling in coal mine goaf, as provided in an embodiment of this application. Figure 2 This invention provides a schematic diagram of a goaf in a global coordinate system according to an embodiment of the present application. Figure 3 This illustration shows a schematic diagram of directional hole layout based on a three-dimensional numerical model of a goaf area, provided in an embodiment of this application. Figure 4 This illustration shows a schematic diagram of goaf grid division provided in an embodiment of this application; Figure 5 This application provides an embodiment of a surface diagram showing the spatial distribution of porosity in a goaf. Figure 6 This application provides an embodiment of a surface diagram showing the spatial distribution of permeability in a goaf. Figure 7 The numerical simulation cloud diagram of the grout liquid integral number provided in the embodiments of this application is shown; Figure 8 The response surface plot and contour plot of the interaction between grouting pressure and dynamic viscosity of grout as provided in the embodiments of this application are shown. Figure 9 The diagram shows the response surface and contour plot of the interaction between grouting pressure and porous medium porosity as provided in the embodiments of this application on the grout diffusion volume. Figure 10 The response surface plot and contour plot of the interaction between the dynamic viscosity of the slurry and the porosity of the porous medium provided in the embodiments of this application are shown. Figure 11 A schematic diagram of the borehole design for fly ash grouting and filling engineering in goaf areas provided in an embodiment of this application is shown. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this technical solution clearer, the following detailed description, in conjunction with specific embodiments, further illustrates this technical solution. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this technical solution.

[0013] Example 1: Please see as follows Figure 1 The flowchart shown is a method for predicting the diffusion distance of grout from directional drilling in coal mine goaf areas. Figure 1 As shown, the method includes: S1. Define a global coordinate system for the working scenario of the goaf and establish a three-dimensional numerical model of the goaf. At the same time, adopt a hybrid meshing strategy to divide the goaf and grouting borehole areas into meshes.

[0014] S1 specifically includes: S11. Take the intersection of the middle part of the goaf and the longwall face and the top plane of the floor as the origin of the coordinate system. Let the direction along the strike and pointing to the depth of the goaf be the positive x-axis, the direction along the dip and pointing to the return air side be the positive y-axis, and the direction perpendicular to the top plane of the floor and pointing upwards be the positive z-axis, thus defining the global coordinate system.

[0015] S12. Set the strike length, dip width, and vertical height of the three-dimensional numerical model of the goaf.

[0016] S13. In order to describe the "O"-shaped ring distribution characteristics of "relatively dense in the middle and developed around the cracks", two concentric and coaxial elliptical boundaries are established in the xy plane and stretched along the z-axis to form an elliptical cylindrical surface, thereby dividing the goaf into a compaction stability zone, a load-affected zone and a natural accumulation zone from the inside to the outside.

[0017] As an example, please refer to... Figure 2 The diagram shows a goaf area in the global coordinate system. a 1 , a 2 , b 1, b 2 These are the lengths of the major and minor semi-axes of the two ellipses, representing the compaction stability zone and the load-affected zone, respectively.

[0018] S14. A short-distance feather-shaped branch hole pattern is adopted. A horizontal main hole is laid out along the strike in the middle of the goaf. Branch holes are arranged sequentially along the strike at equal intervals of 50m from its starting point. The left and right sides are staggered. Each branch hole maintains a small angle with the main hole and points to the roadways on both sides. The main hole and the branch holes are explicitly modeled in the model as cylindrical channels with a radius of 0.074m.

[0019] As an example, please refer to... Figure 3 The diagram shows the directional borehole layout based on a three-dimensional numerical model of the goaf. The model dimensions are: strike length 500m, dip width 300m, and vertical height 6.41m. The major and minor axes of the inner ellipse are a1=87.5m and b1=52.5m, respectively; the major and minor axes of the outer ellipse are a2=200m and b2=120m, respectively.

[0020] S15. The main body of the goaf adopts a free tetrahedral grid, while the grouting borehole area generates regular hexahedral units by mapping the inlet circular surface and sweeping along the axial direction. A boundary layer grid is set at the borehole wall to refine the near-wall flow field.

[0021] As an example, please refer to... Figure 4 The diagram shows the mesh generation of the goaf. Based on a model height of 6.41m, the goaf is uniformly divided into 9 layers along the z-axis, with a maximum element size of 6m and a maximum element growth rate of 1.30. Local mesh refinement is performed at the tees between the main borehole and branch boreholes, and near the borehole ends, to improve the resolution of local seepage and pressure gradients. All mesh quality indicators meet the software's recommended standards, and no malformed elements are present. The final model contains 5,045,814 domain elements, 273,058 boundary elements, and 25,282 edge elements, which meets the requirements for subsequent numerical calculations.

[0022] S2. Based on the "O"-shaped ring theory and the key layer theory, a three-dimensional spatial distribution model of porosity and permeability in the goaf is established.

[0023] In this step, within the goaf, the porosity and permeability of the porous media are not constants but closely related to spatial location. According to the "O"-ring theory and the critical layer theory, the fracturing of the critical layer will cause a large-scale movement of the overlying strata, leading to the formation of numerous mining-induced fractures. Supported by the coal face and working face supports, the basic roof and part of the immediate roof around the goaf form a cantilever beam structure. The central part of the goaf, being far from the coal face, is significantly affected by the weight of the overlying strata, causing the mining-induced fractures in the central part to tend to compact. A connected mining-induced fracture development zone is formed around the goaf, exhibiting an "O"-ring distribution characteristic. Based on this, a three-dimensional spatial distribution model of the porosity and permeability of the goaf is established.

[0024] In practical implementation, a three-dimensional spatial distribution model of porosity in the goaf is established using the following methods: S21. Based on the "O"-shaped ring theory and the key layer theory, the distribution models of porosity in the goaf along the x-axis, y-axis, and z-axis are established as follows: On the y=0 section of the goaf, along the x-axis, the porosity φ x The distance from the cut line to the incision site shows a trend of first decreasing and then increasing, with an overall approximately symmetrical distribution as follows: ; In the formula, φ x Porosity along the x-axis on the y=0 section of the goaf, dimensionless; D The length of the goaf is in meters. x The distance from a point within the goaf to the working face is expressed in meters (m). On the x=0 section of the goaf, the porosity variation coefficient φ' y Approximately symmetrically distributed along y=0, when extending from the middle of the working face towards the intake and return airways, φ' y All increase with the increase of |y|, as shown below: ; (1) In the formula, φ' y is the coefficient of porosity along the y-axis, which is dimensionless; W The dip width of the goaf, in meters; y Let be the coordinate value of a point within the goaf along the y-axis, in meters (m). Here, based on the lithology of the roof and the failure characteristics of the collapsed rocks in the goaf after mining, the goaf can be divided into a natural accumulation zone, a load-affected zone, and a compaction-stabilized zone. In the natural accumulation zone, due to the relatively small amount of roof subsidence, the collapsed rocks are loosely accumulated, with high porosity that increases exponentially along the vertical direction (positive z-axis). In the compaction-stabilized zone, the pressure of the overlying strata tends to stabilize, and the porosity of the collapsed rocks changes little under long-term compaction, and can be approximated as a constant. The load-affected zone, as a transition zone, has porosity between the two zones, exhibiting continuous variation. Based on this, a porosity variation coefficient along the z-axis in the xy-plane is constructed.

[0025] In the xy plane along the z-axis, the porosity variation coefficient φ' z The following piecewise function relationship is satisfied: ; (2) in, ; (3) In the formula, φ' z is the coefficient of porosity along the z-axis, which is dimensionless; z Let be the coordinate value of a point within the goaf along the z-axis, in meters (m). a 1 , a 2 , b 1 , b 2 Let be the lengths of the major and minor semi-axes of the two ellipses, representing the compaction stability zone and the load-affected zone, respectively, in meters (m). f ( x, y ) is a normalized spatial position coefficient with a value range of (0, 1). It is used to describe the relative position of any point (x, y) in the load-affected zone with respect to the inner and outer elliptical boundaries, thereby achieving a smooth transition of porosity in space.

[0026] S22, Using φ x ,φ' y and φ' z The product of these terms represents the three-dimensional spatial continuous distribution equation of porosity φ within the goaf, as follows: (4) As an example, the porosity of the goaf is a function of spatial location. Taking a goaf with a strike length D = 500m, dip width W = 300m, vertical height H = 5m, major semi-axis a1 = 87.5m, minor semi-axis b1 = 52.5m of the inner ellipse, and major semi-axis a2 = 200m and minor semi-axis b2 = 120m of the outer ellipse as an example, the following results are obtained: Figure 5 The diagram shows the spatial distribution of porosity in the goaf. Figure 5(a) is a surface diagram showing the spatial distribution of porosity at z=0m. Figure 5 (b) is a surface diagram of the spatial distribution of porosity at z=5m.

[0027] Porosity and permeability are fundamental parameters describing the properties of porous media. Numerous experimental studies have shown a correlation between the two, and this relationship varies depending on the conditions of different porous media. However, the overall trend indicates a positive correlation between porosity and permeability; that is, the higher the porosity, the higher the permeability. Based on this, a three-dimensional spatial continuous distribution equation for permeability in goaf areas is established.

[0028] In practical implementation, a three-dimensional spatial distribution model of permeability in the goaf is established using the following methods: S23. By fitting the variation curves of porosity and permeability of porous media, the following exponential relationship equation between the two is established: ; (5) In the formula, κ is the permeability of the porous medium, and m 2 φ represents the porosity of the porous medium, which is dimensionless. S24. Based on the three-dimensional spatial continuous distribution equation of porosity φ in the goaf, the three-dimensional spatial continuous distribution equation of permeability κ in the goaf is obtained as follows: (6) As an example, please refer to... Figure 6 The diagram shows the spatial distribution of permeability in the goaf. Figure 6 (a) is a surface plot of the permeability spatial distribution at z=0m. Figure 6 (b) is a surface plot of the permeability spatial distribution at z=5m.

[0029] S3. By introducing the two-phase flow theory of slurry and water with coupling of free medium and porous medium flow and the horizontal collection method, a slurry diffusion distance prediction model is established to simulate the displacement process of groundwater by slurry from directional drilling grouting in goaf areas.

[0030] In this step, the displacement of groundwater by slurry under high pressure within the coal mine goaf can be considered a two-phase flow problem involving the coupling of free and porous media. The flow of the free media is described by the Navier-Stokes equations, while the flow of the porous media is described by the Brinkman equations. These equations explain momentum transfer through macroscopic viscosity effects and pressure gradients, and can be seen as an extension of Darcy's law. To quantitatively characterize the proportion of a certain phase in a local volume, this application defines a phase volume fraction. S iFurthermore, in porous media, fluid exists only in the pore space, and its motion is subject to volume forces such as gravity, as well as the resistance generated by the solid skeleton. Therefore, the incompressible Brinkman equation is used to describe the flow in porous media.

[0031] In practical implementation, the slurry diffusion distance prediction model is established using the following methods: S31. Define the sum of the integrals of water and slurry as always being 1: ; (7) In the formula, S i It is the volume fraction of the phase (water or slurry); N The number of phases is N. When N=2, it represents a two-phase flow. S 1 , S 2 S1 and S2 are the volume fractions of water and grout, respectively, and satisfy S1 + S2 = 1. Before grouting begins, the goaf is full of water, i.e., S1 = 1. When the groundwater is completely replaced by the grout, S1 = 0.

[0032] S32. The transient, incompressible Navier-Stokes equations are used to describe the flow of slurry in the free medium of the goaf: ; (8) In the formula, ρ It is the fluid density, kg / m³ 3 ; u It is a velocity vector, in m / s; p It is pressure, Pa; I It is an identity matrix, dimensionless; μ It is the hydrodynamic viscosity, Pa·s; F It is a volume force vector, N / m 3 .

[0033] S33. The incompressible Brinkman equation is used to describe the flow of slurry in porous media: ; (9) In the formula, φ is the porosity of the porous medium, which is dimensionless; κ It is the permeability of porous media, m 2 ; β It is the Forchheimer coefficient, 1 / m; considering the low grouting flow rate, the inertia term is ignored. .

[0034] S34. The level set method is used to track the interface between the free medium and the porous medium, and the abrupt changes in density and viscosity at the interface are smoothed.

[0035] The evolution equation for the level set function used to track the interface between free and porous media is expressed as: ; (10) In the formula, It is a smooth step function that is 0 in one phase and 1 in another phase; γ This is to reinitialize the parameters, m / s; ε 1s It is the interface thickness control parameter, in meters (m). The following formula is used to smooth out abrupt changes in density and viscosity at the interface: ; (11) In the formula, ρ1 and μ1 are the density and dynamic viscosity of groundwater, respectively; ρ2 and μ2 are the density and dynamic viscosity of slurry, respectively.

[0036] S4. Using grouting pressure, grout dynamic viscosity, and porous media permeability as influencing factors, and grout diffusion volume as the response variable, a three-factor, three-level response surface experiment was designed to obtain the optimal parameter combination for each influencing factor and the corresponding predicted results of the grout volume fraction in the goaf.

[0037] In this step, Response Surface Methodology (RSM) is a process optimization method that combines experimental design and mathematical modeling. This method establishes a mathematical model containing linear, quadratic, and pairwise interaction terms for each significant factor through a reasonably designed finite number of experiments. This model is used to accurately analyze the relationship between each factor and the response value, and to quickly and effectively determine the optimal conditions for a multi-factor system. RSM has advantages such as fewer experiments, shorter cycle time, and higher accuracy, and is currently widely used in many fields.

[0038] There are numerous response surface methodology methods, among which Box-Behnken (BBD) and Central Composite Design (CCD) are the most widely used. When the number of experimental factors is the same, BBD requires fewer experiments than CCD because it does not include axial points, thus making it more efficient. Furthermore, BBD's experimental points are located at the center of the cube's edges, avoiding experiments at extreme levels and making it easier to meet safety requirements. Therefore, it is particularly suitable for research scenarios with high safety requirements, such as grouting treatment in goaf areas.

[0039] Based on this, this application pre-determines the influencing factors of grout diffusion as grouting pressure, grout dynamic viscosity and porous media permeability. Based on the determined influencing factors and their level ranges, a 3-factor, 3-level response surface experiment is designed using Design-Expert software with grout diffusion volume as the response variable and in accordance with the BBD principle.

[0040] The simulation process satisfies the following basic assumptions: (1) The slurry is an isotropic, incompressible, continuous medium; (2) The dynamic viscosity of the slurry changes only with time, and the dynamic viscosity is the same at different locations at the same time; (3) The grout flow is mainly laminar, with turbulence only occurring in local areas near the grouting hole; (4) The slurry diffusion mode is complete displacement diffusion, and the mixing of water and slurry at the slurry-water interface is not considered; (5) The sidewalls satisfy the no-slip boundary conditions; (6) Before grouting, the goaf is in a single water phase saturation state and is in static water balance. The initial pore water pressure is set according to the static water pressure distribution.

[0041] Furthermore, the initial conditions for the slurry diffusion distance prediction model are set as follows: Before grouting, it is assumed that the pores in the goaf are completely filled with groundwater and are in a state of hydrostatic equilibrium. At an elevation Z0 connected to the atmosphere, the pore water pressure is set to 0 MPa. Then, the initial pore water pressure satisfies the hydrostatic pressure distribution relationship: ;(12) In the formula, ρ1 = 1000 kg / m 3 The density of groundwater is g = 9.81 m / s². 2 This represents the acceleration due to gravity, and the direction of the acceleration due to gravity is consistent with the negative direction of the vertical coordinate. The boundary conditions for the slurry diffusion distance prediction model are set as follows: The horizontal main boreholes arranged along the roadway are used as grouting inlets, and a specified pressure boundary condition is applied to this boundary. The grouting pressure is taken as the actual grouting pressure value of the project. The cut-out that connects to the goaf is used as the outlet, and a specified pressure boundary of 0MPa is applied at this point to represent the free outflow condition connected to the atmosphere. All other outer boundaries are uniformly provided with impermeable boundary conditions.

[0042] Furthermore, the effects of temperature and physical property parameters varying with time and space are not considered in the calculations. Meanwhile, to describe the displacement of groundwater by the grout, mass fraction concentration is used for definition. The concentration at the grouting inlet is set to 1 (pure grout), while the initial goaf is fully saturated, and the concentration within that area is set to 0 (pure water). As the simulation progresses, the concentration field evolves continuously over time.

[0043] As an example, please refer to the response surface experimental design and results shown in Table 1, and as shown in... Figure 7 The numerical simulation cloud map shown represents the integral number of the grouting slurry liquid.

[0044] Table 1. Response Surface Experiment Design and Results

[0045] Depend on Figure 7 It is evident that the grout diffusion process exhibits distinct staged spatiotemporal evolution characteristics. In the initial stage of grouting, the pressure gradient near the borehole opening is significant, causing the grout to preferentially enter the naturally deposited, loose, and fractured rock mass within the goaf, characterized by high porosity and permeability, forming a continuous high-volume-fraction grout band along the dominant seepage channels. As grouting continues, the seepage resistance along the main borehole direction gradually increases, leading to a decrease in grouting pressure within the borehole. The effective grouting pressure obtained by branch boreholes far from the borehole opening continuously decreases, resulting in a shortened effective diffusion distance of the grout around them, exhibiting an overall distribution pattern of decreasing pressure from borehole to borehole along the main borehole direction. The presence of dominant seepage channels such as fissures causes the grout to diffuse primarily upwards in the vertical direction, while significantly enhancing its horizontal diffusion capacity. The results show that under these conditions, the grout diffusion range in the horizontal direction is greater than 25m, the vertical upward diffusion range is greater than 5m, and the vertical downward diffusion range is greater than 2m, exhibiting an overall asymmetric diffusion characteristic of "longer at the top, shorter at the bottom, and farther laterally." Comprehensive analysis suggests that permeability in the goaf primarily controls the diffusion morphology and seepage channel orientation, while porosity mainly affects the diffusion distance and grout consumption per unit volume. Grouting pressure has a significant amplification effect on the diffusion range, but its marginal effect decreases as the diffusion process progresses. Grout density and dynamic viscosity jointly regulate the vertical differentiation intensity and interface stability. These characteristics can provide a basis for the subsequent optimization of grouting parameters and the rational setting of branch hole spacing.

[0046] (1) Analysis of variance: Based on the response surface methodology results, a quadratic polynomial regression equation was used to fit the grouting pressure (X1), grout dynamic viscosity (X2), and porous media permeability (X3) to obtain the grout diffusion volume (V): (13) Please refer to the analysis of variance results of the regression equation shown in Table 2. The model F=1253.71, P<0.0001, reaching highly significant at the 99% confidence level, indicating that the established quadratic regression model is generally significant and can well characterize the functional relationship between various factors and slurry diffusion volume. The lack-of-fit term is not significant (F=0.5696, P=0.6641>0.05), and the residuals mainly come from experimental pure errors, indicating a reasonable model structure. The R-squared value of the model is... 2 =0.9994, adjusted R 2 =0.9986, predicted R 2 =0.9964, and AdeqPrecision=107.01>4, indicating that the model has high fitting accuracy, strong predictive ability, and good signal-to-noise ratio, and can be used to optimize experimental conditions.

[0047] Among the main effects, the permeability of the porous media had a highly significant impact on the grout diffusion volume (F=10980.75, P<0.0001), making it the dominant factor controlling grout diffusion; the effect of grouting pressure was also highly significant (F=127.22, P<0.0001). Grout dynamic viscosity was significant at the 95% confidence level (F=5.82, P=0.0466), but its effect was significantly weaker than that of porous media permeability and grouting pressure, and can be considered a secondary factor. Therefore, under the conditions of this experiment, the order of influence of each factor on the grout diffusion volume is: porous media permeability > grouting pressure > grout dynamic viscosity.

[0048] In the quadratic term, The effects were both significant (F = 6.57 and 133.00, respectively; P = 0.0373 and <0.0001, respectively). It is highly significant at a 99% confidence level, while The significance level was not reached (F=0.2206, P=0.6529>0.05). In the interaction term, the effects of X1X3 and X2X3 were significant (F=10.32 and 11.99, respectively, P=0.0148 and 0.0105, respectively), while X1X2 did not reach a significant level (F=2.66, P=0.1471>0.05). Based on the combined analysis of the main effects, quadratic terms, and interaction terms, the importance of each significant term in the model, ranked by its contribution to the response variable, is as follows: , The effect on the response variable is negligible.

[0049] Table 2. Analysis of Variance Table of Regression Equations

[0050] R 2 =0.9994, adjusted R 2 =0.9986, predicted R 2 =0.9964.

[0051] **: Extremely significant difference (P < 0.01); *: Significant difference (P < 0.05); NS: No significant difference.

[0052] (2) Response surface interaction analysis: Please see as follows Figure 8 The response surface plot and contour plot of the interaction between grouting pressure and grout dynamic viscosity on grout diffusion volume are shown below. Figure 9 The response surface plot and contour plot of the interaction between grouting pressure and porous media porosity on grout diffusion volume are shown below. Figure 10The diagram shows the response surface and contour plot of the interaction between the dynamic viscosity of the slurry and the porosity of the porous medium on the slurry diffusion volume.

[0053] Within the range of parameters tested, the slurry diffusion volume increases significantly with increasing grouting pressure and porous media permeability, and decreases monotonically with increasing slurry dynamic viscosity. No internal extreme point was observed, indicating that the optimal parameter combination is located on the high pressure, low viscosity, and high permeability side. Figure 8 The data shows that the grouting pressure is significantly positively correlated with the grout diffusion volume, and the increase in grout dynamic viscosity has an inhibitory effect on diffusion. The contour lines are basically parallel, indicating that the X1X2 interaction is not obvious. Figure 9 The results show that both grouting pressure and porous media permeability can promote the increase of diffusion volume. Among them, the effect gradient of porous media permeability on diffusion is much greater than that of grouting pressure. The contour lines are slightly curved, reflecting a certain X1X3 interaction effect. Figure 10 The results show that increased porous media permeability significantly increases diffusion volume, while increased slurry dynamic viscosity decreases it. The X2X3 interaction mainly reflects the varying degrees of influence of porous media permeability on slurry diffusion at different slurry dynamic viscosity levels. In summary, porous media permeability is the dominant factor controlling slurry diffusion, followed by grouting pressure, while slurry dynamic viscosity is an inhibitory factor with a relatively weak impact.

[0054] (3) Parameter optimization and verification: By optimizing and predicting the experimental data, the optimal parameter combination for grouting in coal mine goaf areas was determined to be: grouting pressure 2 MPa, grout dynamic viscosity 0.0015 Pa·s, and porous media permeability (2.959 × 10⁻⁶). -13 2.025×10 -12 1.385×10 -11 )m 2 Under this parameter combination, the regression model predicts a slurry diffusion volume of up to 118753.272 m³. 3 To test the predictive ability of the regression model as a surrogate model for the COMSOL Multiphysics numerical model, three sets of numerical simulations were conducted in COMSOL Multiphysics software using the aforementioned optimal parameter combination, without data used in the model fitting. The results show that the average slurry diffusion volume is 115079.038 m³. 3 The relative error between the model and the regression prediction is only 3.27%. This indicates that the RSM model can approximate the multiphysics numerical calculation results well and can be used for the optimization and rapid prediction of grouting parameters in goaf areas.

[0055] To further verify the reliability of the model, a similar simulation experiment of slurry diffusion in the goaf was conducted. An acrylic box filled with gangue was used as the container in the experiment; samples were prepared using a uniform laying and water injection method to ensure the comparability of the media conditions among the groups. The permeability of the medium was altered by adjusting the gangue particle size distribution and compaction degree, with a focus on studying the effects of grouting pressure, slurry dynamic viscosity, and porous media permeability on the slurry diffusion distance. The results showed that: with increasing grouting pressure, the slurry diffusion distance increased; with increasing slurry dynamic viscosity, the flow resistance increased, and the diffusion distance gradually decreased; with increasing porous media permeability, the seepage capacity significantly increased, and the diffusion range expanded accordingly. These trends are consistent with the conclusions of numerical simulation and response surface analysis, indicating that the model's characterization of the main controlling factors is reasonable.

[0056] Based on the results of 3D laser scanning and borehole inspection at the 85209 working face, it is known that after the fly ash slurry is injected into the goaf, its solid particles mainly accumulate along the strike of the goaf, concentrated within a range of approximately 100–130 m. The solid diffusion range observed in the field is on the same order of magnitude as the numerical simulation results: the slurry diffusion volume predicted by the numerical simulation is approximately 1.19 × 10⁻⁶ m. 5 m 3 The corresponding characteristic diffusion length is approximately 102 m. Therefore, the established model has good applicability and reliability on an engineering scale, and the field observation results further verify the rationality of the model's predictions. Example 2: Determination of influencing factors and horizontal range of slurry diffusion: (1) Factor selection and determination based on two-level fractional factorial design: To efficiently screen key control factors with the fewest possible experiments before conducting RSM, this application employs a two-level factorial design. Considering the collinearity between porosity and permeability in porous media, grouting pressure (A), grout density (B), grout dynamic viscosity (C), and porous media permeability (D) were selected as factors to be investigated, with two levels for each factor (Table 3). A 2D model with resolution IV was used. 4-1 The factorial design table (Table 4) uses D=ABC as the generator, and the defined relationship is I=ABCD. Under this design, the main effects of each factor and the interaction between any two factors do not overlap, and the interaction between two factors has paired aliases (AB≡CD, AC≡BD, AD≡BC), which can complete the significance analysis of the main effects with the fewest number of trials.

[0057] Table 3. Factors under consideration and their levels

[0058] Note: The permeability values ​​in parentheses for porous media correspond from left to right to the compaction stability zone, the load-affected zone, and the natural deposition zone, respectively.

[0059] Table 4. 2 with resolution IV 4-1Fractal Factorization Design Table

[0060] This application uses "grout diffusion volume" as the response variable and employs COMSOL Multiphysics software to numerically simulate the grouting process in coal mine goaf areas. A single simulation time is set to 10 hours to obtain experimental data. Subsequently, Minitab22 software is used to perform model fitting and variance analysis on the experimental results, identifying the three factors with the most significant impact on the response value. The results (Table 5) show that the F-value of the model term is 51.34, and the P-value is 0.019 < 0.05, indicating that the first-order regression model obtained based on a two-level fractional factorial design has overall significance at the 95% confidence level and can be used to analyze the influence of various factors on grout diffusion volume. Among the main effects, the p-values ​​for porous media permeability and grouting pressure were 0.003 and 0.029, respectively, both less than 0.05, indicating a significant impact on grout diffusion volume. The p-value for grout dynamic viscosity was 0.067, slightly higher than 0.05, but its F-value was relatively large, indicating that it still had some influence on the response variable. The p-value for grout density was 0.996, and its influence on the response variable was negligible. In summary, grouting pressure (X1), grout dynamic viscosity (X2), and porous media permeability (X3) were identified as the main controlling factors affecting grout diffusion volume.

[0061] Table 5. Analysis of Variance Table of Regression Equations

[0062] (2) Level determination based on the steepest climb test: After identifying the controlling factors, to quickly approach the maximum response region and reasonably determine the center point of the response surface methodology (RSM) test design, the steepest ramp method was used to optimize the levels of each factor, with a single simulation time set to 5 hours. This method is based on a first-order regression model fitted to the two-level factorial design experimental data. The regression coefficients of the controlling factors are extracted to establish the model's gradient vector. The change in slurry dynamic viscosity is used as the baseline step size. Based on the relative magnitude and sign of the regression coefficients of each factor, the step size and direction of change of grouting pressure and porous media permeability are determined, thus obtaining the test path along the steepest ramp direction. In all steepest ramp tests, the slurry density is fixed at 1400 kg / m³. The step size is gradually increased along this path. When the response value no longer increases significantly or shows a decreasing trend, it is considered to have reached or is close to the maximum response region, and the nearby test points are selected as the center point of the subsequent RSM test design. The corresponding steepest ramp test scheme is shown in Table 6.

[0063] Table 6. Test Scheme for the Steepest Climb

[0064] As shown in Table 6, along the steepest slope direction, the grout diffusion volume at each test point monotonically increases with the step length. However, the growth rate of diffusion volume between adjacent tests gradually decreases from 57.72% to 14.95%, showing a significant decreasing trend. Notably, the diffusion volume increment between groups 5 and 6 shows a decrease for the first time, indicating that the test has entered a period of diminishing returns. Considering the engineering feasibility of parameters such as grout diffusion volume and its growth rate, grouting pressure, and grout dynamic viscosity, this application selects the test values ​​from group 5 of the steepest slope test (X1=1.9MPa, X2=0.0018Pa·s, X3=(1.371×10⁻⁶)). -13 9.381×10 -13 6.417×10 -12 The central point is used as the center point for all factor levels in the response surface methodology. Based on this center point, one level value is set in each of the intervals above and below it, collectively constituting the factor levels of the response surface methodology. The correspondence between each factor level value and its coded value is shown in Table 7.

[0065] Table 7. Design Factor Coding and Level

[0066] Example 3:

[0067] A certain mine uses long-distance pipelines to transport fly ash slurry for filling the goaf of the working face. Due to the long transportation distance and the fine particles and high water-cement ratio of the fly ash slurry, the slurry is prone to stratification, segregation, and localized incomplete filling during transportation, thus affecting the filling effect. Therefore, based on the actual working conditions of the fly ash grouting and reinforcement project in the goaf of this mine, the following key engineering parameters affecting the slurry filling effect have been determined, as shown in Table 8.

[0068] Table 8. Main parameters of fly ash grouting and backfilling project in goaf area

[0069] Currently, there is no consensus on methods for predicting the grout diffusion range, and reliable theoretical basis is still lacking for the layout of grouting boreholes in engineering practice. Therefore, this application optimizes the borehole layout scheme for this project based on the established grout diffusion distance prediction model.

[0070] The grouting pressure is P = 2.0 MPa, the dynamic viscosity of the grout is μ = 0.00158 Pa·s, and the permeability of the goaf is k = 2.381 × 10⁻⁶. -11 m 2 Substituting the values ​​into the quadratic polynomial regression equation for the slurry diffusion volume, the calculated slurry diffusion volume is V = 109746.43 m³. 3The corresponding diffusion distances in the horizontal, upward, and downward directions are h1=27m, h2=5m, and h3=2.1m, respectively. Therefore, the theoretical limit control radius for slurry diffusion in the goaf is 27m, and the theoretical limit spacing between branch holes is 54m.

[0071] The fly ash slurry flows primarily in laminar form within the grouting borehole, and its pressure drop ΔP along the flow path satisfies Poiseuille's law: ;(14) In the formula, Q is the fluid flow rate, m 3 / s; L is the horizontal hole length, m; d is the borehole diameter, mm.

[0072] As shown in the above formula, the pressure drop increases approximately linearly with the conveying length L. When the main borehole length L = 550m and the borehole diameter d = 75mm, if the theoretical limit branch hole spacing is still used, it may lead to a significant reduction in the branch hole orifice pressure and the effective diffusion radius in front. Considering the pressure drop along the main borehole and the spatial heterogeneity of porosity and permeability in the goaf, the theoretical limit hole spacing 2h1 needs to be reduced to ensure sufficient overlap of the slurry diffusion range between adjacent branch holes. To improve the safety margin of the design, a correction factor η = 0.75 is introduced, and the reasonable branch hole spacing is: ; (15) That is, while ensuring a moderate overlap in the grout diffusion range of adjacent branch holes, the theoretical limit hole spacing is reduced by approximately 25% to mitigate the adverse effects of grouting pressure attenuation along the flow path and uncertainties in pore permeability parameters. Based on the above analysis, the hole spacing design for the fly ash grouting and filling renovation project in the goaf of this mine is 40m, and the actual drilling locations are as follows: Figure 11 The schematic diagram of the borehole design for the fly ash grouting and filling project in the goaf is shown.

[0073] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the ideas of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of the present invention.

Claims

1. A method for predicting the diffusion distance of grout from directional drilling in coal mine goaf areas, characterized in that, The method includes: S1. Define a global coordinate system for the working scenario of the goaf and establish a three-dimensional numerical model of the goaf. At the same time, adopt a hybrid meshing strategy to divide the goaf and the grouting borehole area into meshes. S2. Based on the "O"-shaped ring theory and the key layer theory, a three-dimensional spatial distribution model of porosity and permeability in the goaf is established. S3. Introduce the two-phase flow theory of slurry water coupling between free medium and porous medium and the horizontal collection method to establish a slurry diffusion distance prediction model to simulate the displacement process of groundwater by slurry from directional drilling grouting in goaf areas. S4. Using grouting pressure, grout dynamic viscosity, and porous media permeability as influencing factors, and grout diffusion volume as the response variable, a three-factor, three-level response surface experiment was designed to obtain the optimal parameter combination for each influencing factor and the corresponding predicted results of the grout volume fraction in the goaf.

2. The method as described in claim 1, characterized in that, S1 specifically includes: S11. Take the intersection of the middle part of the goaf and the longwall face and the top plane of the bottom plate as the origin of the coordinate system. Let the direction along the strike and pointing to the depth of the goaf be the positive x-axis, the direction along the dip and pointing to the return air side be the positive y-axis, and the direction perpendicular to the top plane of the bottom plate and pointing upwards be the positive z-axis, thus defining the global coordinate system. S12. Set the strike length, dip width, and vertical height of the three-dimensional numerical model of the goaf; S13. In order to describe the distribution characteristics of the "O"-shaped rings, which are "relatively dense in the middle and have developed fissures around the edges", two concentric and coaxial elliptical boundaries are established in the xy plane and stretched along the z-axis to form an elliptical cylindrical surface, thereby dividing the goaf into a compacted stable zone, a load-affected zone and a natural accumulation zone from the inside to the outside. S14. A short-distance feather-shaped branch hole pattern is adopted. A horizontal main hole is laid out along the strike in the middle of the goaf. Branch holes are arranged sequentially along the strike at equal intervals of 50m from its starting point. The left and right sides are staggered. Each branch hole maintains a small angle with the main hole and points to the roadways on both sides. The main hole and the branch holes are explicitly modeled in the model as cylindrical channels with a radius of 0.074m. S15. The main body of the goaf adopts a free tetrahedral grid, while the grouting borehole area generates regular hexahedral units by mapping the inlet circular surface and sweeping along the axial direction. A boundary layer grid is set at the borehole wall to refine the near-wall flow field.

3. The method as described in claim 1, characterized in that, The three-dimensional spatial distribution model of porosity in the goaf is established in S2 in the following way: S21. Based on the "O"-shaped ring theory and the key layer theory, the distribution models of porosity in the goaf along the x-axis, y-axis, and z-axis are established as follows: On the y=0 section of the goaf, along the x-axis, the porosity φ x The distance from the cut line to the incision site shows a trend of first decreasing and then increasing, with an overall approximately symmetrical distribution as follows: ； In the formula, φ x Porosity along the x-axis on the y=0 section of the goaf, dimensionless; D The length of the goaf is in meters. x The distance from a point within the goaf to the working face is expressed in meters (m). On the x=0 section of the goaf, the porosity variation coefficient φ' y Approximately symmetrically distributed along y=0, when extending from the middle of the working face towards the intake and return airways, φ' y All increase with the increase of |y|, as shown below: ； In the formula, φ' y is the coefficient of porosity along the y-axis, which is dimensionless; W The dip width of the goaf, in meters; y Let be the coordinate value of a point within the goaf along the y-axis, in meters (m). In the xy plane along the z-axis, the porosity variation coefficient φ' z The following piecewise function relationship is satisfied: ； in, ； In the formula, φ' z is the coefficient of porosity along the z-axis, which is dimensionless; z Let be the coordinate value of a point within the goaf along the z-axis, in meters (m). a 1 , a 2 , b 1 , b 2 Let be the lengths of the major and minor semi-axes of the two ellipses, representing the compaction stability zone and the load-affected zone, respectively, in meters (m). f ( x, y ) is a normalized spatial position coefficient, with a value range of (0, 1), used to describe the relative position of any point (x, y) within the load-affected zone with respect to the inner and outer elliptical boundaries, thereby achieving a smooth spatial transition of porosity. S22, using φ x ,φ' y and φ' z The product of these terms represents the three-dimensional spatial continuous distribution equation of porosity φ within the goaf, as follows: 。 4. The method as described in claim 3, characterized in that, The three-dimensional spatial distribution model of permeability in the goaf is established in S2 in the following way: S23. By fitting the variation curves of porosity and permeability of porous media, the following exponential relationship equation between the two is established: ； In the formula, κ is the permeability of the porous medium, and m 2 ; φ is the porosity of the porous medium, which is dimensionless; S24. Based on the three-dimensional spatial continuous distribution equation of porosity φ in the goaf, the three-dimensional spatial continuous distribution equation of permeability κ in the goaf is obtained as follows:

5. The method as described in claim 1, characterized in that, S3 specifically includes: S31. Define the sum of the integrals of water and slurry as always being 1: ； In the formula, S i It is the volume fraction of the phase (water or slurry); N The number of phases is N. When N=2, it represents a two-phase flow. S 1 , S 2 S1 and S2 are the volume fractions of water and grout, respectively, and satisfy S1 + S2 = 1. Before grouting begins, the goaf is full of water, i.e., S1 = 1. When the groundwater is completely replaced by the grout, S1 = 0. S32. The transient, incompressible Navier-Stokes equations are used to describe the flow of slurry in the free medium of the goaf: ； In the formula, ρ It is the fluid density, kg / m³ 3 ; u It is a velocity vector, in m / s; p It is pressure, Pa; I It is an identity matrix, dimensionless; μ It is the hydrodynamic viscosity, Pa·s; F It is a volume force vector, N / m 3 ; S33. The incompressible Brinkman equation is used to describe the flow of slurry in porous media: ； In the formula, It is the porosity of porous media, which is dimensionless; κ It is the permeability of porous media, m 2 ; β It is the Forchheimer coefficient, 1 / m; considering the low grouting flow rate, the inertia term is ignored. ; S34. The level set method is used to track the interface between the free medium and the porous medium, and the abrupt changes in density and viscosity at the interface are smoothed.

6. The method as described in claim 1, characterized in that, The evolution equation of the level set function used to track the interface between the free medium and the porous medium in S34 is expressed as follows: ； In the formula, It is a smooth step function that is 0 in one phase and 1 in another phase; γ This is to reinitialize the parameters, m / s; ε 1s It is the interface thickness control parameter, in meters (m). The following formula is used to smooth out abrupt changes in density and viscosity at the interface: ； In the formula, ρ1 and μ1 are the density and dynamic viscosity of groundwater, respectively; ρ2 and μ2 are the density and dynamic viscosity of slurry, respectively.

7. The method as described in claim 1, characterized in that, The simulation process satisfies the following basic assumptions: (1) The slurry is an isotropic, incompressible, continuous medium; (2) The dynamic viscosity of the slurry changes only with time, and the dynamic viscosity is the same at different locations at the same time; (3) The grout flow is mainly laminar, with turbulence only occurring in local areas near the grouting hole; (4) The slurry diffusion mode is complete displacement diffusion, and the mixing of water and slurry at the slurry-water interface is not considered; (5) The sidewalls satisfy the no-slip boundary conditions; (6) Before grouting, the goaf is in a single water phase saturation state and is in static water balance. The initial pore water pressure is set according to the static water pressure distribution.

8. The method as described in claim 1, characterized in that, The initial conditions for the slurry diffusion distance prediction model are set as follows: Before grouting, it is assumed that the pores in the goaf are completely filled with groundwater and are in a state of hydrostatic equilibrium. At an elevation Z0 connected to the atmosphere, the pore water pressure is set to 0 MPa. Then, the initial pore water pressure satisfies the hydrostatic pressure distribution relationship: ； In the formula, ρ1 = 1000 kg / m 3 The density of groundwater is g = 9.81 m / s². 2 This represents the acceleration due to gravity, and the direction of the acceleration due to gravity is consistent with the negative direction of the vertical coordinate. The boundary conditions for the slurry diffusion distance prediction model are set as follows: The horizontal main boreholes arranged along the roadway are used as grouting inlets, and a specified pressure boundary condition is applied to this boundary. The grouting pressure is taken as the actual grouting pressure value of the project. The cut-out that connects to the goaf is used as the outlet, and a specified pressure boundary of 0MPa is applied at this point to represent the free outflow condition connected to the atmosphere. All other outer boundaries are uniformly provided with impermeable boundary conditions.

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